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    Diffmeans Diffmeans Presentation Transcript

    • Difference of the Means Andrew Martin PS 372 University of Kentucky
    • ANOVA
      • For quantitative (or interval- and ratio-level ) data the analysis of variance is appropriate.
      • Analysis of variance aka ANOVA.
      • The independent variable, however, is generally still nominal or ordinal.
    • ANOVA tells political scientists …
      • (1) if there are any differences among the means
      • (2) which specific means differ and by how much
      • (3) whether the observed differences in Y could have arisen by chance or whether they reflect real variation among the categories or groups in X
    • Two important concepts …
      • Effect size —The difference between one mean and the other.
      • Difference of means test —The larger the difference of means, the more likely the difference is not due to chance and is instead due to a relationship between the independent and dependent variables.
    • Setting up an example
      • Suppose you want to test the effect of negative political ads on intention of voting in the next election.
      • You set up a control group and a test group. Each group watches a newscast, but the test group watches negative TV ads during the commercial breaks. The control group watches a newscast without a campaign ad.
      • You create a pre- and post-test of both groups to compare the effects of both ads.
    • Difference of the Means
      • Effect = Mean (test group) – Mean (control group)
    • Difference of the Means
      • Although different statistics use different formulas, each means test has two identical properties:
      • (1) The numerator indicates the difference of the means
      • (2) The denominator indicates the standard error of the difference of the means.
    • Difference of the Means
      • A means test will compare the means of two
      • different samples.
      • The larger the N for both samples, the greater
      • confidence that the observed difference in the
      • sample (D) will correctly estimate the
      • population difference (∆).
    • Difference of the Means
      • Difference of the means tests the null hypothesis that there is no difference between the means.
      • You can basically test the significance of a means difference by employing a hypothesis test or calculating a confidence interval.
    • Difference of the Means
      • Logic is the same as for earlier z and t tests
      • Estimated difference of the means divided by the estimated standard error
      • z is for large samples
    • Large Sample Difference of Means
      • Comparing the mean Obama thermometer score for men and women:
      • Men: Mean (45), Sample Size (400), Variance (10.2)
      • Women: Mean (55), Sample Size (500), Variance (11.4)
      • H 0 : There is no difference between the two samples.
      • H A : µ women - µ men > 0; α = .01, one-tail test
    • Difference of the Means
      • 55-45 =
      • √ (10.2/400 + 11.4/500)
      • 10 =
      • √ (.0255 + .0228)
      • 10 =
      • .220
      • Z obs = 45.454
    • Difference of the Means
      • If | Z obs | ≥ Z crit , reject H 0 in favor of H A
      • | Z obs | = 45.454 > Z crit (2.325)
      • So, we reject H 0 in favor of H A