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Analyzing Quantitative Data
Research Question
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The researcher is interested in comparing the effectiveness of the three assessment models. The hypothesis relates to this comparison and is stated as follows.
H0: :1 = :2 = :3
H1: :i = :k for some i, k
The null and alternative hypotheses can be quite intimidating when written in algebraic notation. Perhaps the following explanation can help you understand them.
H0 designates the null hypothesis. The notation :1, :2, and :3 designate the population means for groups 1, 2, and 3 respectively. Thus, the first line suggests the means of the three groups are equal.
H1 designates the alternative hypothesis. Because there are three groups, there are three pairs of means to compare. The first involves Groups 1 and 2, the second Groups 1 and 3, and the third Groups 2 and 3. A notational shorthand is used where the subscript i designates one of the groups and the subscript k another different group. The notation :i = :k suggests at least one pair of the group means is not equal. Therefore, the alternative hypothesis is: the mean for Group 1 might be different than the mean for Group 2, the mean for Group 1 might be different than the mean for Group 3, and/or the mean for Group 2 might be different than the mean for Group 3. Which specific pairs are different will have to be determined with the Tukey post hoc procedure.
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