Student's T-Test Good Enough For Beer T-shirt

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Beer and statistics. It’s a beautiful combination. What could be better? (How ’bout some hot wings to go with it?)

This fun design makes a fantastic gift for statisticians, data scientists, op-ex professionals, industrial engineers, and six sigma black belts.

It depicts a serious William Sealy Gosset, aka Student, raising a glass of his statistically controlled Guinness stout, toasting the t-test and the t-distribution which he discovered while seeking a method for testing small samples.

#IYKYK

If you don’t know, there’s a long-simmering debate in statistics that comes down to this: Is the t-test robust enough for non-normal distributions?

A non-parametric test bearing the names of Henry Mann and Don Whitney, and occasionally Frank Wilcoxon, is often suggested for use when comparing non-normal datasets. It tests the medians of two independent variables for significant difference. It’s typically called the Mann-Whitney U test, but sometimes stated as the Wilcoxon rank-sum test. Anyhow, the claim is that this test is appropriate when the datasets do not “meet the assumptions of normality required by the t-test.”

The opposing claim is that the normality assumption can often be ignored thanks to the central limit theorem (CTL). Take this quote from Thomas Pyzdek: “…after teaching that normality should be tested, I tell my students that departures from normality can often be handled by ignoring them, if they are not too great.”

Here’s The Stat’s Geek: “Provided our sample size isn’t too small, we shouldn’t be overly concerned if our data appear to violate the normal assumption. Also, for the same reasons, the 95% confidence interval for the difference in group means will have correct coverage, even when X is not normal (again, when the sample size is sufficiently large). Of course, for small samples, or highly skewed distributions, the above asymptotic result may not give a very good approximation, and so the type 1 error rate may deviate from the nominal 5% level.” … And thus in small samples (n < 30) we may need to turn to non-parametric tests.

Here’s a thread of comments from that The Stats Geek article:

“This website’s description and explanation of the ‘normality assumption’ of t-tests (and by extension to ANOVA and MANOVA and regression) is simply incorrect. Parametric tests do not assume normality of sample scores nor even of the underlying population of scores from which samples scores are taken. …”

“[Commenter] is right, here. The t-test doesn’t assume normality. Only in small samples are non-parametric tests necessary.”

“Y’all are both wrong and the author is right. in support of your criticism you mention the central limit theorem, but the central limit theorem shows that (under certain conditions) sample means converge in distribution to a NORMAL distribution. they do not converge to a T-DISTRIBUTION.”

It’s a hot debate. Perhaps it can be tempered with a couple cold Guinness pints.

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Our comfy t-shirts are soft and lightweight with the right amount of stretch.

• 100% combed and ring-spun cotton (Heather colors contain polyester)
• Fabric weight: 4.2 oz./yd.² (142 g/m²)
• Pre-shrunk fabric
• Side-seamed construction
• Shoulder-to-shoulder taping
• Blank product sourced from Nicaragua, Mexico, Honduras, or the US

This product is made especially for you as soon as you place an order, which is why it takes us a bit longer to deliver it to you. Making products on demand instead of in bulk helps reduce overproduction, so thank you for making thoughtful purchasing decisions!

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