# Class_14 - Testing Hypotheses about Differences among...

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Testing Hypotheses about Testing Hypotheses about Differences among Differences among Several Means Several Means

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The t-test compares independent means TWO AT A TIME . Whenever we encounter a research situation in which we need to compare THREE or MORE independent-sample means, we would have to make multiple t-tests. This is clear from the numerator of the t-test: ( 29 ( 29 1 2 ˆ 1 2 1 2 Y Y Y Y t - - - - = σ μ μ
Statistically, this is undesirable. Recall that each t-test is conducted with a chance of incorrectly rejecting the null hypothesis. The magnitude of this chance is determined when we decide upon an alpha level. With alpha set at 0.05 , there is a 5 percent chance of committing a Type I error each time we perform a t-test. When we perform 100 t-tests , we will INCORRECTLY reject the null hypothesis 5 times . Clearly, the chance of error increases in proportion to the number of t-tests we make.

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That is, each student's score could be predicted by knowing the value of μ (the average exam performance of all PPD 404 students in general) plus knowing how students differ from one another in every respect except their instructor.
α would NOT equal 0.0, and our prediction would need

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In performing an analysis of variance, we do not test the differences among means directly. Instead, we make two different estimates of the
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• Fall '07
• Velez

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