Lecture+11+su10+_independent+samples+t-test_

Lecture+11+su10+_independent+samples+t-test_ - Sociology...

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02/23/11 Soc 210 summer 2010 1 Sociology 210 Lecture 11: The t Test for Two Independent Samples
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02/23/11 Soc 210 summer 2010 2 Motivation Most of the time we are interested in comparing means of two groups rather than comparing the mean of one group to some hypothesized value This is called a two-sample hypothesis test (vs. one-sample before) Many comparisons of two groups result from dividing a larger sample into subsamples according to classification on some variable (e.g., gender or race) If the overall sample was randomly selected, these subsamples constitute independent random samples of their corresponding subpopulations But because each subsample is smaller than the overall sample, their statistics will not be as precise in estimating the parameters of their respective subpopulations as the overall sample is at estimating the parameters of the overall population
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02/23/11 Soc 210 summer 2010 3 Hypotheses for the Difference of Means Goal: evaluate mean difference between two populations, μ 1 μ 2 , based on samples from each of those populations Two-tailed test H a : μ 1 - μ 2 0, equivalently, H a : μ 1 μ 2 (the means of the two populations are not equal) H 0 : μ 1 μ 2 = 0, equivalently, H 0 : μ 1 = μ 2 (the means are equal, i.e. no difference)
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02/23/11 Soc 210 summer 2010 4 Hypotheses for the Difference of Means One-tailed test : H a : μ 1 - μ 2 < 0, equivalently, H a : μ 1 < μ 2 H a : μ 1 - μ 2 > 0, equivalently, H a : μ 1 > μ 2 (the mean of one population is greater than the mean of the other population) H 0 : μ 1 - μ 2 0, equivalently, H 0 : μ 1 μ 2 H 0 : μ 1 - μ 2 0, equivalently, H 0 : μ 1 μ 2 (the means are equal or different in the opposite direction of what is predicted by H a )
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02/23/11 Soc 210 summer 2010 5
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