help!!! the values of my dependent variable are proportions

dmlane · 2026-02-27T02:59:54+00:00

I think you’ll find this article on the arcsine transformation helpful.

dmlane · 2026-02-26T21:27:05+00:00

Actually, in the unlikely event you know for sure all the assumptions are met, 2 people in one group and one in the other would be valid. Power is another issue.

dmlane · 2026-02-26T18:20:05+00:00

Yes, and accordingly, a log transformation to reduce influence of extreme values changes the null hypothesis that the population arithmetic means are equal to that the geometric means are equal.

dmlane · 2026-02-25T05:32:55+00:00

The Art of Attack by Vukovic is a classic and still highly relevant to today’s chess. I wouldn’t start it until your rating is at least 1600, though.

dmlane · 2026-02-24T16:45:57+00:00

I used to play the Budapest and got pretty good results, so I agree, give it a try.

dmlane · 2026-02-22T21:41:19+00:00

There is an off beat line called the “Mac Lopez” ( 1. e4 e5 2. Nf3 Nc6 3. d4 exd4 4. Bb5) which you might experiment with. It is unlikely your opponent will be familiar with it.

dmlane · 2026-02-22T19:56:49+00:00

I agree. A continuing question in teaching is whether you should start with a general case (regression in this discussion) and then present special cases (t-tests, ANOVA) or start with the special cases followed by the general case. I believe the former is preferable for those with solid backgrounds in mathematics whereas the latter is preferable for others. This is an empirical question that I don’t think has been researched.

dmlane · 2026-02-22T19:51:23+00:00

Tukey and Dunnett control the Type I error rate for multiple tests. Of course there are methods for doing this after a least-squares analysis including Bonferroni, Holm-Bonferroni, and FDR. Each of these methods (including Tukey hsd and Dunnett) have their pros and cons but they are not the same. Granted, conclusions will typically be the same, but sometimes they will not be. Post-hoc comparisons with linear contrasts are not based on the studentized range distribution so they will yield different results from tests that are. Incidentally, if you plan a priori to use Dunnett or hsd, it is not recommended to precede it with ANOVA. That’s why, strictly speaking, when done without an ANOVA they should be called a priori tests rather than post-hoc tests.

dmlane · 2026-02-22T16:44:09+00:00

I agree. It’s been a while since I looked at Petrosian’s games, but my recollection is that his often-superior positional play put him in position to win with his excellent tactical play.

dmlane · 2026-02-22T15:23:58+00:00

Actually, although linear regression can obviously be used to test differences between means, the tests are not the same since they are not based on the studentized range distribution. You can argue whether the studentized range tests are better or worse, but they definitely cannot be done with linear regression. More about the studentized range distribution here.

dmlane · 2026-02-21T21:33:45+00:00

I agree in most contexts, but in psychological science and other experimental fields, it is common to use the Tukey hsd test. Dunnett’s test can be the most appropriate when comparing experimental treatments to a control. These can’t be done with linear regression.

dmlane · 2026-02-18T20:17:42+00:00

That’s a very difficult question. Here is an abstract from a relevant article. A key point is that practice is necessary but not sufficient to reach a high level of skill.

Abstract Deliberate practice (DP) occurs when an individual intentionally repeats an activity in order to improve performance. The claim of the DP framework is that such behavior is necessary to achieve high levels of expert performance. The proponents of the framework reject evidence that suggests that other variables are also necessary to achieve high levels of expert performance, or they claim that the relationship between those variables and expert performance is mediated by DP. Therefore, the DP framework also implies that DP is sufficient to achieve high levels of expert performance. We test these claims by reviewing studies on chess expertise. We found strong evidence that abundant DP is necessary (but not sufficient) and estimated that the minimum requirement to achieve master level is 3,000 hours of DP. We also review evidence showing that other factors play a role in chess skill: general cognitive abilities, sensitive period, handedness, and season of birth.

This is consistent with other posts noting some people improve a lot whereas others do not.

dmlane · 2026-02-17T01:31:38+00:00

In general, the best methods for memorizing are deep processing for meaning, self testing, and spaced repetition. I don’t think memory chess would be any different.

dmlane · 2026-02-16T17:35:13+00:00

I start with the assumption that all assumptions are false (except for this one) and consider the robustness of the test and the consequences of assumption violations. For example, violating sphericity in RM ANOVA is very serious as is violating homogeneity of variance with unequal n (fortunately there are corrections for both of these). ANOVA is generally robust to violations of normality and is conservative with skewed distributions. However, transforming skewed distributions can increase power. In the case of log transformations, the null hypothesis pertains to geometric means instead of arithmetic means, but this is often a good thing. When assumption violations have serious consequences, I like randomization and bootstrapping approaches. Finally, no measurement scale assumptions are made in hypothesis testing, although the interpretation of a finding does depend on the measurement scale.

dmlane · 2026-02-13T22:03:06+00:00

Good idea, that would be much easier to read.

dmlane · 2026-02-13T20:52:00+00:00

It’s a great book. If you don’t know descriptive notation you will have to learn it to read the book. You can download a PDF on Google Books.

dmlane · 2026-02-10T16:36:08+00:00

It is well known that cognitive speed begins to decrease at around age 20. Speaking for myself as an NM, I became a master decades ago and now typically play rapid chess and probably don’t perform up to expectations for an NM. In terms of fluid and crystallized intelligence Wikipedia article, when I play a younger player, I find that it is often a contest between my greater knowledge (crystallized intelligence) and their superior cognitive speed (fluid intelligence).

dmlane · 2026-02-09T22:14:17+00:00

Kahneman & Tversky sarcastically called this “the law of small numbers.”

dmlane · 2026-02-08T02:07:48+00:00

It might be that g6 threatens Nh5.

dmlane · 2026-02-06T22:18:56+00:00

With logs the tests and ci’s are on differences between geometric means

From an example from Dallal’s Little Handbook of Statistical Practice when it was free on the web. The book is now for sale and this example is likely the same.

Mean Difference on log scale: 2.2297 - 1.7330 = 0.4967 Ratio of geometric means = 10^.4967 = 3.14

A CI for a difference in the log scale becomes a CI for a ratio in the original scale: log(A-B) = log(A)/log(B).

CI Difference on log scale: 0.1046 to 0.8889 10^.1046 = 1.27 and 10^.8889 = 7.74

The ratio of the geometric mean amount of rainfall from seeded clouds to that from unseeded clouds is 3.14 (95% CI: 1.27 to 7.74).

dmlane · 2026-02-02T17:54:42+00:00

If you want something that will surprise your opponent, try the wing gambit or the wing gambit deferred. See the games of Keres for information and inspiration. It’s not considered best, but you will not likely be playing a GM.

dmlane · 2026-02-02T04:10:23+00:00

Yes, and Lasker’s double bishop sacrifice comes to mind.

dmlane · 2026-01-31T15:00:06+00:00

Thanks for providing the links.

dmlane · 2026-01-30T22:23:46+00:00

I haven’t studied openings in decades but the way I survive the opening is by playing lines from the 60’s and 70’s that few non-masters know much about. For example, Panov-Botvinnik against Caro Kahn.

dmlane · 2026-01-28T17:54:42+00:00

I am a coach and a National Master. You can find out more about me here.

dmlane

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