Analysis of Variance. v Single classification analysis of variance determines whether a relationship exists between a dependent variable and several classifications.

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Presentation transcript:

Analysis of Variance

v Single classification analysis of variance determines whether a relationship exists between a dependent variable and several classifications of one independent variable. v Multiple classification analysis of variance determines the relationship between one dependent variable and classifications of two or more independent variables.

v Since the variance (or its square root, the standard deviation) is an average distance of the raw scores from the mean of that distribution, this functional relationship can be used to determine mean differences by analyzing variances. Analysis of Variance

Within Group Variation

Total Variation

Among Group Variation

Degrees of Freedom v Among group degrees of freedom equals number of groups minus one (k-1) v Within group degrees of freedom equals the number of groups times the number within each group minus one k(N-1) v Total group degrees of freedom equals the total number of subjects minus one (kN-1) OR Degrees of freedom among plus the degrees of freedom within

Analysis of Variance SourceSSdfMSF Among Within Total7014

Analysis of Variance Example exhibits significant difference at the alpha =.01 level of significance F.05 WITH 2 AND 12 df. = 3.88 F.01 WITH 2 AND 12 df. = 6.93 Result: 8 > 6.93; Reject Ho