Statistics: Chapter 11

Post hoc test

A statistical procedure computed following a significant ANOVA to determine which pair or pairs of group means significantly differ.

One way within subjects ANOVA

A statistical procedure used to test hypotheses for one factor with two or more levels concerning the variance among group means. This test is used when the same participants are observed at each level of a factor and the variance in any one population is unknown

Mean square between groups

The variance attributed to differences between group means. It is the numerator of the test statistic

Mean square error/mean square within groups

The variance attributed to differences within each group. It is the denominator of the test statistic

Between persons variation

The variance attributed to the differences between person means averaged across groups. Using a within subjects design, the same participants are observed across groups, so this source of variation is removed from the error term in the denominator of the test statistic for the one way within subjects ANOVA

Between-groups variation

The variation attributed to mean differences between groups

Within-groups variation

The variation attributed to mean differences within each group. This source of variation cannot be attributed to or caused by having different groups and is therefore called error variation

Levels of the factor

symbolized as the k. the number of groups or different ways in which an independent or quasi independent variable is observed

Mean square between persons

A measure of the variance attributed to differences in scores between persons

F distribution

A positively skewed distribution derived from a sampling distribution of F ratios

Between-subjects design

A research design in which we select independent samples, meaning that different participants are observed at each level of a factor

Studentized range statistic (q)

A statistic sed to determine critical values for comparing pairs of means at a given range. This statistic is used in the formula to find the critical value for Tukey's HSD post hoc test

Pairwise comparison

A statistical comparison for the difference between two group means. A post hoc test evaluates all possible pairwise comparisons for an ANOVA with any number of groups

Experimentwise alpha

The alpha level or overall probability of committing a Type I error, when multiple tests are conducted on the same data

Analysis of variance (ANOVA)

statistical procedure used to test hypotheses for one or more factors concerning the variance among two or more group means, where the variance in one or more populations is unknown

Source of variation

Any variation that can be measured in a study. In the one-way between subjects ANOVa, there are two sources of variation: variation attributed to differences between group means and variation attributed to error

One-way between subjects ANOVA

Statistical procedure used to test hypotheses for one factor with two or more levels concerning the variance among group means. This test s used when different participants are observed at each level of a factor and variance in any one population is unknown

Testwise alpha

The alpha level or probability of committing a Type I error for each test or pairwise comparison made on the same data

Degrees of freedom error

The degrees of freedom associated with the error variance in the denominator. They are equal to the total sample size minus the number of groups (k)

Degrees of freedom between persons

The degrees of freedom associated with the variance of person means averaged across groups. They are equal to the number of participants minus 1

Degrees of freedom between groups

The degrees of freedom associated with the variance of the group means in the numerator of the test statistic. Equal to the number of groups (k) minus 1

Sum of squares total

The overall sum of squares across all groups

Sum of squares between groups

The sum of squares attributed to variability between groups

Sum of squares between persons

The sum of squares attributed to variability in participant scores across groups

Sum of squares within groups/sum of squares error

The sum of squares attributed to variability within each group

F statistic/F obtained

The test statistic for an ANOVA. Computed as the mean square (or variance) between groups divided by the mean square (or variance) within groups