Statistical Sciences 1024A/B Chapter 21: Chapter 21 - Comparing Two Means

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Western University
Statistical Sciences
Statistical Sciences 1024A/B
Lori Murray

March 23, 2017 Chapter 21: Comparing Two Means 21.1 TwoSample Problems Comparing two populations or two treatments is one of the most common situations encountered in statistical practice. We call such situations twosample problems. 21.2 Comparing Two Population Means Conditions: We have two independent simple random samples (SRS) from two distinct populations Both populations are Normally distributed with unknown means and standard deviations. In practice, it is enough that the distributions have similar shapes and that the data have no strong outliers 1s the mean of the first population 2s the mean of the second population We want to make inferences about and 1or 2 1 2 21.3 TwoSample t Procedures The twosample t statistic is: The t statistic has a t distribution but with what degrees of freedom? Option 1 o Use software. Note that the degrees of freedom may not be a whole number Option 2 o Without software, use the smaller of (n 1). This is the conservatice approach. 1 The twosample confidence interval for 1 is:2 The choice of the minimum of (n 11 and (n 12 as degrees of freedom to determine t* will result in a wider confidence interval than the exactcorrect degrees of freedom (option 1) 21.5 Robustness Again The twosample statistic is the most robust (less sensitive to departures from out conditions for inference for comparing two means) when both sample sizes are equal and both sample distributions are similar. But even when we deviate from this, twosample tests tend to remain quite robust. As a guideline, a combined sample size (n + 1 ) 2f 40 or more will allow you to work even with the most skewed distributions
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