Comparing Two Means or Two Proportions比较两个或两个比例.ppt

Sociology 601 Class 8: September 24, 2009 6.6: Small-sample inference for a proportion 7.1: Large sample comparisons for two independent sample means. 7.2: Difference between two large sample proportions. * 7.1 Large sample comparisons for two independent means So far, we have been making estimates and inferences about a single sample statistic Now, we will begin making estimates and inferences for two sample statistics at once. many real-life problems involve such comparisons two-group problems often serve as a starting point for more involved statistics, as we shall see in this class. * Independent and dependent samples Two independent random samples: Two subsamples, each with a mean score for some other variable example: Comparisons of work hours by race or sex example: Comparison of earnings by marital status Two dependent random samples: Two observations are being compared for each “unit” in the sample example: before-and-after measurements of the same person at two time points example: earnings before and after marriage husband-wife differences * Comparison of two large-sample means for independent groups Hypothesis testing as we have done it so far: Test statistic: z = (Ybar - ?o) / (s /SQRT(n)) What can we do when we make inferences about a difference between population means (?2 - ?1)? Treat one sample mean as if it were ?o ? (NO: too much type I error) Calculate a confidence interval for each sample mean and see if they overlap? (NO: too much type II error) * Figuring out a test statistic for a comparison of two means Is Y2 –Y1an appropriate way to evaluate ?2 - ?1? Answer: Yes. We can appropriately define (?2 - ?1) as a parameter of interest and estimate it in an unbiased way with (Y2 – Y1) just as we would estimate ? with Y. This line of argument may seem trivial, but it becomes important when we work with variance and standard deviations. * Figuring out a standard error for a comparison of two means Comparing standard errors: AF 21