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I saw a discussion about positive kurtosis at this question

It does not discuss negative kurtosis for parametric tests and I was wondering what the implications are of negative kurtosis on the statistics such as the t statistic. When searching for an answer, often it is mentioned somewhere in the line of 'it is required because your analysis depends on normality', but I find it difficult to see the implication when not true such as with negative kurtosis. The explanations and examples given at the question mentioned above were very insightful.

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High kurtosis indicates outlier potential, which reduces power greatly. Low kurtosis indicates the opposite, so that power should be fine, perhaps better than under normality even. There can be problems with Type I error rates, but the CLT should help here. So low kurtosis situations are not usually a problem.

But the best way to answer this kind of question is with a simulation study. Simulate data from low kurtosis distributions. Find the empirical power and empirical type I error rates. Compare those with simulations of data from (i) normal distributions and (ii) distributions with high kurtosis. Write a report. Share it with the world!

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