Using the t procedures Comparing two means Except in the case of small samples, the The goal of inference is to compare the responses to two treatments or to compare assumption that the data are an SRS from the characteristics of two populations the population of interest is more important We have a separate sample from each than the assumption that the population treatment or each population distribution is normal Unlike the matched pairs designs, there is no matching of the units in the two samples and the two samples can be of different data differ from those for matched pairs Sample size less than 15. Use t Assumptions for comparing two procedures if the data are close to normal means If the data are clearly nonnormal or if outliers are present, do not use t. Ve have two srss from two distinct Sample size at least 15. The t proced opulations. The samples are independent can be used except in the presence of That is, one sample has no infiuence on outliers or strong skewness the other Matching violates independence. for example. We measure the same Large samples. The t procedures can be variable for both samples used even for clearly skewed distributions Both populations are normally distributed when the sample is large, roughly n 240 The means and standard deviations of the populations are unknown23 45 Using the t procedures • Except in the case of small samples, the assumption that the data are an SRS from the population of interest is more important than the assumption that the population distribution is normal. 46 • Sample size less than 15. Use t procedures if the data are close to normal. If the data are clearly nonnormal or if outliers are present, do not use t. • Sample size at least 15. The t procedures can be used except in the presence of outliers or strong skewness. • Large samples. The t procedures can be used even for clearly skewed distributions when the sample is large, roughly . n ≥ 40 24 47 Comparing two means • The goal of inference is to compare the responses to two treatments or to compare the characteristics of two populations. • We have a separate sample from each treatment or each population. • Unlike the matched pairs designs, there is no matching of the units in the two samples and the two samples can be of different sizes. Inference procedures for two-sample data differ from those for matched pairs. 48 Assumptions for comparing two means • We have two SRSs, from two distinct populations. The samples are independent. That is, one sample has no influence on the other. Matching violates independence, for example. We measure the same variable for both samples. • Both populations are normally distributed. The means and standard deviations of the populations are unknown