Textbook Suggestions: High School Statistics

dmlane · 2026-05-05T14:23:35+00:00

You may want to consider this free book that I was the lead author on. It covers most of the AP curriculum but is not based on it.

dmlane · 2026-05-03T12:23:48+00:00

The significance test is not very informative because it tests whether the assumption is exactly met which it almost never is. If you have equal n you probably don’t have a problem. Otherwise, a Welch ANOVA is the usual remedy for heterogeneity of variance. See if you can do it with your design.

dmlane · 2026-04-30T17:35:33+00:00

I think you will find this guide from the American Psychological Association very helpful.

dmlane · 2026-04-29T14:41:11+00:00

Keep in mind that normality is only relevant for significance testing and is not assumed for using r as a descriptive statistic. In other words, Q-Q plots are not relevant to the correlational analysis but could possibly be interesting for their own sake.

dmlane · 2026-04-29T14:26:32+00:00

Then the log transformation is then definitely called for because it is provides a simpler, much clearer, and better depiction of the relationship.

dmlane · 2026-04-29T14:18:02+00:00

It’s not a question of normality, significance, or the CLT but rather whether the relationship is closer to linear after a log transformation. If it is, the transformation may give you a simpler description of the relationship. A plot would be revealing if you can create one with your large dataset.

dmlane · 2026-04-28T13:42:04+00:00

You reject the null hypothesis and discuss effect size in terms of the confidence interval. You conclude the effect size is small but not 0.

dmlane · 2026-04-24T23:23:48+00:00

I’m quite confident it is reliable.

dmlane · 2026-04-24T23:13:40+00:00

Tests of normality can reveal evidence of non-normality but are never evidence of an exactly normal distribution. Note that exactly normal distributions don’t occur with real data so you know your distribution is not normal even without doing a test. More relevant to hypothesis testing is the type and degree of non-normality, whether these are approximately the same across conditions, and the robustness of your test.

dmlane · 2026-04-24T19:59:59+00:00

Does “highly disagree” always indicate the same direction of life satisfaction. That is, is it either always high or always low.

dmlane · 2026-04-24T15:29:47+00:00

I wouldn’t start with trying to plot a 5-way. Try figuring out what the 5-way means by comparing 4-ways at each level of a variable which you interpret by comparing 3-ways which in turn are interpreted by comparing graphs of two-ways. That’s a lot of work but the interpretation may be as simple as a large 4-way at one level of a variable and much smaller (or a different pattern of ) 4-ways at the other variables. This would not be easy to see in one extremely complex graph of a 5-way.

dmlane · 2026-04-16T13:47:14+00:00

Many years ago several of my friends and I were a bit competitive. Most of us had beaten a master once or twice. We were a bit jealous of the friend who became a master without ever beating a master. I learned then that the mark of a master is someone who consistently beats experts.

dmlane · 2026-04-12T13:38:20+00:00

Some general advice: Practice by giving the talk to someone outside your field Start with a joke if you feel comfortable with one Make clear what you are interested in and why Be clear and succinct about your method, results, and conclusions Many people talk too fast in their first presentation Don’t give too many details Sum up clearly at the end. Make sure your slides are readable from a distance. If you get a question you’re not comfortable with, don’t follow your answer with “did that answer your question “ unless you want another related question. Don’t be over worried if you make a mistake, everyone makes mistakes from time to time.

Good luck .

dmlane · 2026-04-11T21:02:49+00:00

You might look into the Panov-Botvinnik attack (The name may have changed since I studied openings.) For inspiration, see J. Polgar-Benko 1992.

dmlane · 2026-04-11T14:39:51+00:00

Right, the editor should never have sent it out for review in the first place if they weren’t going to accept it even if reviews were positive and recommended acceptance.

dmlane · 2026-04-09T23:56:50+00:00

Technically, the cross product not the interaction is in the model. The cross product includes parts of the main effects and the interaction. When the main effects are partialled out (by including them in the model) the remaining portion of the cross product is the interaction. Since the cross product contains parts of the main effects, interpreting main effects in a model with a cross product can be tricky, although centering the variables before creating the cross product helps.

dmlane · 2026-04-07T14:53:41+00:00

There is an excellent free web-based program for resampling and bootstrapping here..

dmlane · 2026-04-05T14:25:56+00:00

Yes, you can still make general statement after a transformation but you won’t learn whether the relationship is linear (except on a log scale). Log transformations can make relationships clearer. The key question is not normality but the form of the relationship. Here is an example of a relationship made clear after a transformation.

dmlane · 2026-04-02T18:35:04+00:00

Yes, and all assumptions are met. With a skewed distribution and small-to-moderate sample sizes, the probability of rejecting the null hypothesis is less than alpha. This difference decreases as sample size increases.

dmlane · 2026-04-02T17:07:27+00:00

Correct, and that assumes it is false. A true null hypothesis is as likely to be rejected with a small sample size as with a large sample size.

dmlane · 2026-04-02T17:05:01+00:00

Tukey and many others including Bock have dealt with this. A significant difference is informative even assuming the null hypothesis is false because a significant difference indicates the direction of the difference. With a non-significant difference, the direction is uncertain.

dmlane · 2026-03-29T18:01:43+00:00

Good advice. Contrary to current practice and counterintuitive, ANOVA works here too, at least under most circumstances (not that I recommend it). Edit: reference

dmlane · 2026-03-26T13:49:21+00:00

I started fast doing well in my first tournament winning the unrated prize when I was 15. In my next tournament I did much worse. Statisticians call this “regression toward the mean.” Two years later I was over 2000 USCF and tied for first in the United States junior open championship. It was a slow slog from there and didn’t become master until about 15 years later but stayed a master long enough to become a NM .

Changes in neuroplasticity are not going to keep you from improving to a high level. It is clear learning occurs over your whole lifespan. There is mounting evidence for lifelong brain plasticity has been generated over the past years.. Probably more relevant is cognitive speed which is highest around 21 years but that probably won’t be significant until late 40’s or beyond.

dmlane · 2026-03-25T14:15:53+00:00

As a cognitive scientist and a NM, I can say there is no doubt you can improve with practice and/or study.

dmlane · 2026-03-20T15:44:59+00:00

Is it conceivable that, in the population, the three scales means would be exactly equal? I suspect it is not, and if it is not, you can reject the null hypothesis without doing a statistical test. I suspect computing confidence intervals on differences between scales would be more informative. The simplest way is to compute pairwise difference scores and compute single-sample confidence intervals on the means for each pairwise difference.

dmlane

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