STAT 100 Lecture 19: Inference Independent Two Sample Means
University of Maryland
Statistics and Probability
Week 15 Lecture 19 May 1st, 2017 Inference Independent Two Sample Means TwoSample Problems The goal of inference is to compare the responses of two treatments or to compare the characteristics of two populations. We have a separate sample from each treatment or each population. Individuals for one sample have no inuence upon which individuals are selected for a second sample. Each sample is separate. The units are not matched, and the samples can be of differing sizes. Comparing Two Population Means One of the most common goal in inference of two populations is to compare the average or typical responses in the two populations. That is comparing the means of each of the populations. Test claims regarding the difference of two populations means from independent samples. Two samples are independent if one sample has no inuence on the other. (Matched pairs violate independence since one sample directly affects the other sample) Construct and interpret condence intervals regarding the difference of two population means. TwoSample Problems What if we want to compare the mean of some quantitative variable for the individuals in two populations, Population 1 and Population 2? Our parameters of interest are the population means 1 and 2. The best approach is to take separate random samples from each population and to compare the sample means. Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters 1 and 2 are the true mean responses for Treatment 1 and Treatment 2, respectively. We use the mean response in the two groups to make the comparison. Conditions for Comparing Two Means We have two independent SRSs, from two distinct populations That is, one sample has no inuence on the other matching violates independence We measure the same variable for both samples. Both populations are Normally distributed the means and standard deviations of the populations are unknown In practice, it is enough that the distributions have similar shapes and that the data have no strong outliers.