STA6126 Chapter 7

# STA6126 Chapter 7 - Chapter 7 Comparing Two Populations 7.1...

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Chapter 7 Comparing Two Populations 7.1 Some new concepts The framework: Until now we had one population, one random sample from that population and just one parameter (μ or π) with an unknown value and we made inference about the unknown value of the parameter. In this Chapter We have two populations, a population of X’s [say, {X 1 , X 2 , …, X N } ] and a population of Y’s, [say, {Y 1 , Y 2 , …, Y M }]. If X and Y are both quantitative variables, the population means are μ X and μ Y , and standard deviations are σ X and σ Y , respectively; we are interested in making inferences about the difference of population means, μ X – μ Y . If both X and Y are categorical variables, each with two categories, then the parameter of interest is the difference between the proportion of “Success”s, denoted by π X , in the population of X’s and proportion of “Success”s, denoted by π Y in the population of Y’s. We select (simple) random sample of size n X from the population of X’s and a (simple) random sample of size n Y from the population of Y’s to make inferences about the difference of the parameters of interest in the respective populations. The samples can be either independent of each other or they may be dependent on each other. Definition: Two random samples are said to be independent samples if the selection of a unit from one population has no effect on the selection or non-selection of another unit from the second population. Otherwise the samples are said to be dependent samples. Independent samples are used in most applications. However, in some applications the selection of one unit will from one of the populations determines the selection of another one from the second population. Such samples are said to be dependent samples. In such applications one unit from each population come in pairs. Thus we have a random sample of pairs . These pairs either come naturally (e.g., twins-studies, studies of married couples, observations on the same person under two different conditions, etc.) or the pairs are created by the experimenter, being matched on as many characteristics as possible, except the one characteristic of interest to the researcher. We have the usual general formulas for confidence intervals and the usual 6 steps of making statistical tests. STA 6126 Chap 7, Page 1 of 21

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Relative Risk Another way of comparing two population parameters is to look at their ratio . Ratio of two population parameters is called the relative risk (RR) . When both X and Y are quantitative variables , we may compare the two population means by looking at / X Y RR μ = which is estimated by / X Y . When both X and Y are categorical variables we may compare the two population proportions by looking at / X Y RR π = which is estimated by / X Y p p . Inferences on relative risk can be made using statistical software (because the formulas
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STA6126 Chapter 7 - Chapter 7 Comparing Two Populations 7.1...

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