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Thorne and Giesen Book Cover
Statistics for the Behavioral Sciences, 4/e
Michael Thorne, Mississippi State University -- Mississippi State
Martin Giesen, Mississippi State University -- Mississippi State

One-Way Analysis of Variance With Post Hoc Comparisons

Definitions


ANOVA  ANalysis Of VAriance-widely used test to compare two or more groups
one-way ANOVA  analysis of variance involving only one independent variable
additivity  the property of variance that, for individual samples, the variance of a sum of parts is equal to the sum of the variances of the parts
key deviations  for the one-way ANOVA, the key deviations are between each score in a group and the group's mean and between each group mean and the total mean
total variability  variability in data based on the deviation between each score and the total mean
within-groups variability  part of the ANOVA test based on the deviation between each score in a group and the group mean; variability within a group
individual differences  differences between experimental participants because of different participant backgrounds, experiences, abilities, motives, etc.
experimental error  source of variability in data caused by such things as imprecise measuring equipment, momentary changes in experimenter and subject attention, and slight changes in background conditions during data collection
between-groups variability  part of the ANOVA test based on the deviation between each group mean and the total mean; variability between the groups
treatment effect  variability in data caused by administration of the independent variable
total sum of squares  sum of the squared deviation of each score from the total mean in the analysis of variance
within-groups sum of squares  the sum of the squared deviations of each score in a group from its group mean, with the squared deviations summed across groups
between-groups sum of squares  the square of the deviation between each group mean and the total mean multiplied by the number of subjects in a particular group and summed over groups
ANOVA summary table  table used to summarize the results of the analysis of variance
mean square  the analyzed variance in the ANOVA test, found by dividing each sum of squares by the appropriate df
F ratio  ratio of the variability between groups to the variability within groups; test statistic for the ANOVA test
post-ANOVA tests  unplanned group comparisons following a significant F ratio
a posteriori test  same as post-ANOVA test
post hoc test  same as post-ANOVA test
a priori test  test designed to look at specific hypotheses before the experiment is done
Fisher LSD test  least significant difference test; powerful post-ANOVA test that compares pairwise differences in means with a computed least significant difference
protected t test  another name for the Fisher LSD test
pairwise comparisons  comparing several groups one pair at a time
Tukey HSD test  post-ANOVA test that compares each mean difference with a computed HSD, or honestly significant difference
studentized range statistic  statistic sometimes used instead of the F statistic for making group comparisons
repeated measures ANOVA  form of the ANOVA test used in situations in which the same (or matched) participants are tested on more than two occasions