STATS FINAL NOTES

# STATS FINAL NOTES - Two-sample t methods- Allow us to draw...

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Two-sample t methods- Allow us to draw conclusions about the difference between the means of 2 independent groups. The two-sample methods make relatively few assumptions about the underlying populations, so they are usually the method of choice for comparing two sample means. However, the Student’s t-models are only 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. Two-sample t-interval for the difference between means - A confidence interval for the difference between the means of two independent groups found as WHERE, And the number of degrees of freedom is given by a special formula. Two-sample t-test for the difference between means - Is a hypothesis test for the difference between the means of two independent groups. It tests the null Hypothesis: H o : μ 1 - μ 2 = Δ 0 , Where the hypothesized difference , Δ 0 , is almost always 0 , using the statistic With the number of degrees of freedom given by the special formula. Pooling- Data from two or more populations may sometimes be combined, or pooled, to estimate a statistic (typically a pooled variance) 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. 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. *Pooled t-intervals- A confidence interval for the difference between the means of two independent groups used when we are willing and able to make the additional assumption that the variances of the groups are equal where, the pooled variance is and the number of degrees of freedom is (n 1 – 1) + (n 2 –1) *Pooled t-test – A hypothesis test for the difference in the means of two independent groups when we are willing and able to assume that the variances of the groups are equal. IT TESTS THE NULL HYPOTHESIS H o : μ 1 - μ 2 = Δ 0 , where the hypothesized difference, Δ 0, is almost always 0, using the statistic where the pooled standard error is defined as for the pooled interval and the degrees of freedom is (n 1 – 1) + (n 2 1) Paired Data Data are paired when the observations are collected in pairs or the observations in one group are naturally related to observation sin the other. The simplest form of pariing is to measure each subject twice- often before and after a

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## This note was uploaded on 05/10/2008 for the course ILRST 2100 taught by Professor Vellemanp during the Spring '07 term at Cornell University (Engineering School).

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STATS FINAL NOTES - Two-sample t methods- Allow us to draw...

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