UASTAT151Ch14 - 14.1 Comparing Several Means Use t-tools NO...

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14.1 Comparing Several Means Use t -tools? NO! Æ Reason? Compound uncertainty - In any test, there is uncertainty such that we reject H 0 when it’s true, or Type I error. By comparing multiple means and using ONE t -test for each pair, the “overall” Type I error will compound. - For example, consider 3 means that are equal and each t -test uses α = 0.05. Thus, there’s a 5% chance to show a difference when there isn’t (recall H 0 assumes no diff.). The chance of detecting at least one difference among the three means is roughly 1 – 0.95 3 = 0.143 or 14.3% when the means are EQUAL! (Note: 14.3% is the “overall” Type I error.) - For 5 means, the “overall” Type I error becomes approximately 40%. Def’n: ANalysis Of VAriance (ANOVA) is a procedure to test the equality of three or more population means. NOTE: the name of the test refers to comparing different sources of variability; it WILL test differences among means. Test requires the following assumptions: 1. The populations are all normally distributed.
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