Term
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Definition
| two-sample t-methods allow us to draw conclusions about the difference between the means of two independent groups; the two-sample methods make relatively few assumptions about the underling populations, so they are usually the method of choice for comparing two sample means; however the Student's t-models are onlyu approximations for their true sampling distribution; to make that approximation work well, the two-sample t-methods have a special rule for estimating degrees of freedom |
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Term
| Two-sample t-interval for the difference between means |
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Definition
| a confidence interval for the difference between the means of two independent groups found as (y1-y2) +/- t*df x SE(y1-y2) where SE(y1-y2) = sqrt(s1^2/n1 + s2^2/n2) and the degrees of freedom is given by a special formula |
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Term
| Two-sample t-test for the difference between means |
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Definition
| a hypothesis test for the difference between the means of two independent groups; it tests H0: m1-m2=0, where the hypothesized difference is almost always zero, using the statistic t(df) = ((y1-y2)-0)/SE(y1-y2) with the number of degrees of freedom given by the special formula |
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Term
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Definition
| data from two or more populations may sometimes be combined, or pooled, to estimate a statistic when we are willing to assume that the estimated value is the same in both populations; the resulting larger sample size may lead to an estimate with lower sample variance; however, pooled estimates are appropriate only when the required assumptions are true |
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Term
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Definition
| pooled t-methods provide inferences about the difference between the means of two independent populations under the assumption that both populations have the same standard deviation; when the assumption is justified, pooled-t methods generally produce slightly narrower confidence intervals and more powerful significance tests than two-sample t-methods; when the assumption is not justified, they generally produce worse results-sometimes substantially worse |
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