560 CHAPTER 10 Chi-Square Tests and the F -Distribution In the guidelines for finding the test statistic for a one-way ANOVA test, the notation SSB represents the sum of squares between the samples. SSB = n1(x1 - x)2 + n 2(x2 - x)2 + c + n k(xk - x)2 = Σni(xi - x)2 Also, the notation SSW represents the sum of squares within the samples. SSW = 1n1 - 12s 2 i + 1n2 - 12s 2 2 + c+ 1n k - 12s 2 k = Σ1ni - 12s 2 i Performing a One-Way Analysis of Variance Test In Words In Symbols 1. Verify that the samples are random and independent, the populations have normal distributions, and the population variances are equal. 2. Identify the claim. State the null State H0 and Ha. and alternative hypotheses. 3. Specify the level of significance. Identify a. 4. Determine the degrees of freedom d.f.N = k - 1 for the numerator and the d.f.D = N - k denominator. 5. Determine the critical value. Use Table 7 in Appendix B. 6. Determine the rejection region. 7. Find the test statistic and sketch F = MSB MSW the sampling distribution. 8. Make a decision to reject or fail If F is in the rejection to reject the null hypothesis. region, then reject H0. Otherwise, fail to reject H0. 9. Interpret the decision in the context of the original claim. GUIDELINES Tables are a convenient way to summarize the results of a one-way analysis of variance test. ANOVA summary tables are set up as shown below. ANOVA Summary Table Variation Sum of squares Degrees of freedom Mean squares F Between SSB d.f.N = k - 1 MSB = SSB d.f.N MSB MSW Within SSW d.f.D = N - k MSW = SSW d.f.D
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