Chapter 9 Review - Part I

# Chapter 9 Review - Part I - Chapter 9 : Comparing Two...

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Chapter 9 : Comparing Two Groups In chapters 7 and 8, we learned how to construct confidence intervals of and test hypothesis about means and proportions corresponding to population. Now, we shall extend the above method to groups or populations i.e we will learn how to construct confidence intervals and hypothesis tests about the difference of proportions and means corresponding to two populations . By doing this, we can compare the characteristics of the subjects belonging to these two groups. Eg : We want to compare the proportions of male and female in the U.S who believe in miracles. Here the two groups/populations are respectively the populations of all American males and females and the characteristic we want to compare (between the two populations) is “ belief in miracles ”. The two groups mentioned above can be compared with regard to a or outcome. For categorical outcomes, we compare (population) , and for quantitative outcomes, we compare (population) .

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Eg : In the above example, our outcome (or response ) variable is “ whether a male or female believe in miracles ” which, obviously is (since it has only two categories viz “ Yes ” and “ No ”) On the other hand, the two groups being compared form the two categories of a variable (a variable which only takes “0” or “1” values), often known as the variable (since it “explains” or “causes” the outcome). Eg : In the above example, the explanatory variable is ” which takes the value 1 for males and 0 for females – it specifies the two groups. We are interested in studying whether and how “belief in miracles” depends on “gender”. In order to compare the two groups, we have to select samples from those groups. If the observations in one sample are independent of those in the other, then those are called samples . Eg : Suppose we want to compare two drugs. We select a sample of patients and randomly allocate them to the two drugs. These two groups of patients (and also the observations coming from them) will constitute independent samples since they were
randomly allocated to the two groups corresponding to the two drugs. Two samples are if the same subjects appear in both the samples. Also, if each subject in one sample is matched (or paired ) with a subject in the other, the samples are dependent and the data is known as “ matched pairs data ”. Eg :

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## This note was uploaded on 04/18/2008 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.

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Chapter 9 Review - Part I - Chapter 9 : Comparing Two...

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