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If you have 3 means that need to be compared, you should not simply do multiple t-tests because ________.

a. it's too time consuming.
b. the joint alpha level decreases.
c. you inflate the experiment wise alpha.
d. you will be forever shunned by statiscians.

1 Answer

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c. You inflate the experiment-wise alpha.

If you have 3 means that need to be compared, you should not simply do multiple t-tests because you will inflate the experiment-wise alpha. The experiment-wise alpha is the probability of making a Type I error (rejecting a true null hypothesis) in any of the tests in the series. When multiple t-tests are conducted, the overall chance of making a Type I error increases with the number of comparisons. This is called the problem of multiple comparisons or the family-wise error rate problem.

To control for this problem, you need to use multiple comparison procedures that adjust the alpha level for the number of comparisons being made, such as the Bonferroni correction, Tukey's HSD (honestly significant difference) test, or the Scheffe test. These procedures reduce the risk of making a Type I error and increase the chance of detecting true differences among the means.
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