[tpoacher]

> the larger the group, the less likely the group is to be atypical.

Not true (unless I misunderstood what you were trying too say). The probability that a sample will be atypical under the null is exactly the significance level, and does not depend on its size.

What does change with size is that the distribution around the statistic gets more concentrated, meaning your threshold moves to the left, towards lower effect sizes.

Which also means that for smaller sample sizes, it is harder to reach significance, unless you're dealing with a fairly large effect size.