Illuminating Statistical Analysis Using Scenarios and Simulations

34Multiple Means and Variance Ratios: ANOVA

Statistical Scenarios—Analysis of Variance (ANOVA)

You have 1–7 scaled opinions for random samples of 30 Democrats, 30 Republicans, and 30 Independents in the community. You want to know whether the evidence suggests that there is a difference in the average opinion between any of the three political groups in the overall community population. Null hypothesis: there is not.

For each of the four separate scenarios below, which sample statistic values convince you that there is a population difference in the means between at least two of the political groups? Pay attention to (1) how far apart the sample means are, and (2) how high the sample variances are.

Scenario 1
Opinion statistics	Democrat	Republican	Independent
Sample mean	3.9	4.0	4.1	Means close together
Sample variance	0.9	1.0	1.1	Low variance

Scenario 2
Opinion statistics	Democrat	Republican	Independent
Sample mean	3.0	4.0	5.0	Means Far apart
Sample variance	0.9	1.0	1.1	Low variance

Scenario 3
Opinion statistics	Democrat	Republican	Independent
Sample mean	3.9	4.0	5.0	One mean far apart
Sample variance	0.9	1.0	1.1	Low variance

Scenario 4
Opinion statistics	Democrat	Republican	Independent
Sample mean	3.0	4.0	5.0	Means far apart
Sample variance	8.9	9.0	9.1	Higher variance

Variance ratios and the -distribution can be used in an ...