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Annotated Output | Post Hoc Comparisons
Computer Output
The table of descriptive statistics provides the baseline information.
The values of the group statistics are calculated separately for each group or condition. They are not identical to the values obtained from analyzing the variable as a whole.
The table from the ANOVA is useful in the intermediate steps for determining overall group differences and for providing some necessary information for calculations.
The table of inferential statistics shows the key elements to be interpreted.
For the 1 vs. 2 comparison, HSD = -2.309 and p = .106. This would not be considered a statistically significant diffeence.
For the 1 vs. 3 comparison, HSD = -2.887 and p = .043. This would be considered a statistically significant difference.
For the 2 vs. 3 comparison, HSD = -0.577 and p = .835. This would not be considered a statistically significant difference.
For each comparison, the researcher estimates the true population mean difference adjusted for multiple comparisons (knowing that the estimates could be incorrect).
For the 1 vs. 2 comparison, the 95% CI is [−8.836, 0.836].
For the 1 vs. 3 comparison, the 95% CI is [−9.836, −0.164].
For the 2 vs. 3 comparison, the 95% CI is [−5.836, 3.836].
Cohen’s d for each comparison can be calculated but is not shown here.
APA Style
Post hoc tests build on the ANOVA results and provide a more focused comparison among the groups and usually follows a presentation of the ANOVA (which already includes the descriptive information).
A series of Tukey’s HSD comparisons revealed that the first group (n = 3, M = 2.00, SD = 2.45) scored substantially and significantly lower Outcome scores than the third group (n = 3, M = 7.00, SD = 2.45), 95% CI [-9.84, -.16], t(9) = -2.89, p = 043. However, the other comparisons revealed effectively little and not significant differences between the other groups (ps > .05).
Alternatively, the means, standard deviations, and confidence intervals could be presented in a table or figure associated with this text.