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Unformatted text preview: Outline Introduction Comparing Two Means Comparing Two Proportions Power and Sample Size Calculation NOT COVERED Lecture 26 Chapter 10: Comparing Two Populations Michael Akritas Michael Akritas Lecture 26 Chapter 10: Comparing Two Populations Outline Introduction Comparing Two Means Comparing Two Proportions Power and Sample Size Calculation NOT COVERED Introduction Comparing Two Means T CIs for 1 2 T Tests for 1 2 Comparing Two Proportions Z CIs for p 1 p 2 Z Tests for p 1 p 2 Power and Sample Size Calculation NOT COVERED Comparison of Means Comparison of Proportions Michael Akritas Lecture 26 Chapter 10: Comparing Two Populations Outline Introduction Comparing Two Means Comparing Two Proportions Power and Sample Size Calculation NOT COVERED I Here we will use CIs and hypothesis testing for comparing two population means, and two population proportions. I The mean and variance of population i , i = 1 , 2, are denoted by i , 2 i . If the two populations are Bernoulli, then i = p i , and 2 i = p i (1 p i ). I The comparison will be based on a simple r.s. from each of the two populations: X 11 ,..., X 1 n 1 from population 1, and X 21 ,..., X 2 n 2 from population 2. I The sample mean and sample variances are denoted by X i = 1 n i n i X j =1 X in i , S 2 i = 1 n i 1 n i X j =1 ( X ij X i ) 2 , i = 1 , 2 . I In the Bernoulli case only b p i (or T i = n i b p i ) is typically given. Michael Akritas Lecture 26 Chapter 10: Comparing Two Populations Outline Introduction Comparing Two Means Comparing Two Proportions Power and Sample Size Calculation NOT COVERED The Two Approaches I One approach to the comparison is based on the contrast X 1 X 2 or b p 1 b p 2 . I An alternative approach for comparing means uses the ranks of the observations. I With the exception of the section on paired data, we will make the further assumption that the two samples are independent. I Before computing the T CIs and tests for comparing two means it is a good idea to construct boxplots. This is similar to making an xy scatterplot before fitting the simple linear regression model. Michael Akritas Lecture 26 Chapter 10: Comparing Two Populations Outline Introduction Comparing Two Means Comparing Two Proportions Power and Sample Size Calculation NOT COVERED Example (Comparative Boxplot) To compare the strengths of coldrolled steel and twosided galvanized steel, n 1 = 32 strength measurements of coldrolled and n 2 = 35 measurements of twosided galvanized steel are made. The data are given in http://www.stat.psu.edu/ ~ mga/401/ Data/SteelStrengthData.txt . Construct comparative boxplots. Solution. The R commands for doing this are: library(psych); df=read.clipboard() # Reads data in data frame df y=df$Value; x=df$Sample # Measurements in y, sample index in x boxplot(y x) [or boxplot(y x, col=grey)] boxplot(y x,notch=TRUE) # Gives approximate CIs for medians....
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 Fall '00
 Akritas

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