Imagine that you had sampled 1,000,000 females and 1,000,000 males to test whether or not females have a higher IQ than males. IQs are normally distributed with a mean of 100 and a standard deviation of 16. You are excited to find that females have an average IQ of 101 in your sample, while males have an IQ of 99. Does this difference seem important? Do you really need to carry out a t-test for differences in means to determine whether or not this difference is statistically significant? What does this result tell you about testing hypotheses when sample sizes are very large?

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The Answer of Imagine that you had sampled 1,000,000 females and 1,000,000 males to test whether or not females have a higher IQ than males. IQs are normally distributed with a mean of 100 and a standard deviation of 16. You are excited to find that females have an average IQ of 101 in your sample, while males have an IQ of 99. Does this difference seem important? Do you really need to carry out a t-test for differences in means to determine whether or not this difference is statistically significant? What does this result tell you about testing hypotheses when sample sizes are very large?

Imagine That You Had Sampled 1,000,000 Females and 1,000,000 Males