If the sample size is less than 30, you can still use the t-test for two independent samples, provided the data is approximately normally distributed and the variances between the groups are equal (homogeneity of variance). If these assumptions are not met, consider using a non-parametric test like the Mann-Whitney U test.

The argument has been made that you should use Welch's t-test routinely, instead of Student's t-test. And not need to worry about the homogeneity of variance. You can read up on this and decide for yourself.

Daniyel Yaacov Bilar , I'm not sure I can endorse this recipe book. I'll just make a few comments.

• What's the difference between Recipe 1 and Recipe 2 ? They look basically the same. There are some differences, but I don't know if the differences between the two are omissions or if there's some point to the differences.
• There's nothing magical about a sample size of 30. No decision should be made based on whether the sample size is greater than 30 or not.
• It's a bad idea to test model assumptions with hypothesis tests like Levene's, Shapiro-Wilk, and so on.
• The nonparametric tests you mention test a different hypothesis than a t-test. One isn't a substitute for the other. It's better for the analyst to decide what hypothesis they actually want to test, and then figure the best way to do this, rather than have their data dictate what hypothesis they test.

IYH Dear Sal Mangiafico

Thank you for your questions. Thinking it through: This type of cookbook is not the appropriate way to approach the question (I made a bunch of assumptions about the original question and questioner).

Re difference between Recipe 1 and Recipe 2: Recipe 1 for sample sizes ≥ 30, where as a rough rule of thumb the Central Limit Theorem (CLT) justifies assumption of normality for the sampling distribution (see eg https://researchdatapod.com/understanding-central-limit-theorem-clt-practical-examples/). Recipe 2 emphasizes *caution* when assuming normality and HOV, as the CLT's guarantees are weaker.

You are right: The researcher's understanding of their data's characteristics, using EDA and the study's context rather than a sample size cutoff, as well as aligning the statistical test with the research hypothesis, rather than just finding a substitute test, is the correct way to go.

I'll edit my answer to reflect this.