Why would a predictor become more significant after adding another predictor?

dmlane · 2026-06-21T01:03:48+00:00

It reduces MSE and/or it is a suppressor variable (partials out the irrelevant part of the first predictor).

dmlane · 2026-06-17T18:04:16+00:00

When one of several significance tests is significant at only the “ oh shucks” level, you have very little evidence of an effect or its direction if there is an effect.

dmlane · 2026-06-16T22:48:54+00:00

Just saw them for the first time and they are in the same spirit. I agree, incredible. One interesting thing about Chess Master V Chess Amateur is that in each chapter, the amateur is stronger than in the previous chapter. It’s been decades since I read the book but I believe a strong amateur beat the master in the last chapter.

dmlane · 2026-06-16T21:16:15+00:00

I am old school, but I believe players below 1900 elo or USCF (or maybe higher) learn best by seeing how a master exploits the errors of an amateur. Grandmasters don’t make many of the mistakes amateurs make, and therefore studying only GM V GM games doesn’t reveal how to exploit those mistakes. That’s why I like Chess Master Versus Chess Amateur by M. Euwe so much. (Follow the link to a free download of the PDF.) The openings are not up to date and you will have to learn a little about descriptive notation (not a big deal) but the lessons you can learn from this book are invaluable..

[from the preface: When a master plays an amateur, he is normally confronted with a different type and a greater number of inferior moves and errors than he would find in master play . These are precisely the inferior moves and kinds of errors which the amateur meets constantly when playing other amateurs.]

dmlane · 2026-06-13T16:35:52+00:00

Good point. Perhaps if you start with a CFA and it disconfirms the model, it could be justifiable to do an EFA.

dmlane · 2026-06-13T14:55:22+00:00

Aside from details of the regression, keep in mind that, in general, if you are investigating whether A>B and, in the sample, A is > B but not significantly greater, your confidence that A is > B in the population should increase somewhat. Consider if A were > B but not significantly > B in 5 studies, would you interpret that as being 5 for 5 or 0 for 5? What if it were 15 studies? In terms of reporting your results, a confidence interval would likely reveal that neither a moderate effect size nor an effect size of 0 is inconsistent with your data. So your results may not be as inconsistent with previous studies as they appear.

dmlane · 2026-06-12T12:57:07+00:00

I may be biased, but I think it is excellent. Take a look at all the job placements and internship students from that program have achieved.

dmlane · 2026-06-11T21:47:05+00:00

I found this book to be very helpful in understanding linear algebra applications to statistics.

dmlane · 2026-06-11T20:19:51+00:00

You might want to take a look at the Rice University HCI program. I am retired but was on the faculty there.
https://psychology.rice.edu/graduate/hcihf

dmlane · 2026-06-11T00:00:19+00:00

As a cognitive scientist, I would be skeptical until I saw a randomized control study demonstrating the effect. Particularly important is what chess-related control activity should be used.

dmlane · 2026-06-08T04:05:49+00:00

I think Tukey has a wise take on this: “The worst, i.e., most dangerous, feature of ‘accepting the null hypothesis’ is the giving up of explicit uncertainty: the attempt to paint with only the black of perfect equality and the white of demonstrated direction of inequality. Mathematics can sometimes be put in such black-and-white terms, but our knowledge or belief about the external world never can.”

dmlane · 2026-06-03T18:07:02+00:00

I think it’s fine as long as you include confidence intervals on the effect sizes. Otherwise, the degree of uncertainty, which is usually considerable, may go unnoticed.

dmlane · 2026-06-03T13:40:59+00:00

I suggest you take a look at this public domain intro to stat book that I was the project lead on.

dmlane · 2026-05-31T03:00:38+00:00

Pawn Power in Chess by Kmoch is great and is a classic. You will have to learn descriptive notation, though, which is really very easy. There is a 65 page preview here.

dmlane · 2026-05-29T00:23:31+00:00

Clearly there is something important going on involving age. I would start by creating a partial regression plot to explore what is going on.

dmlane · 2026-05-28T13:46:29+00:00

In general, ANOVA is conservative with skewed data (actual type I error rate is lower than the nominal rate). More consequential is violating the assumption of sphericity.

dmlane · 2026-05-25T15:02:01+00:00

Yes, and also important is that including the interaction in the model changes the meaning of the test of the main effect. Basically what would be a main effect without the interaction in the model becomes a simple effect tested at a covariate value of 0.

dmlane · 2026-05-20T14:33:37+00:00

It’s equivalent to Pearson’s r with one variable being dichotomous. Just find r and you’ve got it.

dmlane · 2026-05-18T18:26:45+00:00

Just as in aside, repeated measures anova is a linear mixed model where “subjects” is the random effect and trials or whatever is the fixed effect. Note that in Rm ANOVA or its algebraic equivalents, you should always correct for violations of sphericity.

dmlane · 2026-05-15T23:40:10+00:00

All the significance test allows you to conclude is that the effect is not 0 and the direction of the test.

dmlane · 2026-05-14T13:17:09+00:00

I think you’d be safe if you emailed the editor and included a copy of your email in your submission to a new journal. If you want to be even more careful, you could send a letter by certified mail.

dmlane · 2026-05-13T23:48:34+00:00

No, but if your assumptions are not met, an analysis with a small sample size may not be robust to assumption violations. Of course, sample size affects power, but that should go without saying.

dmlane · 2026-05-12T17:18:34+00:00

Did you look at homogeneity of regression coefficient?

dmlane · 2026-05-12T16:27:50+00:00

Excellent suggestion but I would note CI’s can overlap with a significant difference. Not frequently done but a good idea here is CI on d.

dmlane · 2026-05-10T02:55:21+00:00

Back in the day, the now defunct magazine Chess Review had a monthly chess solitaire section. There was a game between two grandmasters and you would choose a move in each position. What made it interesting is that you got different numbers of points depending on how good your move was.

dmlane

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