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  • 1. Difference of the Means Andrew Martin PS 372 University of Kentucky
  • 2. 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.
  • 3. 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
  • 4. 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.
  • 5. 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.
  • 6. Difference of the Means
    • Effect = Mean (test group) – Mean (control group)
  • 7. 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.
  • 8. 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 (∆).
  • 9. 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.
  • 10. 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
  • 11. 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
  • 12. Difference of the Means
    • 55-45 =
    • √ (10.2/400 + 11.4/500)
    • 10 =
    • √ (.0255 + .0228)
    • 10 =
    • .220
    • Z obs = 45.454
  • 13. 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