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PPA 415 – Research Methods in Public Administration

PPA 415 – Research Methods in Public Administration. Lecture 7 – Analysis of Variance. Introduction. Analysis of variance (ANOVA) can be considered an extension of the t-test. The t-test assumes that the independent variable has only two categories.

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PPA 415 – Research Methods in Public Administration

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  1. PPA 415 – Research Methods in Public Administration Lecture 7 – Analysis of Variance

  2. Introduction • Analysis of variance (ANOVA) can be considered an extension of the t-test. • The t-test assumes that the independent variable has only two categories. • ANOVA assumes that the nominal or ordinal independent variable has two or more categories.

  3. Introduction • The null hypothesis is that the populations from which the each of samples (categories) are drawn are equal on the characteristic measured (usually a mean or proportion).

  4. Introduction • If the null hypothesis is correct, the means for the dependent variable within each category of the independent variable should be roughly equal. • ANOVA proceeds by making comparisons across the categories of the independent variable.

  5. Computation of ANOVA • The computation of ANOVA compares the amount of variation within each category (SSW) to the amount of variation between categories (SSB). • Total sum of squares.

  6. Computation of ANOVA • Sum of squares within (variation within categories). • Sum of squares between (variation between categories).

  7. Computation of ANOVA • Degrees of freedom.

  8. Computation of ANOVA • Mean square estimates.

  9. Computation of ANOVA • Computational steps for shortcut. • Find SST using computation formula. • Find SSB. • Find SSW by subtraction. • Calculate degrees of freedom. • Construct the mean square estimates. • Compute the F-ratio.

  10. Five-Step Hypothesis Test for ANOVA. • Step 1. Making assumptions. • Independent random samples. • Interval ratio measurement. • Normally distributed populations. • Equal population variances. • Step 2. Stating the null hypothesis.

  11. Five-Step Hypothesis Test for ANOVA. • Step 3. Selecting the sampling distribution and establishing the critical region. • Sampling distribution = F distribution. • Alpha = .05 (or .01 or . . .). • Degrees of freedom within = N – k. • Degrees of freedom between = k – 1. • F-critical=Use Appendix D, p. 499-500. • Step 4. Computing the test statistic. • Use the procedure outlined above.

  12. Five-Step Hypothesis Test for ANOVA. • Step 5. Making a decision. • If F(obtained) is greater than F(critical), reject the null hypothesis of no difference. At least one population mean is different from the others.

  13. ANOVA – Example 1 – JCHA 2000 What impact does marital status have on respondent’s rating Of JCHA services? Sum of Rating Squared is 615

  14. ANOVA – Example 1 – JCHA 2000 • Step 1. Making assumptions. • Independent random samples. • Interval ratio measurement. • Normally distributed populations. • Equal population variances. • Step 2. Stating the null hypothesis.

  15. ANOVA – Example 1 – JCHA 2000 • Step 3. Selecting the sampling distribution and establishing the critical region. • Sampling distribution = F distribution. • Alpha = .05. • Degrees of freedom within = N – k = 38 – 5 = 33. • Degrees of freedom between = k – 1 = 5 – 1 = 4. • F-critical=2.69.

  16. ANOVA – Example 1 – JCHA 2000 • Step 4. Computing the test statistic.

  17. ANOVA – Example 1 – JCHA 2000

  18. ANOVA – Example 1 – JCHA 2000

  19. ANOVA – Example 1 – JCHA 2000. • Step 5. Making a decision. • F(obtained) is 1.93. F(critical) is 2.69. F(obtained) < F(critical). Therefore, we fail to reject the null hypothesis of no difference. Approval of JCHA services does not vary significantly by marital status.

  20. ANOVA – Example 2 – Ford-Carter Disaster Data Set What impact does Presidential administration have on the president’s recommendation of disaster assistance?

  21. ANOVA – Example 2 – Ford-Carter Disaster Data Set • Step 1. Making assumptions. • Independent random samples. • Interval ratio measurement. • Normally distributed populations. • Equal population variances. • Step 2. Stating the null hypothesis.

  22. ANOVA – Example 2 – Ford-Carter Disaster Data Set • Step 3. Selecting the sampling distribution and establishing the critical region. • Sampling distribution = F distribution. • Alpha = .05. • Degrees of freedom within = N – k = 371 – 2 = 369. • Degrees of freedom between = k – 1 = 2 – 1 = 1. • F-critical=3.84.

  23. ANOVA – Example 2 – Ford-Carter Disaster Data Set • Step 4. Computing the test statistic.

  24. ANOVA – Example 2 – Ford-Carter Disaster Data Set • Step 5. Making a decision. • F(obtained) is 5.288. F(critical) is 3.84. F(obtained) > F(critical). Therefore, we can reject the null hypothesis of no difference. Approval of federal disaster assistance does vary by presidential administration.

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