The tables of statistics can be used to determine the inferential statistics.
Summary Statistics for the Data
N M SD Skew Kurt
Level1 4.000 2.000 2.449 0.544 -2.944
Level2 4.000 6.000 2.449 0.544 -2.944
Level3 4.000 7.000 2.449 -0.544 -2.944
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 tables of inferential statistics show the key elements to be calculated.
Confidence Intervals for the Posthoc Mean Differences
Diff SE df LL UL
Level1 v Level2 4.000 1.732 9.000 -0.836 8.836
Level1 v Level3 5.000 1.732 9.000 0.164 9.836
Level2 v Level3 1.000 1.732 9.000 -3.836 5.836
Hypothesis Tests for the Posthoc Mean Differences
Diff SE df t p
Level1 v Level2 4.000 1.732 9.000 2.309 0.106
Level1 v Level3 5.000 1.732 9.000 2.887 0.043
Level2 v Level3 1.000 1.732 9.000 0.577 0.835
Confidence Intervals for the Posthoc Standardized Mean Differencens
d SE LL UL
Level1 v Level2 1.633 0.943 -0.215 3.481
Level1 v Level3 2.041 1.007 0.068 4.015
Level2 v Level3 0.408 0.825 -1.209 2.025
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 [-0.836, 8.836].
For the 1 vs. 3 comparison, the 95% CI is [0.164, 9.836].
For the 2 vs. 3 comparison, the 95% CI is [-3.836, 5.836].
Cohen’s d for each comparison can be calculated but is not shown here.
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 [0.16, 9.84], 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.