Question

This problem demonstrates a possible (though rare) situation that can occur with group comparisons. The groups are sections and the dependent variable is an exam score. Section 1 77.6 69.1 53.5 68.2 73.9 63.3 61.3 71.9 60.2 Section 2 58.5 61.3 57.5 34.5 73.2 37.1 50.3 51.2 76.8 Section 3 67.6 63.7 60.5 71.7 65 66.8 58.5 74.2 68.2 Run a one-factor ANOVA (fixed effect) with α = 0.05 α = 0.05 . Report the F-ratio to 3 decimal places and the P-value to 4 decimal places. F = F = p = p = What is the conclusion from the ANOVA? reject the null hypothesis: at least one of the group means is different fail to reject the null hypothesis: not enough evidence to suggest the group means are different Calculate the group means for each section: Section 1: M 1 = M 1 = Section 2: M 2 = M 2 = Section 3: M 3 = M 3 = Report means accurate to 2 decimal places. Conduct 3 independent sample t-tests for each possible pair of sections. (Though we will see later that it might not be appropriate, retain the significance level α = 0.05 α = 0.05 .) Report the P-value (accurate to 4 decimal places) for each pairwise comparison. Compare sections 1 & 2: p = p = Compare sections 1 & 3: p = p = Compare sections 2 & 3: p = p = Based on these comparisons, which pair of groups have statistically significantly different means? group 1 mean is statistically different from group 2 mean group 1 mean is statistically different from group 3 mean group 2 mean is statistically different from group 3 mean none of the group means are statistically significantly different from each other Thought for reflection: What do the results of the pairwise comparisons suggest about the original conclusion from the ANOVA?

Answer 1