August 9, 2012
Hi Dan,

Thank you for lying about my looks over time Dan. I only wish it were true.

And I think the Ball and Brown presentations along with the other plenary sessions at the 2012 American Accounting Association Annual Meetings will eventually be available on the AAA Commons. Even discussants of plenary speakers had to sign video permission forms, so our presentations may also be available on the Commons. I was a discussant of the Deirdre McCloskey plenary presentation on Monday, August 6. If you eventually view me on this video you can judge how badly Dan Stone lies.

My fellow discussants were impressive, including Rob Bloomfield from Cornell, Bill Kinney from the University of Texas (one of my former doctoral students), and Stanimir Markov from UT. Dallas. Our moderator was Sudipta Basu from Temple University.

The highlight of the AAA meetings for me was having an intimate breakfast with Deirdre McCloskey. She and I had a really fine chat before four others joined us for this breakfast hosted by the AAA prior to her plenary presentation. What a dedicated scholar she is across decades of writing huge and detailed history books --- http://en.wikipedia.org/wiki/Deirdre_McCloskey

In my viewpoint she's the finest living economic historian in the world. Sadly, she may also be one of the worst speakers in front of a large audience. Much of this is no fault of her own, and I admire her greatly for having the courage to speak in large convention halls. She can't be blamed for having a rather crackling voice and a very distracting stammer. Sometimes she just cannot get a particular word out.

My second criticism is that when making a technical presentation rather than something like a political speech, it really does help to have a few PowerPoint slides that highlight some the main bullet points. The AAA sets up these plenary sessions with two very large screens and a number of other large screen television sets that can show both the speaker's talking head and the speaker's PowerPoint slides.

I the case of Deidre's presentation and most other technical presentations, it really helped to have read studied her material before the presentation. For this presentation I had carefully studied her book quoted at

The Cult of Statistical Significance: How Standard Error Costs Us Jobs, Justice, and Lives, by Stephen T. Ziliak and Deirdre N. McCloskey (Ann Arbor: University of Michigan Press, ISBN-13: 978-472-05007-9, 2007)
http://www.cs.trinity.edu/~rjensen/temp/DeirdreMcCloskey/StatisticalSignificance01.htm

Page 206
The textbooks are wrong. The teaching is wrong. The seminar you just attended is wrong. The most prestigious journal in your scientific field is wrong.

You are searching, we know, for ways to avoid being wrong. Science, as Jeffreys said, is mainly a series of approximations to discovering the sources of error. Science is a systematic way of reducing wrongs or can be. Perhaps you feel frustrated by the random epistemology of the mainstream and don't know what to do. Perhaps you've been sedated by significance and lulled into silence. Perhaps you sense that the power of a Roghamsted test against a plausible Dublin alternative is statistically speaking low but you feel oppressed by the instrumental variable one should dare not to wield. Perhaps you feel frazzled by what Morris Altman (2004) called the "social psychology rhetoric of fear," the deeply embedded path dependency that keeps the abuse of significance in circulation. You want to come out of it. But perhaps you are cowed by the prestige of Fisherian dogma. Or, worse thought, perhaps you are cynically willing to be corrupted if it will keep a nice job

She is now writing a sequel to that book, and I cannot wait.

A second highlight for me in these 2012 AAA annual meetings was a single sentence in the Tuesday morning plenary presentation of Gergory S. Berns, the Director of the (Brain) Center for Neuropolicy at Emory University. In that presentation, Dr. Berns described how the brain is divided up into over 10,000 sectors that are then studied in terms of blood flow (say from reward or punishment) in a CAT Scan. The actual model used is the ever-popular General Linear Model (GLM) regression equation.

The sentence in question probably passed over almost everybody's head in the audience but mine. He discussed how sample sizes are so large in these brain studies  that efforts are made to avoid being mislead by obtaining statistically significant GLM coefficients (due to large sample sizes) that are not substantively significant. BINGO! Isn't this exactly what Deidre McCloskey was warning about in her plenary session a day earlier?

This is an illustration of a real scientist knowing what statistical inference dangers lurk in large samples --- dangers that so many of our accountics scientist researchers seemingly overlook as they add those Pearson asterisks of statistical significance to questionable findings of substance in their research.

And Dr. Berns did not mention this because he was reminded of this danger in Deirdre's presentation the day before. Dr. Berns was not at the meetings the day before and did not listen to Dierdre's presentation. Great scientists have learned to be especially knowledgeable of the limitations of statistical significance testing --- which is really intended more for small samples rather than very large samples are used in capital markets studies by accountics scientists.

Eight Econometrics Multiple-Choice Quiz Sets from David Giles
You might have to go to his site to get the quizzes to work.
Note that there are multiple questions for each quiz set.
Click on the arrow button to go to a subsequent question.

### Would You Like Some Hot Potatoes? http://davegiles.blogspot.com/2014/10/would-you-like-some-hot-potatoes.html

O.K., I know - that was a really cheap way of getting your attention.

However, it worked, and this post really is about Hot Potatoes - not the edible variety, but some teaching apps. from "Half-Baked Software" here at the University of Victoria.

To quote:
"The Hot Potatoes suite includes six applications, enabling you to create interactive multiple-choice, short-answer, jumbled-sentence, crossword, matching/ordering and gap-fill exercises for the World Wide Web. Hot Potatoes is freeware, and you may use it for any purpose or project you like."
I've included some Hot Potatoes multiple choice exercises on the web pages for several of my courses for some years now. Recently, some of the students in my introductory graduate econometrics course mentioned that these exercises were quite helpful. So, I thought I'd share the Hot Potatoes apps. for that course with readers of this blog.

There are eight multiple-choice exercise sets in total, and you can run  them from here:

Quiz 1 ; Quiz 2 ; Quiz 3 ; Quiz 4; Quiz 5 ; Quiz 6Quiz  7 ; Quiz 8 .

I've also put the HTML and associated PDF files on the code page for this blog. If you're going to download them and use them on your own computer or website, just make sure that the PDF files are located in the same folder (directory) as the HTML files.

I plan to extend and update these Hot Potatoes exercises in the near future, but hopefully some readers will find them useful in the meantime.

From my "Recently Read" list:
• Born, B. and J. Breitung, 2014. Testing for serial correlation in fixed-effects panel data models. Econometric Reviews, in press.
• Enders, W. and Lee. J., 2011. A unit root test using a Fourier series to approximate smooth breaks, Oxford Bulletin of Economics and Statistics, 74, 574-599.
• Götz, T. B. and A. W. Hecq, 2014. Testing for Granger causality in large mixed-frequency VARs. RM/14/028, Maastricht University, SBE, Department of Quantitative Economics.
• Kass, R. E., 2011. Statistical inference: The big picture. Statistical Science, 26, 1-9.
• Qian, J. and L. Su, 2014. Structural change estimation in time series regressions with endogenous variables. Economics Letters, in press.
• Wickens, M., 2014. How did we get to where we are now? Reflections on 50 years of macroeconomic and financial econometrics. Discussion No. 14/17, Department of Economics and Related Studies, University of York.

Statistical Science Reading List for June 2014 Compiled by David Giles in Canada ---
http://davegiles.blogspot.com/2014/05/june-reading-list.html

Put away that novel! Here's some really fun June reading:
• Berger, J., 2003. Could Fisher, Jeffreys and Neyman have agreed on testing?. Statistical Science, 18, 1-32.
• Canal, L. and R. Micciolo, 2014. The chi-square controversy. What if Pearson had R? Journal of Statistical Computation and Simulation, 84, 1015-1021.
• Harvey, D. I., S. J. Leybourne, and A. M. R. Taylor, 2014. On infimum Dickey-Fuller unit root tests allowing for a trend break under the null. Computational Statistics and Data Analysis, 78, 235-242.
• Karavias, Y. and E. Tzavalis, 2014. Testing for unit roots in short panels allowing for a structural breaks. Computational Statistics and Data Analysis, 76, 391-407.
• King, G. and M. E. Roberts, 2014. How robust standard errors expose methodological problems they do not fix, and what to do about it. Mimeo., Harvard University.
• Kuroki, M. and J. Pearl, 2014. Measurement bias and effect restoration in causal inference. Biometrika, 101, 423-437.
• Manski, C., 2014. Communicating uncertainty in official economic statistics. Mimeo., Department of Economics, Northwestern University.
• Martinez-Camblor, P., 2014. On correlated z-values in hypothesis testing. Computational Statistics and Data Analysis, in press.

"Econometrics and 'Big Data'," by David Giles, Econometrics Beat:  Dave Giles’ Blog, University of Victoria, December 5, 2013 ---
http://davegiles.blogspot.ca/2013/12/econometrics-and-big-data.html

In this age of "big data" there's a whole new language that econometricians need to learn. Its origins are somewhat diverse - the fields of statistics, data-mining, machine learning, and that nebulous area called "data science".

What do you know about such things as:

• Decision trees
• Support vector machines
• Neural nets
• Deep learning
• Classification and regression trees
• Random forests
• Penalized regression (e.g., the lasso, lars, and elastic nets)
• Boosting
• Bagging
• Spike and slab regression?

Probably not enough!

If you want some motivation to rectify things, a recent paper by Hal Varian will do the trick. It's titled, "Big Data: New Tricks for Econometrics", and you can download it from here. Hal provides an extremely readable introduction to several of these topics.

He also offers a valuable piece of advice:
"I believe that these methods have a lot to offer and should be more widely known and used by economists. In fact, my standard advice to graduate students these days is 'go to the computer science department and take a class in machine learning'."
Interestingly, my son (a computer science grad.) "audited" my classes on Bayesian econometrics when he was taking machine learning courses. He assured me that this was worthwhile - and I think he meant it! Apparently there's the potential for synergies in both directions.

"Statistical Significance - Again " by David Giles, Econometrics Beat:  Dave Giles’ Blog, University of Victoria, December 28, 2013 ---
http://davegiles.blogspot.com/2013/12/statistical-significance-again.html

### Statistical Significance - Again

With all of this emphasis on "Big Data", I was pleased to see this post on the Big Data Econometrics blog, today.

When you have a sample that runs to the thousands (billions?), the conventional significance levels of 10%, 5%, 1% are completely inappropriate. You need to be thinking in terms of tiny significance levels.

I discussed this in some detail back in April of 2011, in a post titled, "Drawing Inferences From Very Large Data-Sets". If you're of those (many) applied researchers who uses large cross-sections of data, and then sprinkles the results tables with asterisks to signal "significance" at the 5%, 10% levels, etc., then I urge you read that earlier post.

It's sad to encounter so many papers and seminar presentations in which the results, in reality, are totally insignificant!

Also see
"Drawing Inferences From Very Large Data-Sets,"   by David Giles, Econometrics Beat:  Dave Giles’ Blog, University of Victoria, April 26, 2013 ---
http://davegiles.blogspot.ca/2011/04/drawing-inferences-from-very-large-data.html

. . .

Granger (1998; 2003has reminded us that if the sample size is sufficiently large, then it's virtually impossible not to reject almost any hypothesis. So, if the sample is very large and the p-values associated with the estimated coefficients in a regression model are of the order of, say, 0.10 or even 0.05, then this really bad news. Much, much, smaller p-values are needed before we get all excited about 'statistically significant' results when the sample size is in the thousands, or even bigger. So, the p-values reported above are mostly pretty marginal, as far as significance is concerned. When you work out the p-values for the other 6 models I mentioned, they range from  to 0.005 to 0.460. I've been generous in the models I selected.

Here's another set of  results taken from a second, really nice, paper by
Ciecieriski et al. (2011) in the same issue of Health Economics:

Continued in article

Jensen Comment
My research suggest that over 90% of the recent papers published in TAR use purchased databases that provide enormous sample sizes in those papers. Their accountics science authors keep reporting those meaningless levels of statistical significance.

What is even worse is when meaningless statistical significance tests are used to support decisions.

Also see
"Drawing Inferences From Very Large Data-Sets,"   by David Giles, Econometrics Beat:  Dave Giles’ Blog, University of Victoria, April 26, 2013 ---
http://davegiles.blogspot.ca/2011/04/drawing-inferences-from-very-large-data.html

. . .

Granger (1998; 2003has reminded us that if the sample size is sufficiently large, then it's virtually impossible not to reject almost any hypothesis. So, if the sample is very large and the p-values associated with the estimated coefficients in a regression model are of the order of, say, 0.10 or even 0.05, then this really bad news. Much, much, smaller p-values are needed before we get all excited about 'statistically significant' results when the sample size is in the thousands, or even bigger. So, the p-values reported above are mostly pretty marginal, as far as significance is concerned. When you work out the p-values for the other 6 models I mentioned, they range from  to 0.005 to 0.460. I've been generous in the models I selected.

Here's another set of  results taken from a second, really nice, paper by
Ciecieriski et al. (2011) in the same issue of Health Economics:

Continued in article

Jensen Comment
My research suggest that over 90% of the recent papers published in TAR use purchased databases that provide enormous sample sizes in those papers. Their accountics science authors keep reporting those meaningless levels of statistical significance.

What is even worse is when meaningless statistical significance tests are used to support decisions.

Question
In statistics what is a "winsorized mean?"

Answer in Wikipedia ---
http://en.wikipedia.org/wiki/Winsorized_mean

An analogy that takes me back to my early years of factor analysis is Procreates Analysis ---
http://en.wikipedia.org/wiki/Procrustes_analysis

"The Role of Financial Reporting Quality in Mitigating the Constraining Effect of Dividend Policy on Investment Decisions"
Authors

Santhosh Ramalingegowda (The University of Georgia
Chuan-San Wang (National Taiwan University)
Yong Yu (The University of Texas at Austin)

The Accounting Review, Vol. 88, No. 3, May 2013, pp. 1007-1040

Miller and Modigliani's (1961) dividend irrelevance theorem predicts that in perfect capital markets dividend policy should not affect investment decisions. Yet in imperfect markets, external funding constraints that stem from information asymmetry can force firms to forgo valuable investment projects in order to pay dividends. We find that high-quality financial reporting significantly mitigates the negative effect of dividends on investments, especially on R&D investments. Further, this mitigating role of financial reporting quality is particularly important among firms with a larger portion of firm value attributable to growth options. In addition, we show that the mitigating role of high-quality financial reporting is more pronounced among firms that have decreased dividends than among firms that have increased dividends. These results highlight the important role of financial reporting quality in mitigating the conflict between firms' investment and dividend decisions and thereby reducing the likelihood that firms forgo valuable investment projects in order to pay dividends.

. . .

Panel A of Table 1 reports the descriptive statistics of our main and control variables in Equation (1). To mitigate the influence of potential outliers, we winsorize all continuous variables at the 1 percent and 99 percent levels. The mean and median values of Total Investment are 0.14 and 0.09 respectively. The mean and median values of R&D Investment (Capital Investment) are 0.05 (0.06) and 0.00 (0.04), respectively. Because we multiply RQ−1 by −1 so that higher RQ−1 indicates higher reporting quality, RQ−1 has negative values with the mean and median of −0.05 and −0.04, respectively. The above distributions are similar to prior research (e.g., Biddle et al. 2009). The mean and median values of Dividend are 0.01 and 0.00, respectively, consistent with many sample firms not paying any dividends. The descriptive statistics of control variables are similar to prior research (e.g., Biddle et al. 2009). Panels B and C of Table 1 report the Pearson and Spearman correlations among our variables. Consistent with dividends having a constraining effect on investments (Brav et al. 2005; Daniel et al. 2010), we find that Total Investment and R&D Investment are significantly negatively correlated with Dividend.

Continued in article

Jensen Comment
With statistical inference testing on such an enormous sample size this may be yet another accountics science illustration of misleading statistical inferences that Deirdre McCloskey warned about (The Cult of Statistical Significance) in a plenary session at the 2011 AAA annual meetings in 2012 ---
http://www.cs.trinity.edu/~rjensen/temp/DeirdreMcCloskey/StatisticalSignificance01.htm
I had the privilege to be one of the discussants of her amazing presentation.

The basic problem of statistical inference testing on enormous samples is that the null hypothesis is almost always rejected even when departures from the null are infinitesimal.

2012 AAA Meeting Plenary Speakers and Response Panel Videos ---
http://commons.aaahq.org/hives/20a292d7e9/summary
I think you have to be a an AAA member and log into the AAA Commons to view these videos.
Bob Jensen is an obscure speaker following the handsome Rob Bloomfield
in the 1.02 Deirdre McCloskey Follow-up Panel—Video ---
http://commons.aaahq.org/posts/a0be33f7fc

My threads on Deidre McCloskey and my own talk are at
http://www.cs.trinity.edu/~rjensen/temp/DeirdreMcCloskey/StatisticalSignificance01.htm

September 13, 2012 reply from Jagdish Gangolly

Bob,

Thanks you so much for posting this.

What a wonderful speaker Deidre McCloskey! Reminded me of JR Hicks who also was a stammerer. For an economist, I was amazed by her deep and remarkable understanding of statistics.

It was nice to hear about Gossett, perhaps the only human being who got along well with both Karl Pearson and R.A. Fisher, getting along with the latter itself a Herculean feat.

Gosset was helped in the mathematical derivation of small sample theory by Karl Pearson, he did not appreciate its importance, it was left to his nemesis R.A. Fisher. It is remarkable that he could work with these two giants who couldn't stand each other.

In later life Fisher and Gosset parted ways in that Fisher was a proponent of randomization of experiments while Gosset was a proponent of systematic planning of experiments and in fact proved decisively that balanced designs are more precise, powerful and efficient compared with Fisher's randomized experiments (see http://sites.roosevelt.edu/sziliak/files/2012/02/William-S-Gosset-and-Experimental-Statistics-Ziliak-JWE-2011.pdf )

I remember my father (who designed experiments in horticulture for a living) telling me the virtues of balanced designs at the same time my professors in school were extolling the virtues of randomisation.

In Gosset we also find seeds of Bayesian thinking in his writings.

While I have always had a great regard for Fisher (visit to the tree he planted at the Indian Statistical Institute in Calcutta was for me more of a pilgrimage), I think his influence on the development of statistics was less than ideal.

Regards,

Jagdish

Jagdish S. Gangolly
Department of Informatics College of Computing & Information
State University of New York at Albany
Harriman Campus, Building 7A, Suite 220
Albany, NY 12222 Phone: 518-956-8251, Fax: 518-956-8247

Hi Jagdish,

You're one of the few people who can really appreciate Deidre's scholarship in history, economics, and statistics. When she stumbled for what seemed like forever trying to get a word out, it helped afterwards when trying to remember that word.

Interestingly, two Nobel economists slugged out the very essence of theory some years back. Herb Simon insisted that the purpose of theory was to explain. Milton Friedman went off on the F-Twist tangent saying that it was enough if a theory merely predicted. I lost some (certainly not all) respect for Friedman over this. Deidre, who knew Milton, claims that deep in his heart, Milton did not ultimately believe this to the degree that it is attributed to him. Of course Deidre herself is not a great admirer of Neyman, Savage, or Fisher.

Friedman's essay "The Methodology of Positive Economics" (1953) provided the epistemological pattern for his own subsequent research and to a degree that of the Chicago School. There he argued that economics as science should be free of value judgments for it to be objective. Moreover, a useful economic theory should be judged not by its descriptive realism but by its simplicity and fruitfulness as an engine of prediction. That is, students should measure the accuracy of its predictions, rather than the 'soundness of its assumptions'. His argument was part of an ongoing debate among such statisticians as Jerzy Neyman, Leonard Savage, and Ronald Fisher.

.
Many of us on the AECM are not great admirers of positive economics ---
http://www.trinity.edu/rjensen/theory02.htm#PostPositiveThinking

Everyone is entitled to their own opinion, but not their own facts.
Senator Daniel Patrick Moynihan --- FactCheck.org ---
http://www.factcheck.org/

Then again, maybe we're all entitled to our own facts!

"The Power of Postpositive Thinking," Scott McLemee, Inside Higher Ed, August 2, 2006 --- http://www.insidehighered.com/views/2006/08/02/mclemee

In particular, a dominant trend in critical theory was the rejection of the concept of objectivity as something that rests on a more or less naive epistemology: a simple belief that “facts” exist in some pristine state untouched by “theory.” To avoid being naive, the dutiful student learned to insist that, after all, all facts come to us embedded in various assumptions about the world. Hence (ta da!) “objectivity” exists only within an agreed-upon framework. It is relative to that framework. So it isn’t really objective....

What Mohanty found in his readings of the philosophy of science were much less naïve, and more robust, conceptions of objectivity than the straw men being thrashed by young Foucauldians at the time. We are not all prisoners of our paradigms. Some theoretical frameworks permit the discovery of new facts and the testing of interpretations or hypotheses. Others do not. In short, objectivity is a possibility and a goal — not just in the natural sciences, but for social inquiry and humanistic research as well.

Mohanty’s major theoretical statement on PPR arrived in 1997 with Literary Theory and the Claims of History: Postmodernism, Objectivity, Multicultural Politics (Cornell University Press). Because poststructurally inspired notions of cultural relativism are usually understood to be left wing in intention, there is often a tendency to assume that hard-edged notions of objectivity must have conservative implications. But Mohanty’s work went very much against the current.

“Since the lowest common principle of evaluation is all that I can invoke,” wrote Mohanty, complaining about certain strains of multicultural relativism, “I cannot — and consequently need not — think about how your space impinges on mine or how my history is defined together with yours. If that is the case, I may have started by declaring a pious political wish, but I end up denying that I need to take you seriously.”

PPR did not require throwing out the multicultural baby with the relativist bathwater, however. It meant developing ways to think about cultural identity and its discontents. A number of Mohanty’s students and scholarly colleagues have pursued the implications of postpositive identity politics. I’ve written elsewhere about Moya, an associate professor of English at Stanford University who has played an important role in developing PPR ideas about identity. And one academic critic has written an interesting review essay on early postpositive scholarship — highly recommended for anyone with a hankering for more cultural theory right about now.

Not everybody with a sophisticated epistemological critique manages to turn it into a functioning think tank — which is what started to happen when people in the postpositive circle started organizing the first Future of Minority Studies meetings at Cornell and Stanford in 2000. Others followed at the University of Michigan and at the University of Wisconsin in Madison. Two years ago FMS applied for a grant from Mellon Foundation, receiving $350,000 to create a series of programs for graduate students and junior faculty from minority backgrounds. The FMS Summer Institute, first held in 2005, is a two-week seminar with about a dozen participants — most of them ABD or just starting their first tenure-track jobs. The institute is followed by a much larger colloquium (the part I got to attend last week). As schools of thought in the humanities go, the postpositivists are remarkably light on the in-group jargon. Someone emerging from the Institute does not, it seems, need a translator to be understood by the uninitated. Nor was there a dominant theme at the various panels I heard. Rather, the distinctive quality of FMS discourse seems to derive from a certain very clear, but largely unstated, assumption: It can be useful for scholars concerned with issues particular to one group to listen to the research being done on problems pertaining to other groups. That sounds pretty simple. But there is rather more behind it than the belief that we should all just try to get along. Diversity (of background, of experience, of disciplinary formation) is not something that exists alongside or in addition to whatever happens in the “real world.” It is an inescapable and enabling condition of life in a more or less democratic society. And anyone who wants it to become more democratic, rather than less, has an interest in learning to understand both its inequities and how other people are affected by them. A case in point might be the findings discussed by Claude Steele, a professor of psychology at Stanford, in a panel on Friday. His paper reviewed some of the research on “identity contingencies,” meaning “things you have to deal with because of your social identity.” One such contingency is what he called “stereotype threat” — a situation in which an individual becomes aware of the risk that what you are doing will confirm some established negative quality associated with your group. And in keeping with the threat, there is a tendency to become vigilant and defensive. Steele did not just have a string of concepts to put up on PowerPoint. He had research findings on how stereotype threat can affect education. The most striking involved results from a puzzle-solving test given to groups of white and black students. When the test was described as a game, the scores for the black students were excellent — conspicuously higher, in fact, than the scores of white students. But in experiments where the very same puzzle was described as an intelligence test, the results were reversed. The black kids scores dropped by about half, while the graph for their white peers spiked. The only variable? How the puzzle was framed — with distracting thoughts about African-American performance on IQ tests creating “stereotype threat” in a way that game-playing did not. Steele also cited an experiment in which white engineering students were given a mathematics test. Just beforehand, some groups were told that Asian students usually did really well on this particular test. Others were simply handed the test without comment. Students who heard about their Asian competitors tended to get much lower scores than the control group. Extrapolate from the social psychologist’s experiments with the effect of a few innocent-sounding remarks — and imagine the cumulative effect of more overt forms of domination. The picture is one of a culture that is profoundly wasteful, even destructive, of the best abilities of many of its members. “It’s not easy for minority folks to discuss these things,” Satya Mohanty told me on the final day of the colloquium. “But I don’t think we can afford to wait until it becomes comfortable to start thinking about them. Our future depends on it. By ‘our’ I mean everyone’s future. How we enrich and deepen our democratic society and institutions depends on the answers we come up with now.” Earlier this year, Oxford University Press published a major new work on postpositivist theory, Visible Identities: Race, Gender, and the Self,by Linda Martin Alcoff, a professor of philosophy at Syracuse University. Several essays from the book are available at the author’s Web site. Steve Kachelmeier wrote the following on May 7, 2012 I like to pose this question to first-year doctoral students: Two researchers test a null hypothesis using a classical statistical approach. The first researcher tests a sample of 20 and the second tests a sample of 20,000. Both find that they can reject the null hypothesis at the same exact "p-value" of 0.05. Which researcher can say with greater confidence that s/he has found a meaningful departure from the null? The vast majority of doctoral students respond that the researcher who tested 20,000 can state the more meaningful conclusion. I then need to explain for about 30 minutes how statistics already dearly penalizes the small-sample-size researcher for the small sample size, such that a much bigger "effect size" is needed to generate the same p-value. Thus, I argue that the researcher with n=20 has likely found the more meaningful difference. The students give me a puzzled look, but I hope they (eventually) get it. The moral? As I see it, the problem is not so much whether we use classical or Bayesian statistical testing. Rather, the problem is that we grossly misinterpret the word "significance" as meaning "big," "meaningful," or "consequential," when in a statistical sense it only means "something other than zero." In Accountics Science R2 = 0.0004 = (-.02)(-.02) Can Be Deemed a Statistically Significant Linear Relationship "Disclosures of Insider Purchases and the Valuation Implications of Past Earnings Signals," by David Veenman, The Accounting Review, January 2012 --- http://aaajournals.org/doi/full/10.2308/accr-10162 . . . Table 2 presents descriptive statistics for the sample of 12,834 purchase filing observations. While not all market responses to purchase filings are positive (the Q1 value of CAR% equals −1.78 percent), 25 percent of filings are associated with a market reaction of at least 5.32 percent. Among the main variables, AQ and AQI have mean (median) values of 0.062 (0.044) and 0.063 (0.056), respectively. By construction, the average of AQD is approximately zero. ΔQEARN and ΔFUTURE are also centered around zero. Jensen Comment Note that correlations shown in bold face type are deemed statistically significant a .05 level. I wonder what it tells me when a -0.02 correlation is statistically significant at a .05 level and a -0.01 correlation is not significant? I have similar doubts about the distinctions between "statistical significance" in the subsequent tables that compare .10, .05, and .01 levels of significance. Especially note that if David Veenman sufficiently increased the sample size both -.00002 and -.00001 correlations might be made to be statistically significant. Just so David Veenman does not think I only singled him out for illustrative purposes In Accountics Science R2 = 0.000784 = (-.028)(-.028) Can Be Deemed a Statistically Significant Linear Relationship "Cover Me: Managers' Responses to Changes in Analyst Coverage in the Post-Regulation FD Period," by Divya Anantharaman and Yuan Zhang, The Accounting Review, November 2011 --- http://aaajournals.org/doi/full/10.2308/accr-10126 I might have written a commentary about this and submitted it to The Accounting Review (TAR), but 574 referees at TAR will not publish critical commentaries of papers previously published in TAR --- http://www.trinity.edu/rjensen/TheoryTAR.htm How Accountics Scientists Should Change: "Frankly, Scarlett, after I get a hit for my resume in The Accounting Review I just don't give a damn" http://www.cs.trinity.edu/~rjensen/temp/AccounticsDamn.htm One more mission in what's left of my life will be to try to change this http://www.cs.trinity.edu/~rjensen/temp/AccounticsDamn.htm The Cult of Statistical Significance: How Standard Error Costs Us Jobs, Justice, and Lives, by Stephen T. Ziliak and Deirdre N. McCloskey (Ann Arbor: University of Michigan Press, ISBN-13: 978-472-05007-9, 2007) Page 206 Like scientists today in medical and economic and other sizeless sciences, Pearson mistook a large sample size for the definite, substantive significance---evidence s Hayek put it, of "wholes." But it was as Hayek said "just an illusion." Pearson's columns of sparkling asterisks, though quantitative in appearance and as appealing a is the simple truth of the sky, signified nothing. pp. xv-xvi The implied reader of our book is a significance tester, the keeper of numerical things. We want to persuade you of one claim: that William Sealy Gosset (1879-1937) --- aka "Student" of Student's t-test --- was right and that his difficult friend, Ronald A. Fisher, though a genius, was wrong. Fit is not the same thing as importance. Statistical significance is not the same thing as scientific finding. R2. t-statistic, p-value, F-test, and all the more sophisticated versions of them in time series and the most advanced statistics are misleading at best. No working scientist today knows much about Gosset, a brewer of Guinness stout and the inventor of a good deal of modern statistics. The scruffy little Gossset, with his tall leather boots and a rucksack on his back, is the heroic underdog of our story. Gosset, we claim, was a great scientist. He took an economic approach to the logic of uncertainty. For over two decades he quietly tried to educate Fisher. But Fisher, our flawed villain, erased from Gosset's inventions the consciously economic element. We want to bring it back. . . . Can so many scientists have been wrong for the eighty years since 1925? Unhappily yes. The mainstream in science, as any scientist will tell you, is often wrong. Otherwise, come to think of it, science would be complete. Few scientists would make that claim, or would want to. Statistical significance is surely not the only error of modern science, although it has been, as we will show, an exceptionally damaging one. Scientists are often tardy in fixing basic flaws in their sciences despite the presence of better alternatives. ... Continued in the Preface Page 3 A brewer of beer, William Sealy Gosset (1876-1937), proved its (statistical significance) in small samples. He worked at the Guinness Brewer in Dublin, where for most of his working life he was head experimental brewer. He saw in 1905 where the need for a small-smle test because he was testing varieties of hops and barley in field samples with N as small as four. Gosset, who is hardly remembered nowadays, quietly invented many tools of modern applied statistics, including Monte Carlo analysis, the balanced design of experiments, and, especially, Student's t, which is the foundation of small-sample theory and the most commonsly7 used test of statistical significance in the sciences. ... But the value Gosset intended with his test, he said without deviation from 1905 until his death in 1937. was its ability to sharpen statements of substantive or economic significance. ... (he) wrote to his elderly friend, the great Karl Person: "My own war work is obviously to brew Guinness stout in each way as to waste as little labor and material as possible, and I am hoping to help to do something fairly creditable in that way." It seems he did. Page 10 Sizelessness is not what most Fisherians (deciples of Ronald Fisher) believe they are getting. The sizeless scientists have adopted a method of deciding which numbers are significant that has little to do with the humanly significant numbers. The scientists re counting, to be sure: "3.14159***," they proudly report of simply "****." But, as the probablist Bruno de Finetti said, they proudly report scientists are acting as though "addition requires different operations if concerned with pure number or amounts of money" (De Finetti 1971, 486, quoted in Savage 1971a). Substituting "significance" for scientific how much would imply that the value of a lottery ticket is the chance itself, the chance 1 in 38,000, say in or 1 in 1,000,000,000. It supposes that the only source in value in the lottery is sampling variability. It sets aside as irrelevant---simply ignores---the value of the expected prize., the millions that success in the lottery could in fact yield. Setting aside both old and new criticisms of expected utility theory, a prize of$3.56 is very different, other things equal, from a prize of \$356,000,000. No matter. Statistical significance, startlingly, ignores the difference.

Continued on Page 10

Page 15
The doctor who cannot distinguish statistical significance from substantive significance, an F-statistic from a heart attach, is like an economist who ignores opportunity cost---what statistical theorists call the loss function. The doctors of "significance" in medicine and economy are merely "deciding what to say rather than what to do" (Savage 1954, 159). In the 1950s Ronald Fisher published an article and a book that intended to rid decision from the vocabulary of working statisticians (1955, 1956). He was annoyed by the rising authority in highbrow circles of those he called "the Neymanites."

Continued on Page 15

pp. 28-31
An example is provided regarding how Merck manipulated statistical inference to keep its killing pain killer Vioxx from being pulled from the market.

Page 31
Another story. The Japanese government in June 2005 increased the limit on the number of whales that may be annually killed in the Antarctica---from around 440 annually to over 1,000 annually. Deputy Commissioner Akira Nakamae explained why:  "We will implement JARPS-2 [the plan for the higher killing] according to the schedule, because the sample size is determined in order to get statistically significant results" (Black 2005). The Japanese hunt for the whales, they claim, in order to collect scientific data on them. That and whale steaks. The commissioner is right:  increasing sample size, other things equal, does increase the statistical significance of the result. It is, fter all, a mathematical fact that statistical significance increases, other things equal, as sample size increases. Thus the theoretical standard error of JAEPA-2, s/SQROOT(440+560) [given for example the simple mean formula], yields more sampling precision than the standard error JARPA-1, s/SQROOT(440). In fact it raises the significance level to Fisher's percent cutoff. So the Japanese government has found a formula for killing more whales, annually some 560 additional victims, under the cover of getting the conventional level of Fisherian statistical significance for their "scientific" studies.

pp. 250-251
The textbooks are wrong. The teaching is wrong. The seminar you just attended is wrong. The most prestigious journal in your scientific field is wrong.

You are searching, we know, for ways to avoid being wrong. Science, as Jeffreys said, is mainly a series of approximations to discovering the sources of error. Science is a systematic way of reducing wrongs or can be. Perhaps you feel frustrated by the random epistemology of the mainstream and don't know what to do. Perhaps you've been sedated by significance and lulled into silence. Perhaps you sense that the power of a Roghamsted test against a plausible Dublin alternative is statistically speaking low but you feel oppressed by the instrumental variable one should dare not to wield. Perhaps you feel frazzled by what Morris Altman (2004) called the "social psychology rhetoric of fear," the deeply embedded path dependency that keeps the abuse of significance in circulation. You want to come out of it. But perhaps you are cowed by the prestige of Fisherian dogma. Or, worse thought, perhaps you are cynically willing to be corrupted if it will keep a nice job

Costs and Benefits of Significance Testing ---
http://www.cato.org/pubs/journal/cj28n2/cj28n2-16.pdf

Jensen Comment
I'm only part way into the book and reserve judgment at this point. It seems to me in these early stages that they overstate their case (in a very scholarly but divisive  way). However, I truly am impressed by the historical citations in this book and the huge number of footnotes and references. The book has a great index.

For most of my scholastic life I've argued that there's a huge difference between significance testing versus substantive testing. The first thing I look for when asked to review an accountics science study is the size of the samples. But this issue is only a part of this fascinating book.

Deirdre McCloskey will kick off the American Annual Meetings in Washington DC with a plenary session first thing in the morning on August 6, 2012. However she's not a student of accounting. She's the Distinguished Professor of Economics, History, English, and Communication, University of Illinois at Chicago and to date has received four honorary degrees ---
http://www.deirdremccloskey.com/
Also see http://en.wikipedia.org/wiki/Deirdre_McCloskey

I've been honored to be on a panel following her presentation to debate her remarks. Her presentation will also focus on  Bourgeois Dignity: Why Economics Can't Explain the Modern World.

Steven T. Ziliac is a former professor of economics at Carnegie who is now a Professor of Economics specializing in poverty research at Roosevelt University ---
http://en.wikipedia.org/wiki/Stephen_T._Ziliak

Would Nate Silver Touch This Probability Estimate With a 10-Foot Baysian Pole?
"Calculating the Probabilities of a U.S. Default." by Justin Fox, Harvard Business Review Article, October 10, 2013 --- Click Here
http://blogs.hbr.org/2013/10/calculating-the-probabilities-of-a-u-s-default/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+harvardbusiness+%28HBR.org%29&cm_ite=DailyAlert-101113+%281%29&cm_lm=sp%3Arjensen%40trinity.edu&cm_ven=Spop-Email

An argument has been making the rounds that there’s really no danger of default if the U.S. runs up against the debt ceiling — the president could simply make sure that all debt payments are made on time, even as other government bills go unpaid. I’ve heard it from economist Thomas Sowell, investor and big-time political donor Foster Friess, and pundit George Will. It’s even been made right here on HBR.org by Tufts University accounting professor Lawrence Weiss.

The Treasury Department has been saying all along that it can’t do this; it makes 80 million payments a month, and it’s simply not technically capable of sorting out which ones to make on time and which ones to hold off on. I don’t know if this is true, and there may be an element of political posturing in such statements. On the other hand, it is the Treasury Department that has to pay the bills. If they say they’re worried, I can’t help but worry too. When Tony Fratto, who worked in the Treasury Department in the Bush Administration, seconds this concern, I worry even more. Not to mention that this has happened before, in the mini-default of 1979, when Treasury systems went on the fritz in the wake of a brief Congressional standoff over  —  you guessed it — raising the debt ceiling.

Then there’s the question of legality. The second the President or the Treasury Secretary starts choosing which bills to pay, he usurps the spending authority that the U.S. Constitution grants Congress. The Constitution states, in the 14th Amendment, that the U.S. will pay its debts. But there is no clear path to honoring this commitment in the face of a breached debt ceiling. Writing in the Columbia Law Review last year, Neil H. Buchanan of George Washington University Law School and Michael C. Dorf of Cornell University Law School concluded that as every realistic option faced by the president violated the Constitution in some way, the “least unconstitutional” thing to do would not be to stop making some payments but to ignore the debt ceiling. That’s because, in comparison with unilaterally raising taxes or cutting spending to enable the U.S. to continue making its debt payments under the current ceiling, ignoring the debt limit would “minimize the unconstitutional assumption of power, minimize sub-constitutional harm, and preserve, to the extent possible, the ability of other actors to undo or remedy constitutional violations.” And even this option, Buchanan and Dorf acknowledge, is fraught with risk: financial markets might shun the new bonds issued under presidential fiat as “radioactive.”

So assigning a 0% probability to the possibility that running into the debt ceiling will lead to some kind of default doesn’t sound reasonable. What is reasonable? Let’s say 25%, although really that’s just a guess. The likelihood that hitting the ceiling will result in sustained higher interest rates for the U.S. is higher (maybe  50%?) and the likelihood that it will temporarily raise short-term rates is something like 99.99%, since those rates have already been rising.

It’s the kind of thing that makes you wish Nate Silver weren’t too busy hiring people for the new, Disneyfied fivethirtyeight.com to focus on. At this point even Silver would have to resort to guesswork — this is a mostly unprecedented situation we’re dealing with here.  But the updating of his predictions as new information came in would be fascinating to watch, and might even add some calm sanity to the discussion.

Updating is what the Bayesian approach to statistics that Silver swears by is all about. Reasonable people can start out with differing opinions about the likelihood that something will happen, but as new information comes in they should all be using the same formula (Bayes’ formula) to update their predictions, and in the process their views should move closer together. “The role of statistics is not to discover truth,” the late, great Bayesian Leonard “Jimmie” Savage used to say. “The role of statistics is to resolve disagreements among people.” (At least, that’s how his friend Milton Friedman remembered it; the quote is from the book Two Lucky People.)

I tread lightly here, because I’m one of those idiots who never took a statistics class in college, so don’t expect me to be any help on Bayesian methods. But as a philosophy, I think it can be expressed something like this: You’re entitled to your opinion. You’re even entitled to your opinion as to how much weight to give new information as it comes in.  But you need to be explicit about your predictions and weightings, and willing to change your opinion if Bayes theorem tells you to. A political environment where that was the dominant approach would be pretty swell, no?

Not that it would resolve everything. Some Republicans have been making the very Bayesian argument that, after dire predictions about the consequences of the sequester and the government shutdown failed to come true, the argument that a debt ceiling breach would be disastrous has become less credible. As a matter of politics, they have a point: the White House clearly oversold the potential economic consequences of both sequester and shutdown. But I never took those dire claims about the sequester and shutdown seriously, so my views on the dangers associated with hitting the debt ceiling haven’t changed much at all. And while I’m confident that my view is more reasonable than that of the debt-ceiling Pollyannas, I don’t see how I can use Bayesian statistics to convince them of that, or how they can use it to sway me. Until we hit the debt limit.

Nate Silver --- http://en.wikipedia.org/wiki/Nate_Silver

Jensen Comment
David Johnstone's romance with Bayesian probability, in his scholarly messages to the AECM, prompted me once again in my old age to delve into the Second Edition of Causality by Judea Pearl (Cambridge University press).

I like this book and can study various points raised by David. But estimating the probability of default in the context of the above posting by Justin Fox raises many doubts in my mind.

A Database on Each Previous Performance Outcome of a Baseball Player
The current Bayesian hero Nate Silver generally predicts from two types of databases. His favorite database is the history of baseball statistics of individual players when estimating the probability of performance of a current player, especially pitching and batting performance. Fielding performances are more difficult to predict because is such a variance of challenges for each fielded ball. His Pecota system is based upon the statistical history of each player.

A Sequence of  Changing Databases of Election Poll Outcomes
Election polls emerge at frequent points in time (e.g., monthly). These are not usually recorded data points of each potential voter (like data points over time of a baseball player). But they are indicative of the aggregate outcome of all voters who will eventually make a voting choice on election day.

The important point to note in this type of database is that the respondent is predicting his or her own act of voting. The task is not to predict how an act of Congress over which the respondent has no direct control and no inside information about the decision process of individual members of Congress (who could just be bluffing for the media).

The problem Nate has is in the chance that a significant number of voters will change their minds back and forth write up to pulling the lever in a voting booth. This is why Nate has some monumental prediction errors for political voting relative to baseball player performance. One of those errors concerned in predictions regarding the winner of the Senate Seat in Massachusetts after the death of Ted Kennedy. Many voters seemingly changed their minds just before or during election day.

There are no such databases for estimating the probability of USA debt default in October of 2013.
Without a suitable database I don't think Nate Silver would estimate the probability of USA loan default in October of 2013. This begs the question of what Nate might do if a trustworthy poll sampled voters on their estimates of the probability of default. I don't think Nate would trust this database, however, because the random respondents across the USA do not have inside information or expertise for making such probability analysis and are most likely inconsistently informed with respect to which TV networks they watch or newspapers they read.

I do realize that databases of economic predictions of expert economists or expert weather forecasters have some modicum of success. But the key word here is the adjective "expert." I'm not sure there are any experts of the probabilities of one particular and highly circumstantial USA debt default in October of 2013 even though there are experts on forecasting the 2013 GDP.

Bayesian probability is a formalized derivation of a person's belief.
But if there is no justification for for having some confidence in that person's belief then there really is not much use of deriving that person's subjective probability estimate. For example, if you asked me about my belief in regarding the point spread in a football game next Friday night between two high schools in Nevada my belief on the matter is totally useless because I've never even heard of any particular high schools in Nevada let alone their football teams.

I honestly think that what outsiders believe about the debt default issue for October 2013 is totally useless. It might be interesting to compute Bayesian probabilities of such default from Congressional insiders, but most persons in Congress cannot be trusted to be truthful about their responses, and their responses vary greatly in terms of expertise because the degree of inside information varies so among members of Congress. This is mostly a game of political posturing and not a game of statistics.

October 12, 2013 reply from David Johnstone

Dear Bob, I think you are on the Bayesian hook, many Bayesians say how they started off as sceptics or without any wish for a new creed, but then got drawn in when they saw the insights and tools that Bayes had in it. Dennis Lindley says that he set out in his 20s to prove that something was wrong with Bayesian thinking, but discovered the opposite. Don’t be fooled by the fact that most business school PhD programs have in general rejected or never discovered Bayesian methods, they similarly hold onto all sorts of vested theoretical positions for as long as possible.

The thing about Bayes, that makes resistance amusing, is that if you accept the laws of probability, which merely show how one probability relates logically to another, then you have to be “Bayesian” because the theorem is just a law of probability. Basically, you either accept Bayes and the probability calculus, or you go into a no man’s land.

That does not mean that Bayes theorem gives answers by formal calculations all the time. Many probabilities are just seat of the pants subjective assessments. But (i) these are more sensible if they happen to be consistent with other probabilities that we have assessed or hold, and (ii) they may be very inaccurate, since  such judgements are often very hard, even for supposed experts. The Dutch Book argument that is widely used for Bayes is that if you hold two probabilities that are mutually inconsistent by the laws of probability, you can have bets set against you by which you will necessarily lose, whatever the events are. This is the same way by which bookmakers set up arbitrages against their total of bettors, so that they win net whatever horse wins the race. The Bayesian creed is “coherence”, not correctness. Correctness is asking too much, coherence is just asking for consistency between beliefs.

Bayes theorem is not a religion or a pop song, it’s just a law of probability, so romance is out of the question. And if we do conventional “frequentist” statistics (significance tests etc.) we often break these laws in our reasoning, which is remarkable given that we hold ourselves out as so scientific, logical and sophisticated. It is also a cognitive dissonance since at the same time we often start with a theoretical model of behaviour that assumes only Bayesian agents. This is pretty hilarious really, for what it says about people and intellectual behavior, and about how forgiving “nature” is of us, by indulging our cognitive proclivities without stinging us fatally for any inconsistencies.

Bayes theorem recognises that much opinion is worthless, and that shows up in the likelihood function. For example, the probability of a head given rain is the same as the probability of a head given fine, so a coin toss (or equivalent “expert”) gives no help whatsoever in predicting rain. Bayes theorem is only logic, it’s not a forecasting method of itself. While on weather, those people are seriously good forecasters, despite their appearance in many jokes, and leave economic forecasters for dead. Their problems might be “easier” than forecasting markets, but they have made genuine theoretical and practical progress. I have suggested to weather forecasters in Australia that they should run an on-line betting site on “rain events” and let people take them on, there would be very few who don’t get skinned quickly.

I won’t go on more, but if I did it would be to say that it is the principles of logic implicit in Bayes theorem that are so  insightful and helpful about it. These should have been taught to us all at school, when we were learning deductive logic (e.g. sums). I think it is often argued that probability was associated with gambling and uncertainty, offending many religious and social beliefs, and hence was a bit of an underworld historically. Funny that Thomas Bayes was a Rev.

October 13, 2013 reply from Bob Jensen

Hi David,
You're facing an enormous task trying to change accountics scientists who trained only to apply popular GLM statistical inference software like SAS, SPSS, Statistica, Sysstat,  and MATLAB to purchased databases like Betty Crocker follows recipes for baking desserts. Mostly they ignore the tremendous limitations and assumptions of the Cult of Statistical Inference:

The Cult of Statistical Significance: How Standard Error Costs Us Jobs, Justice, and Lives ---
http://www.cs.trinity.edu/~rjensen/temp/DeirdreMcCloskey/StatisticalSignificance01.htm

Do you have any recommendations for Bayesian software such as WinBugs, Bayesian Filtering Library, JAGS, Mathematica and possibly some of the Markov chain analysis software?
http://en.wikipedia.org/wiki/List_of_statistical_packages

Respectfully,

Bob Jensen

May 11, 2012 reply from Jagdish Gangolly

Hopefully this is my last post on this thread. I just could not resist posting this appeal to editors, chairs, directors, reviewers,... by Professor John Kruschke, Professor of Psychological and Brain Sciences and Statistics at Indiana University.

His book on " Doing Bayesian Data Analysis: A Tutorial with R and BUGS " is the best introductory textbook on statistics I have read.

Regards to all,

Jagdish

Here is the open letter: ___________________________________________________

An open letter to Editors of journals, Chairs of departments, Directors of funding programs, Directors of graduate training, Reviewers of grants and manuscripts, Researchers, Teachers, and Students:

Statistical methods have been evolving rapidly, and many people think it’s time to adopt modern Bayesian data analysis as standard procedure in our scientific practice and in our educational curriculum. Three reasons:

1. Scientific disciplines from astronomy to zoology are moving to Bayesian data analysis. We should be leaders of the move, not followers.

2. Modern Bayesian methods provide richer information, with greater flexibility and broader applicability than 20th century methods. Bayesian methods are intellectually coherent and intuitive. Bayesian analyses are readily computed with modern software and hardware.

3. Null-hypothesis significance testing (NHST), with its reliance on p values, has many problems. There is little reason to persist with NHST now that Bayesian methods are accessible to everyone.

My conclusion from those points is that we should do whatever we can to encourage the move to Bayesian data analysis. Journal editors could accept Bayesian data analyses, and encourage submissions with Bayesian data analyses. Department chairpersons could encourage their faculty to be leaders of the move to modern Bayesian methods. Funding agency directors could encourage applications using Bayesian data analysis. Reviewers could recommend Bayesian data analyses. Directors of training or curriculum could get courses in Bayesian data analysis incorporated into the standard curriculum. Teachers can teach Bayesian. Researchers can use Bayesian methods to analyze data and submit the analyses for publication. Students can get an advantage by learning and using Bayesian data analysis.

The goal is encouragement of Bayesian methods, not prohibition of NHST or other methods. Researchers will embrace Bayesian analysis once they learn about it and see its many practical and intellectual advantages. Nevertheless, change requires vision, courage, incentive, effort, and encouragement!

Now to expand on the three reasons stated above.

1. Scientific disciplines from astronomy to zoology are moving to Bayesian data analysis. We should be leaders of the move, not followers.

Bayesian methods are revolutionizing science. Notice the titles of these articles:

Bayesian computation: a statistical revolution. Brooks, S.P. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 361(1813), 2681, 2003.

The Bayesian revolution in genetics. Beaumont, M.A. and Rannala, B. Nature Reviews Genetics, 5(4), 251-261, 2004.

A Bayesian revolution in spectral analysis. Gregory, PC. AIP Conference Proceedings, 557-568, 2001.

The hierarchical Bayesian revolution: how Bayesian methods have changed the face of marketing research. Allenby, G.M. and Bakken, D.G. and Rossi, P.E. Marketing Research, 16, 20-25, 2004

The future of statistics: A Bayesian 21st century. Lindley, DV. Advances in Applied Probability, 7, 106-115, 1975.

There are many other articles that make analogous points in other fields, but with less pithy titles. If nothing else, the titles above suggest that the phrase “Bayesian revolution” is not an overstatement.

The Bayesian revolution spans many fields of science. Notice the titles of these articles:

Bayesian analysis of hierarchical models and its application in AGRICULTURE. Nazir, N., Khan, A.A., Shafi, S., Rashid, A. InterStat, 1, 2009.

The Bayesian approach to the interpretation of ARCHAEOLOGICAL DATA. Litton, CD & Buck, CE. Archaeometry, 37(1), 1-24, 1995.

The promise of Bayesian inference for ASTROPHYSICS. Loredo TJ. In: Feigelson ED, Babu GJ, eds. Statistical Challenges in Modern Astronomy. New York: Springer-Verlag; 1992, 275–297.

Bayesian methods in the ATMOSPHERIC SCIENCES. Berliner LM, Royle JA, Wikle CK, Milliff RF. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM, eds. Bayesian Statistics 6: Proceedings of the sixth Valencia international meeting, June 6–10, 1998. Oxford, UK: Oxford University Press; 1999, 83–100.

An introduction to Bayesian methods for analyzing CHEMISTRY data:: Part II: A review of applications of Bayesian methods in CHEMISTRY. Hibbert, DB and Armstrong, N. Chemometrics and Intelligent Laboratory Systems, 97(2), 211-220, 2009.

Bayesian methods in CONSERVATION BIOLOGY. Wade PR. Conservation Biology, 2000, 1308–1316.

Bayesian inference in ECOLOGY. Ellison AM. Ecol Biol 2004, 7:509–520.

The Bayesian approach to research in ECONOMIC EDUCATION. Kennedy, P. Journal of Economic Education, 17, 9-24, 1986.

The growth of Bayesian methods in statistics and ECONOMICS since 1970. Poirier, D.J. Bayesian Analysis, 1(4), 969-980, 2006.

Commentary: Practical advantages of Bayesian analysis of EPIDEMIOLOGIC DATA. Dunson DB. Am J Epidemiol 2001, 153:1222–1226.

Bayesian inference of phylogeny and its impact on EVOLUTIONARY BIOLOGY. Huelsenbeck JP, Ronquist F, Nielsen R, Bollback JP. Science 2001, 294:2310–2314.

Geoadditive Bayesian models for FORESTRY defoliation data: a case study. Musio, M. and Augustin, N.H. and von Wilpert, K. Environmetrics. 19(6), 630—642, 2008.

Bayesian statistics in GENETICS: a guide for the uninitiated. Shoemaker, J.S. and Painter, I.S. and Weir, B.S. Trends in Genetics, 15(9), 354-358, 1999.

Bayesian statistics in ONCOLOGY. Adamina, M. and Tomlinson, G. and Guller, U. Cancer, 115(23), 5371-5381, 2009.

Bayesian analysis in PLANT PATHOLOGY. Mila, AL and Carriquiry, AL. Phytopathology, 94(9), 1027-1030, 2004.

Bayesian analysis for POLITICAL RESEARCH. Jackman S. Annual Review of Political Science, 2004, 7:483–505.

The list above could go on and on. The point is simple: Bayesian methods are being adopted across the disciplines of science. We should not be laggards in utilizing Bayesian methods in our science, or in teaching Bayesian methods in our classrooms.

Why are Bayesian methods being adopted across science? Answer:

2. Bayesian methods provide richer information, with greater flexibility and broader applicability than 20th century methods. Bayesian methods are intellectually coherent and intuitive. Bayesian analyses are readily computed with modern software and hardware.

To explain this point adequately would take an entire textbook, but here are a few highlights.

* In NHST, the data collector must pretend to plan the sample size in advance and pretend not to let preliminary looks at the data influence the final sample size. Bayesian design, on the contrary, has no such pretenses because inference is not based on p values.

* In NHST, analysis of variance (ANOVA) has elaborate corrections for multiple comparisons based on the intentions of the analyst. Hierarchical Bayesian ANOVA uses no such corrections, instead rationally mitigating false alarms based on the data.

* Bayesian computational practice allows easy modification of models to properly accommodate the measurement scales and distributional needs of observed data.

* In many NHST analyses, missing data or otherwise unbalanced designs can produce computational problems. Bayesian models seamlessly handle unbalanced and small-sample designs.

* In many NHST analyses, individual differences are challenging to incorporate into the analysis. In hierarchical Bayesian approaches, individual differences can be flexibly and easily modeled, with hierarchical priors that provide rational “shrinkage” of individual estimates.

* In contingency table analysis, the traditional chi-square test suffers if expected values of cell frequencies are less than 5. There is no such issue in Bayesian analysis, which handles small or large frequencies seamlessly.

* In multiple regression analysis, traditional analyses break down when the predictors are perfectly (or very strongly) correlated, but Bayesian analysis proceeds as usual and reveals that the estimated regression coefficients are (anti-)correlated.

* In NHST, the power of an experiment, i.e., the probability of rejecting the null hypothesis, is based on a single alternative hypothesis. And the probability of replicating a significant outcome is “virtually unknowable” according to recent research. But in Bayesian analysis, both power and replication probability can be computed in straight forward manner, with the uncertainty of the hypothesis directly represented.

* Bayesian computational practice allows easy specification of domain-specific psychometric models in addition to generic models such as ANOVA and regression.

Some people may have the mistaken impression that the advantages of Bayesian methods are negated by the need to specify a prior distribution. In fact, the use of a prior is both appropriate for rational inference and advantageous in practical applications.

* It is inappropriate not to use a prior. Consider the well known example of random disease screening. A person is selected at random to be tested for a rare disease. The test result is positive. What is the probability that the person actually has the disease? It turns out, even if the test is highly accurate, the posterior probability of actually having the disease is surprisingly small. Why? Because the prior probability of the disease was so small. Thus, incorporating the prior is crucial for coming to the right conclusion.

* Priors are explicitly specified and must be agreeable to a skeptical scientific audience. Priors are not capricious and cannot be covertly manipulated to predetermine a conclusion. If skeptics disagree with the specification of the prior, then the robustness of the conclusion can be explicitly examined by considering other reasonable priors. In most applications, with moderately large data sets and reasonably informed priors, the conclusions are quite robust.

* Priors are useful for cumulative scientific knowledge and for leveraging inference from small-sample research. As an empirical domain matures, more and more data accumulate regarding particular procedures and outcomes. The accumulated results can inform the priors of subsequent research, yielding greater precision and firmer conclusions.

* When different groups of scientists have differing priors, stemming from differing theories and empirical emphases, then Bayesian methods provide rational means for comparing the conclusions from the different priors.

To summarize, priors are not a problematic nuisance to be avoided. Instead, priors should be embraced as appropriate in rational inference and advantageous in real research.

If those advantages of Bayesian methods are not enough to attract change, there is also a major reason to be repelled from the dominant method of the 20th century:

3. 20th century null-hypothesis significance testing (NHST), with its reliance on p values, has many severe problems. There is little reason to persist with NHST now that Bayesian methods are accessible to everyone.

Although there are many difficulties in using p values, the fundamental fatal flaw of p values is that they are ill defined, because any set of data has many different p values.

Consider the simple case of assessing whether an electorate prefers candidate A over candidate B. A quick random poll reveals that 8 people prefer candidate A out of 23 respondents. What is the p value of that outcome if the population were equally divided? There is no single answer! If the pollster intended to stop when N=23, then the p value is based on repeating an experiment in which N is fixed at 23. If the pollster intended to stop after the 8th respondent who preferred candidate A, then the p value is based on repeating an experiment in which N can be anything from 8 to infinity. If the pollster intended to poll for one hour, then the p value is based on repeating an experiment in which N can be anything from zero to infinity. There is a different p value for every possible intention of the pollster, even though the observed data are fixed, and even though the outcomes of the queries are carefully insulated from the intentions of the pollster.

The problem of ill-defined p values is magnified for realistic situations. In particular, consider the well-known issue of multiple comparisons in analysis of variance (ANOVA). When there are several groups, we usually are interested in a variety of comparisons among them: Is group A significantly different from group B? Is group C different from group D? Is the average of groups A and B different from the average of groups C and D? Every comparison presents another opportunity for a false alarm, i.e., rejecting the null hypothesis when it is true. Therefore the NHST literature is replete with recommendations for how to mitigate the “experimentwise” false alarm rate, using corrections such as Bonferroni, Tukey, Scheffe, etc. The bizarre part of this practice is that the p value for the single comparison of groups A and B depends on what other groups you intend to compare them with. The data in groups A and B are fixed, but merely intending to compare them with other groups enlarges the p value of the A vs B comparison. The p value grows because there is a different space of possible experimental outcomes when the intended experiment comprises more groups. Therefore it is trivial to make any comparison have a large p value and be nonsignificant; all you have to do is intend to compare the data with other groups in the future.

The literature is full of articles pointing out the many conceptual misunderstandings held by practitioners of NHST. For example, many people mistake the p value for the probability that the null hypothesis is true. Even if those misunderstandings could be eradicated, such that everyone clearly understood what p values really are, the p values would still be ill defined. Every fixed set of data would still have many different p values.

To recapitulate: Science is moving to Bayesian methods because of their many advantages, both practical and intellectual, over 20th century NHST. It is time that we convert our research and educational practices to Bayesian data analysis. I hope you will encourage the change. It’s the right thing to do.

John K. Kruschke, Revised 14 November 2010, http://www.indiana.edu/~kruschke/

Mean and Median Applet --- http://mathdl.maa.org/mathDL/47/?pa=content&sa=viewDocument&nodeId=3204
Thank you for sharing  Professor Kady Schneiter of Utah State University

This applet consists of two windows, in the first (the investigate window), the user fills in a grid to create a distribution of numbers and to investigate the mean and median of the distribution. The second window (the identify window) enables users to test their knowledge about the mean and the median. In this window, the applet displays a hypothetical distribution and an unspecified marker. The user determines whether the marker indicates the postion of the mean of the distribution, the median, both, or neither. Two activities intended to facilitate using the applet to learn about the mean and median are provided.

Above all, Mr. Silver urges forecasters to become Bayesians. The English mathematician Thomas Bayes used a mathematical rule to adjust a base probability number in light of new evidence

Book Review of The Signal and the Noise
by Nate Silver
Price:  16.44 at Barnes and Noble
http://www.barnesandnoble.com/w/the-signal-and-the-noise-nate-silver/1111307421?ean=9781594204111

"Telling Lies From Statistics:  Forecasters must avoid overconfidence—and recognize the degree of uncertainty that attends even the most careful predictions," by Burton G. Malkiel, The Wall Street Journal, September 24, 2012 ---
http://professional.wsj.com/article/SB10000872396390444554704577644031670158646.html?mod=djemEditorialPage_t&mg=reno64-wsj

It is almost a parlor game, especially as elections approach—not only the little matter of who will win but also: by how much? For Nate Silver, however, prediction is more than a game. It is a science, or something like a science anyway. Mr. Silver is a well-known forecaster and the founder of the New York Times political blog FiveThirtyEight.com, which accurately predicted the outcome of the last presidential election. Before he was a Times blogger, he was known as a careful analyst of (often widely unreliable) public-opinion polls and, not least, as the man who hit upon an innovative system for forecasting the performance of Major League Baseball players. In "The Signal and the Noise," he takes the reader on a whirlwind tour of the success and failure of predictions in a wide variety of fields and offers advice about how we might all improve our forecasting skill.

Mr. Silver reminds us that we live in an era of "Big Data," with "2.5 quintillion bytes" generated each day. But he strongly disagrees with the view that the sheer volume of data will make predicting easier. "Numbers don't speak for themselves," he notes. In fact, we imbue numbers with meaning, depending on our approach. We often find patterns that are simply random noise, and many of our predictions fail: "Unless we become aware of the biases we introduce, the returns to additional information may be minimal—or diminishing." The trick is to extract the correct signal from the noisy data. "The signal is the truth," Mr. Silver writes. "The noise is the distraction."

The first half of Mr. Silver's analysis looks closely at the success and failure of predictions in clusters of fields ranging from baseball to politics, poker to chess, epidemiology to stock markets, and hurricanes to earthquakes. We do well, for example, with weather forecasts and political predictions but very badly with earthquakes. Part of the problem is that earthquakes, unlike hurricanes, often occur without warning. Half of major earthquakes are preceded by no discernible foreshocks, and periods of increased seismic activity often never result in a major tremor—a classic example of "noise." Mr. Silver observes that we can make helpful forecasts of future performance of baseball's position players—relying principally on "on-base percentage" and "wins above replacement player"—but we completely missed the 2008 financial crisis. And we have made egregious errors in predicting the spread of infectious diseases such as the flu.

In the second half of his analysis, Mr. Silver suggests a number of methods by which we can improve our ability. The key, for him, is less a particular mathematical model than a temperament or "framing" idea. First, he says, it is important to avoid overconfidence, to recognize the degree of uncertainty that attends even the most careful forecasts. The best forecasts don't contain specific numerical expectations but define the future in terms of ranges (the hurricane should pass somewhere between Tampa and 350 miles west) and probabilities (there is a 70% chance of rain this evening).

Above all, Mr. Silver urges forecasters to become Bayesians. The English mathematician Thomas Bayes used a mathematical rule to adjust a base probability number in light of new evidence. To take a canonical medical example, 1% of 40-year-old women have breast cancer: Bayes's rule tells us how to factor in new information, such as a breast-cancer screening test. Studies of such tests reveal that 80% of women with breast cancer will get positive mammograms, and 9.6% of women without breast cancer will also get positive mammograms (so-called false positives). What is the probability that a woman who gets a positive mammogram will in fact have breast cancer? Most people, including many doctors, greatly overestimate the probability that the test will give an accurate diagnosis. The right answer is less than 8%. The result seems counterintuitive unless you realize that a large number of (40-year-old) women without breast cancer will get a positive reading. Ignoring the false positives that always exist with any noisy data set will lead to an inaccurate estimate of the true probability.

This example and many others are neatly presented in "The Signal and the Noise." Mr. Silver's breezy style makes even the most difficult statistical material accessible. What is more, his arguments and examples are painstakingly researched—the book has 56 pages of densely printed footnotes. That is not to say that one must always agree with Mr. Silver's conclusions, however.

Continued in article

Bayesian Probability --- http://en.wikipedia.org/wiki/Bayesian_probability

Bayesian Inference --- http://en.wikipedia.org/wiki/Bayesian_inference

Bob Jensen's threads on free online mathematics and statistics tutorials are at
http://www.trinity.edu/rjensen/Bookbob2.htm#050421Mathematics

Multicollinearity --- http://en.wikipedia.org/wiki/Multicollinearity

Question
When we took econometrics we learned that predictor variable independence was good and interdependence was bad, especially higher ordered complicated interdependencies?

"Can You Actually TEST for Multicollinearity?" --- Click Here
http://davegiles.blogspot.com/2013/06/can-you-actually-test-for.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+blogspot%2FjjOHE+%28Econometrics+Beat%3A+Dave+Giles%27+Blog%29

. . .

Now, let's return to the "problem" of multicollinearity.

What do we mean by this term, anyway? This turns out to be the key question!

Multicollinearity is a phenomenon associated with our particular sample of data when we're trying to estimate a regression model. Essentially, it's a situation where there is insufficient information in the sample of data to enable us to enable us to draw "reliable" inferences about the individual parameters of the underlying (population) model.

I'll be elaborating more on the "informational content" aspect of this phenomenon in a follow-up post. Yes, there are various sample measures that we can compute and report, to help us gauge how severe this data "problem" may be. But they're not statistical tests, in any sense of the word

Because multicollinearity is a characteristic of the sample, and not a characteristic of the population, you should immediately be suspicious when someone starts talking about "testing for multicollinearity". Right?

Apparently not everyone gets it!

There's an old paper by Farrar and Glauber (1967) which, on the face of it might seem to take a different stance. In fact, if you were around when this paper was published (or if you've bothered to actually read it carefully), you'll know that this paper makes two contributions. First, it provides a very sensible discussion of what multicollinearity is all about. Second, the authors take some well known results from the statistics literature (notably, by Wishart, 1928; Wilks, 1932; and Bartlett, 1950) and use them to give "tests" of the hypothesis that the regressor matrix, X, is orthogonal.

How can this be? Well, there's a simple explanation if you read the Farrar and Glauber paper carefully, and note what assumptions are made when they "borrow" the old statistics results. Specifically, there's an explicit (and necessary) assumption that in the population the X matrix is random, and that it follows a multivariate normal distribution.

This assumption is, of course totally at odds with what is usually assumed in the linear regression model! The "tests" that Farrar and Glauber gave us aren't really tests of multicollinearity in the sample. Unfortunately, this point wasn't fully appreciated by everyone.

There are some sound suggestions in this paper, including looking at the sample multiple correlations between each regressor, and all of the other regressors. These, and other sample measures such as variance inflation factors, are useful from a diagnostic viewpoint, but they don't constitute tests of "zero multicollinearity".

So, why am I even mentioning the Farrar and Glauber paper now?

Well, I was intrigued to come across some STATA code (Shehata, 2012) that allows one to implement the Farrar and Glauber "tests". I'm not sure that this is really very helpful. Indeed, this seems to me to be a great example of applying someone's results without understanding (bothering to read?) the assumptions on which they're based!

Be careful out there - and be highly suspicious of strangers bearing gifts!

References

Bartlett, M. S., 1950. Tests of significance in factor analysis. British Journal of Psychology, Statistical Section, 3, 77-85.

Farrar, D. E. and R. R. Glauber, 1967. Multicollinearity in regression analysis: The problem revisited.  Review of Economics and Statistics, 49, 92-107.

Shehata, E. A. E., 2012. FGTEST: Stata module to compute Farrar-Glauber Multicollinearity Chi2, F, t tests.

Wilks, S. S., 1932. Certain generalizations in the analysis of variance. Biometrika, 24, 477-494.

Wishart, J., 1928. The generalized product moment distribution in samples from a multivariate normal population. Biometrika, 20A, 32-52.

Multicollinearity --- http://en.wikipedia.org/wiki/Multicollinearity

## Detection of multicollinearity

Indicators that multicollinearity may be present in a model:

1. Large changes in the estimated regression coefficients when a predictor variable is added or deleted
2. Insignificant regression coefficients for the affected variables in the multiple regression, but a rejection of the joint hypothesis that those coefficients are all zero (using an F-test)
3. If a multivariate regression finds an insignificant coefficient of a particular explanator, yet a simple linear regression of the explained variable on this explanatory variable shows its coefficient to be significantly different from zero, this situation indicates multicollinearity in the multivariate regression.
4. Some authors have suggested a formal detection-tolerance or the variance inflation factor (VIF) for multicollinearity:
$\mathrm{tolerance} = 1-R_{j}^2,\quad \mathrm{VIF} = \frac{1}{\mathrm{tolerance}},$
where $R_{j}^2$ is the coefficient of determination of a regression of explanator j on all the other explanators. A tolerance of less than 0.20 or 0.10 and/or a VIF of 5 or 10 and above indicates a multicollinearity problem (but see O'Brien 2007).[1]
5. Condition Number Test: The standard measure of ill-conditioning in a matrix is the condition index. It will indicate that the inversion of the matrix is numerically unstable with finite-precision numbers ( standard computer floats and doubles ). This indicates the potential sensitivity of the computed inverse to small changes in the original matrix. The Condition Number is computed by finding the square root of (the maximum eigenvalue divided by the minimum eigenvalue). If the Condition Number is above 30, the regression is said to have significant multicollinearity.
6. Farrar-Glauber Test:[2] If the variables are found to be orthogonal, there is no multicollinearity; if the variables are not orthogonal, then multicollinearity is present.
7. Construction of a correlation matrix among the explanatory variables will yield indications as to the likelihood that any given couplet of right-hand-side variables are creating multicollinearity problems. Correlation values (off-diagonal elements) of at least .4 are sometimes interpreted as indicating a multicollinearity problem.

## Consequences of multicollinearity

As mentioned above, one consequence of a high degree of multicollinearity is that, even if the matrix XTX is invertible, a computer algorithm may be unsuccessful in obtaining an approximate inverse, and if it does obtain one it may be numerically inaccurate. But even in the presence of an accurate XTX matrix, the following consequences arise:

In the presence of multicollinearity, the estimate of one variable's impact on the dependent variable $Y$ while controlling for the others tends to be less precise than if predictors were uncorrelated with one another. The usual interpretation of a regression coefficient is that it provides an estimate of the effect of a one unit change in an independent variable, $X_{1}$, holding the other variables constant. If $X_{1}$ is highly correlated with another independent variable, $X_{2}$, in the given data set, then we have a set of observations for which $X_{1}$ and $X_{2}$ have a particular linear stochastic relationship. We don't have a set of observations for which all changes in $X_{1}$ are independent of changes in $X_{2}$, so we have an imprecise estimate of the effect of independent changes in $X_{1}$.

In some sense, the collinear variables contain the same information about the dependent variable. If nominally "different" measures actually quantify the same phenomenon then they are redundant. Alternatively, if the variables are accorded different names and perhaps employ different numeric measurement scales but are highly correlated with each other, then they suffer from redundancy.

One of the features of multicollinearity is that the standard errors of the affected coefficients tend to be large. In that case, the test of the hypothesis that the coefficient is equal to zero may lead to a failure to reject a false null hypothesis of no effect of the explanator.

A principal danger of such data redundancy is that of overfitting in regression analysis models. The best regression models are those in which the predictor variables each correlate highly with the dependent (outcome) variable but correlate at most only minimally with each other. Such a model is often called "low noise" and will be statistically robust (that is, it will predict reliably across numerous samples of variable sets drawn from the same statistical population).

So long as the underlying specification is correct, multicollinearity does not actually bias results; it just produces large standard errors in the related independent variables. If, however, there are other problems (such as omitted variables) which introduce bias, multicollinearity can multiply (by orders of magnitude) the effects of that bias.[citation needed] More importantly, the usual use of regression is to take coefficients from the model and then apply them to other data. If the pattern of multicollinearity in the new data differs from that in the data that was fitted, such extrapolation may introduce large errors in the predictions.[3]

## Remedies for multicollinearity

1. Make sure you have not fallen into the dummy variable trap; including a dummy variable for every category (e.g., summer, autumn, winter, and spring) and including a constant term in the regression together guarantee perfect multicollinearity.
2. Try seeing what happens if you use independent subsets of your data for estimation and apply those estimates to the whole data set. Theoretically you should obtain somewhat higher variance from the smaller datasets used for estimation, but the expectation of the coefficient values should be the same. Naturally, the observed coefficient values will vary, but look at how much they vary.
3. Leave the model as is, despite multicollinearity. The presence of multicollinearity doesn't affect the efficacy of extrapolating the fitted model to new data provided that the predictor variables follow the same pattern of multicollinearity in the new data as in the data on which the regression model is based.[4]
4. Drop one of the variables. An explanatory variable may be dropped to produce a model with significant coefficients. However, you lose information (because you've dropped a variable). Omission of a relevant variable results in biased coefficient estimates for the remaining explanatory variables.
5. Obtain more data, if possible. This is the preferred solution. More data can produce more precise parameter estimates (with lower standard errors), as seen from the formula in variance inflation factor for the variance of the estimate of a regression coefficient in terms of the sample size and the degree of multicollinearity.
6. Mean-center the predictor variables. Generating polynomial terms (i.e., for $x_1$, $x_1^2$, $x_1^3$, etc.) can cause some multicolinearity if the variable in question has a limited range (e.g., [2,4]). Mean-centering will eliminate this special kind of multicollinearity. However, in general, this has no effect. It can be useful in overcoming problems arising from rounding and other computational steps if a carefully designed computer program is not used.
7. Standardize your independent variables. This may help reduce a false flagging of a condition index above 30.
8. It has also been suggested that using the Shapley value, a game theory tool, the model could account for the effects of multicollinearity. The Shapley value assigns a value for each predictor and assesses all possible combinations of importance.[5]
9. Ridge regression or principal component regression can be used.
10. If the correlated explanators are different lagged values of the same underlying explanator, then a distributed lag technique can be used, imposing a general structure on the relative values of the coefficients to be estimated.

Note that one technique that does not work in offsetting the effects of multicollinearity is orthogonalizing the explanatory variables (linearly transforming them so that the transformed variables are uncorrelated with each other): By the Frisch–Waugh–Lovell theorem, using projection matrices to make the explanatory variables orthogonal to each other will lead to the same results as running the regression with all non-orthogonal explanators included.

## Examples of contexts in which multicollinearity arises

### Survival analysis

Multicollinearity may represent a serious issue in survival analysis. The problem is that time-varying covariates may change their value over the time line of the study. A special procedure is recommended to assess the impact of multicollinearity on the results. See Van den Poel & Larivière (2004)[6] for a detailed discussion.

### Interest rates for different terms to maturity

In various situations it might be hypothesized that multiple interest rates of various terms to maturity all influence some economic decision, such as the amount of money or some other financial asset to hold, or the amount of fixed investment spending to engage in. In this case, including these various interest rates will in general create a substantial multicollinearity problem because interest rates tend to move together. If in fact each of the interest rates has its own separate effect on the dependent variable, it can be extremely difficult to separate out their effects.

Bob Jensen's threads on the differences between the science and pseudo science ---
http://www.cs.trinity.edu/~rjensen/temp/AccounticsDamn.htm#Pseudo-Science

Simpson's Paradox and Cross-Validation

Simpson's Paradox --- http://en.wikipedia.org/wiki/Simpson%27s_paradox

"Simpson’s Paradox: A Cautionary Tale in Advanced Analytics," by Steve Berman, Leandro DalleMule, Michael Greene, and John Lucker, Significance:  Statistics Making Sense, October 2012 ---
http://www.significancemagazine.org/details/webexclusive/2671151/Simpsons-Paradox-A-Cautionary-Tale-in-Advanced-Analytics.html

Analytics projects often present us with situations in which common sense tells us one thing, while the numbers seem to tell us something much different. Such situations are often opportunities to learn something new by taking a deeper look at the data. Failure to perform a sufficiently nuanced analysis, however, can lead to misunderstandings and decision traps. To illustrate this danger, we present several instances of Simpson’s Paradox in business and non-business environments. As we demonstrate below, statistical tests and analysis can be confounded by a simple misunderstanding of the data. Often taught in elementary probability classes, Simpson’s Paradox refers to situations in which a trend or relationship that is observed within multiple groups reverses when the groups are combined. Our first example describes how Simpson’s Paradox accounts for a highly surprising observation in a healthcare study. Our second example involves an apparent violation of the law of supply and demand: we describe a situation in which price changes seem to bear no relationship with quantity purchased. This counterintuitive relationship, however, disappears once we break the data into finer time periods. Our final example illustrates how a naive analysis of marginal profit improvements resulting from a price optimization project can potentially mislead senior business management, leading to incorrect conclusions and inappropriate decisions. Mathematically, Simpson’s Paradox is a fairly simple—if counterintuitive—arithmetic phenomenon. Yet its significance for business analytics is quite far-reaching. Simpson’s Paradox vividly illustrates why business analytics must not be viewed as a purely technical subject appropriate for mechanization or automation. Tacit knowledge, domain expertise, common sense, and above all critical thinking, are necessary if analytics projects are to reliably lead to appropriate evidence-based decision making.

The past several years have seen decision making in many areas of business steadily evolve from judgment-driven domains into scientific domains in which the analysis of data and careful consideration of evidence are more prominent than ever before. Additionally, mainstream books, movies, alternative media and newspapers have covered many topics describing how fact and metric driven analysis and subsequent action can exceed results previously achieved through less rigorous methods. This trend has been driven in part by the explosive growth of data availability resulting from Enterprise Resource Planning (ERP) and Customer Relationship Management (CRM) applications and the Internet and eCommerce more generally. There are estimates that predict that more data will be created in the next four years than in the history of the planet. For example, Wal-Mart handles over one million customer transactions every hour, feeding databases estimated at more than 2.5 petabytes in size - the equivalent of 167 times the books in the United States Library of Congress.

Additionally, computing power has increased exponentially over the past 30 years and this trend is expected to continue. In 1969, astronauts landed on the moon with a 32-kilobyte memory computer. Today, the average personal computer has more computing power than the entire U.S. space program at that time. Decoding the human genome took 10 years when it was first done in 2003; now the same task can be performed in a week or less. Finally, a large consumer credit card issuer crunched two years of data (73 billion transactions) in 13 minutes, which not long ago took over one month.

This explosion of data availability and the advances in computing power and processing tools and software have paved the way for statistical modeling to be at the front and center of decision making not just in business, but everywhere. Statistics is the means to interpret data and transform vast amounts of raw data into meaningful information.

However, paradoxes and fallacies lurk behind even elementary statistical exercises, with the important implication that exercises in business analytics can produce deceptive results if not performed properly. This point can be neatly illustrated by pointing to instances of Simpson’s Paradox. The phenomenon is named after Edward Simpson, who described it in a technical paper in the 1950s, though the prominent statisticians Karl Pearson and Udney Yule noticed the phenomenon over a century ago. Simpson’s Paradox, which regularly crops up in statistical research, business analytics, and public policy, is a prime example of why statistical analysis is useful as a corrective for the many ways in which humans intuit false patterns in complex datasets.

Simpson’s Paradox is in a sense an arithmetic trick: weighted averages can lead to reversals of meaningful relationships—i.e., a trend or relationship that is observed within each of several groups reverses when the groups are combined. Simpson’s Paradox can arise in any number of marketing and pricing scenarios; we present here case studies describing three such examples. These case studies serve as cautionary tales: there is no comprehensive mechanical way to detect or guard against instances of Simpson’s Paradox leading us astray. To be effective, analytics projects should be informed by both a nuanced understanding of statistical methodology as well as a pragmatic understanding of the business being analyzed.

The first case study, from the medical field, presents a surface indication on the effects of smoking that is at odds with common sense. Only when the data are viewed at a more refined level of analysis does one see the true effects of smoking on mortality. In the second case study, decreasing prices appear to be associated with decreasing sales and increasing prices appear to be associated with increasing sales. On the surface, this makes no sense. A fundamental tenet of economics is that of the demand curve: as the price of a good or service increases, consumers demand less of it. Simpson’s Paradox is responsible for an apparent—though illusory—violation of this fundamental law of economics. Our final case study shows how marginal improvements in profitability in each of the sales channels of a given manufacturer may result in an apparent marginal reduction in the overall profitability the business. This seemingly contradictory conclusion can also lead to serious decision traps if not properly understood.

Case Study 1: Are those warning labels really necessary?

We start with a simple example from the healthcare world. This example both illustrates the phenomenon and serves as a reminder that it can appear in any domain.

The data are taken from a 1996 follow-up study from Appleton, French, and Vanderpump on the effects of smoking. The follow-up catalogued women from the original study, categorizing based on the age groups in the original study, as well as whether the women were smokers or not. The study measured the deaths of smokers and non-smokers during the 20 year period.

Continued in article

What happened to cross-validation in accountics science research?

Over time I've become increasingly critical of the lack of validation in accountics science, and I've focused mainly upon lack of replication by independent researchers and lack of commentaries published in accountics science journals ---
http://www.trinity.edu/rjensen/TheoryTAR.htm

Another type of validation that seems to be on the decline in accountics science are the so-called cross-validations. Accountics scientists seem to be content with their statistical inference tests on Z-Scores, F-Tests, and correlation significance testing. Cross-validation seems to be less common, at least I'm having troubles finding examples of cross-validation. Cross-validation entails comparing sample findings with findings in holdout samples.

Cross Validation --- http://en.wikipedia.org/wiki/Cross-validation_%28statistics%29

When reading the following paper using logit regression to to predict audit firm changes, it struck me that this would've been an ideal candidate for the authors to have performed cross-validation using holdout samples.
"Audit Quality and Auditor Reputation: Evidence from Japan," by Douglas J. Skinner and Suraj Srinivasan, The Accounting Review, September 2012, Vol. 87, No. 5, pp. 1737-1765.

We study events surrounding ChuoAoyama's failed audit of Kanebo, a large Japanese cosmetics company whose management engaged in a massive accounting fraud. ChuoAoyama was PwC's Japanese affiliate and one of Japan's largest audit firms. In May 2006, the Japanese Financial Services Agency (FSA) suspended ChuoAoyama for two months for its role in the Kanebo fraud. This unprecedented action followed a series of events that seriously damaged ChuoAoyama's reputation. We use these events to provide evidence on the importance of auditors' reputation for quality in a setting where litigation plays essentially no role. Around one quarter of ChuoAoyama's clients defected from the firm after its suspension, consistent with the importance of reputation. Larger firms and those with greater growth options were more likely to leave, also consistent with the reputation argument.

Jensen Comment
Rather than just use statistical inference tests on logit model Z-statistics, it struck me that in statistics journals the referees might've requested cross-validation tests on holdout samples of firms that changed auditors and firms that did not change auditors.

I do find somewhat more frequent cross-validation studies in finance, particularly in the areas of discriminant analysis in bankruptcy prediction modes.

Instances of cross-validation in accounting research journals seem to have died out in the past 20 years. There are earlier examples of cross-validation in accounting research journals. Several examples are cited below:

"A field study examination of budgetary participation and locus of control," by  Peter Brownell, The Accounting Review, October 1982 ---
http://www.jstor.org/discover/10.2307/247411?uid=3739712&uid=2&uid=4&uid=3739256&sid=21101146090203

"Information choice and utilization in an experiment on default prediction," Abdel-Khalik and KM El-Sheshai - Journal of Accounting Research, 1980 ---
http://www.jstor.org/discover/10.2307/2490581?uid=3739712&uid=2&uid=4&uid=3739256&sid=21101146090203

"Accounting ratios and the prediction of failure: Some behavioral evidence," by Robert Libby, Journal of Accounting Research, Spring 1975 ---
http://www.jstor.org/discover/10.2307/2490653?uid=3739712&uid=2&uid=4&uid=3739256&sid=21101146090203

There are other examples of cross-validation in the 1970s and 1980s, particularly in bankruptcy prediction.

I have trouble finding illustrations of cross-validation in the accounting research literature in more recent years. Has the interest in cross-validating waned along with interest in validating accountics research? Or am I just being careless in my search for illustrations?

Simpson's Paradox and Cross-Validation

Simpson's Paradox --- http://en.wikipedia.org/wiki/Simpson%27s_paradox

"Simpson’s Paradox: A Cautionary Tale in Advanced Analytics," by Steve Berman, Leandro DalleMule, Michael Greene, and John Lucker, Significance:  Statistics Making Sense, October 2012 ---
http://www.significancemagazine.org/details/webexclusive/2671151/Simpsons-Paradox-A-Cautionary-Tale-in-Advanced-Analytics.html

Analytics projects often present us with situations in which common sense tells us one thing, while the numbers seem to tell us something much different. Such situations are often opportunities to learn something new by taking a deeper look at the data. Failure to perform a sufficiently nuanced analysis, however, can lead to misunderstandings and decision traps. To illustrate this danger, we present several instances of Simpson’s Paradox in business and non-business environments. As we demonstrate below, statistical tests and analysis can be confounded by a simple misunderstanding of the data. Often taught in elementary probability classes, Simpson’s Paradox refers to situations in which a trend or relationship that is observed within multiple groups reverses when the groups are combined. Our first example describes how Simpson’s Paradox accounts for a highly surprising observation in a healthcare study. Our second example involves an apparent violation of the law of supply and demand: we describe a situation in which price changes seem to bear no relationship with quantity purchased. This counterintuitive relationship, however, disappears once we break the data into finer time periods. Our final example illustrates how a naive analysis of marginal profit improvements resulting from a price optimization project can potentially mislead senior business management, leading to incorrect conclusions and inappropriate decisions. Mathematically, Simpson’s Paradox is a fairly simple—if counterintuitive—arithmetic phenomenon. Yet its significance for business analytics is quite far-reaching. Simpson’s Paradox vividly illustrates why business analytics must not be viewed as a purely technical subject appropriate for mechanization or automation. Tacit knowledge, domain expertise, common sense, and above all critical thinking, are necessary if analytics projects are to reliably lead to appropriate evidence-based decision making.

The past several years have seen decision making in many areas of business steadily evolve from judgment-driven domains into scientific domains in which the analysis of data and careful consideration of evidence are more prominent than ever before. Additionally, mainstream books, movies, alternative media and newspapers have covered many topics describing how fact and metric driven analysis and subsequent action can exceed results previously achieved through less rigorous methods. This trend has been driven in part by the explosive growth of data availability resulting from Enterprise Resource Planning (ERP) and Customer Relationship Management (CRM) applications and the Internet and eCommerce more generally. There are estimates that predict that more data will be created in the next four years than in the history of the planet. For example, Wal-Mart handles over one million customer transactions every hour, feeding databases estimated at more than 2.5 petabytes in size - the equivalent of 167 times the books in the United States Library of Congress.

Additionally, computing power has increased exponentially over the past 30 years and this trend is expected to continue. In 1969, astronauts landed on the moon with a 32-kilobyte memory computer. Today, the average personal computer has more computing power than the entire U.S. space program at that time. Decoding the human genome took 10 years when it was first done in 2003; now the same task can be performed in a week or less. Finally, a large consumer credit card issuer crunched two years of data (73 billion transactions) in 13 minutes, which not long ago took over one month.

This explosion of data availability and the advances in computing power and processing tools and software have paved the way for statistical modeling to be at the front and center of decision making not just in business, but everywhere. Statistics is the means to interpret data and transform vast amounts of raw data into meaningful information.

However, paradoxes and fallacies lurk behind even elementary statistical exercises, with the important implication that exercises in business analytics can produce deceptive results if not performed properly. This point can be neatly illustrated by pointing to instances of Simpson’s Paradox. The phenomenon is named after Edward Simpson, who described it in a technical paper in the 1950s, though the prominent statisticians Karl Pearson and Udney Yule noticed the phenomenon over a century ago. Simpson’s Paradox, which regularly crops up in statistical research, business analytics, and public policy, is a prime example of why statistical analysis is useful as a corrective for the many ways in which humans intuit false patterns in complex datasets.

Simpson’s Paradox is in a sense an arithmetic trick: weighted averages can lead to reversals of meaningful relationships—i.e., a trend or relationship that is observed within each of several groups reverses when the groups are combined. Simpson’s Paradox can arise in any number of marketing and pricing scenarios; we present here case studies describing three such examples. These case studies serve as cautionary tales: there is no comprehensive mechanical way to detect or guard against instances of Simpson’s Paradox leading us astray. To be effective, analytics projects should be informed by both a nuanced understanding of statistical methodology as well as a pragmatic understanding of the business being analyzed.

The first case study, from the medical field, presents a surface indication on the effects of smoking that is at odds with common sense. Only when the data are viewed at a more refined level of analysis does one see the true effects of smoking on mortality. In the second case study, decreasing prices appear to be associated with decreasing sales and increasing prices appear to be associated with increasing sales. On the surface, this makes no sense. A fundamental tenet of economics is that of the demand curve: as the price of a good or service increases, consumers demand less of it. Simpson’s Paradox is responsible for an apparent—though illusory—violation of this fundamental law of economics. Our final case study shows how marginal improvements in profitability in each of the sales channels of a given manufacturer may result in an apparent marginal reduction in the overall profitability the business. This seemingly contradictory conclusion can also lead to serious decision traps if not properly understood.

Case Study 1: Are those warning labels really necessary?

We start with a simple example from the healthcare world. This example both illustrates the phenomenon and serves as a reminder that it can appear in any domain.

The data are taken from a 1996 follow-up study from Appleton, French, and Vanderpump on the effects of smoking. The follow-up catalogued women from the original study, categorizing based on the age groups in the original study, as well as whether the women were smokers or not. The study measured the deaths of smokers and non-smokers during the 20 year period.

Continued in article

What happened to cross-validation in accountics science research?

Over time I've become increasingly critical of the lack of validation in accountics science, and I've focused mainly upon lack of replication by independent researchers and lack of commentaries published in accountics science journals ---
http://www.trinity.edu/rjensen/TheoryTAR.htm

Another type of validation that seems to be on the decline in accountics science are the so-called cross-validations. Accountics scientists seem to be content with their statistical inference tests on Z-Scores, F-Tests, and correlation significance testing. Cross-validation seems to be less common, at least I'm having troubles finding examples of cross-validation. Cross-validation entails comparing sample findings with findings in holdout samples.

Cross Validation --- http://en.wikipedia.org/wiki/Cross-validation_%28statistics%29

When reading the following paper using logit regression to to predict audit firm changes, it struck me that this would've been an ideal candidate for the authors to have performed cross-validation using holdout samples.
"Audit Quality and Auditor Reputation: Evidence from Japan," by Douglas J. Skinner and Suraj Srinivasan, The Accounting Review, September 2012, Vol. 87, No. 5, pp. 1737-1765.

We study events surrounding ChuoAoyama's failed audit of Kanebo, a large Japanese cosmetics company whose management engaged in a massive accounting fraud. ChuoAoyama was PwC's Japanese affiliate and one of Japan's largest audit firms. In May 2006, the Japanese Financial Services Agency (FSA) suspended ChuoAoyama for two months for its role in the Kanebo fraud. This unprecedented action followed a series of events that seriously damaged ChuoAoyama's reputation. We use these events to provide evidence on the importance of auditors' reputation for quality in a setting where litigation plays essentially no role. Around one quarter of ChuoAoyama's clients defected from the firm after its suspension, consistent with the importance of reputation. Larger firms and those with greater growth options were more likely to leave, also consistent with the reputation argument.

Jensen Comment
Rather than just use statistical inference tests on logit model Z-statistics, it struck me that in statistics journals the referees might've requested cross-validation tests on holdout samples of firms that changed auditors and firms that did not change auditors.

I do find somewhat more frequent cross-validation studies in finance, particularly in the areas of discriminant analysis in bankruptcy prediction modes.

Instances of cross-validation in accounting research journals seem to have died out in the past 20 years. There are earlier examples of cross-validation in accounting research journals. Several examples are cited below:

"A field study examination of budgetary participation and locus of control," by  Peter Brownell, The Accounting Review, October 1982 ---
http://www.jstor.org/discover/10.2307/247411?uid=3739712&uid=2&uid=4&uid=3739256&sid=21101146090203

"Information choice and utilization in an experiment on default prediction," Abdel-Khalik and KM El-Sheshai - Journal of Accounting Research, 1980 ---
http://www.jstor.org/discover/10.2307/2490581?uid=3739712&uid=2&uid=4&uid=3739256&sid=21101146090203

"Accounting ratios and the prediction of failure: Some behavioral evidence," by Robert Libby, Journal of Accounting Research, Spring 1975 ---
http://www.jstor.org/discover/10.2307/2490653?uid=3739712&uid=2&uid=4&uid=3739256&sid=21101146090203

There are other examples of cross-validation in the 1970s and 1980s, particularly in bankruptcy prediction.

I have trouble finding illustrations of cross-validation in the accounting research literature in more recent years. Has the interest in cross-validating waned along with interest in validating accountics research? Or am I just being careless in my search for illustrations?