OT 575 - research methods part 7

what is analysis of variance (ANOVA)?

a test of statistical significance of the differences between the means of three or more groups; an extension of the t-test

how is ANOVA calculated?

F-test; ratio of the variance between groups (explained variance) to the variance within groups (error variance)

why is between groups variance called "explained variance?"

the differences between the groups can be explained by the treatments given to each group

why is within groups variance called "error variance?"

the differences among the groups cannot be explained by the treatments given to each group

which parametric test is used for independent samples?

one-way ANOVA with post hoc

which nonparametric test is used for independent samples?

kruskal wallis with post hoc

which parametric test is used for dependent/correlated samples?

repeated measures ANOVA with contrast

which nonparametric test is used for dependent/correlated samples?

friedman with contrast

what is one-way ANOVA?

assesses if the observed differences among a set of means are greater than the expected differences (expected by chance alone)

what does the F-test of one-way ANOVA test?

tests if three or more group means are the same or different; does not specify which group is significantly different

when is one-way ANOVA used?

- when the dependent variable is measured using a continuous scale

- when the values of the dependent variable are normally distributed

- when the independent variables are categorical (e.g., experimental, placebo, control group)

which type of test is used when ANOVA is significant?

a post hoc test

what is a post hoc test?

analyzes how groups are differences

list the types of post hoc tests from most stringent to less stringent.

1. bonferroni correction

2. scheffe's test

3. tukey's honest significant difference (HSD)

4. fisher's least significant difference (LSD)

one-way ANOVA decreases the likelihood of committing what type of error?

type I (but increases the chance of committing a type II error)

what are the assumptions of ANOVA?

- samples are randomly drawn from normally distributed populations

- independent variable is categorical (nominal scale)

- dependent variable is measured using a continuous scale

what is levene's stastistic?

a statistical test used for homogeneity of variance; checks whether the variances of two or more groups are equal

example: groups 1 and 2 have a statistical significance of .256, while groups 1 and 3 have a statistical significance of .012. what does this mean?

the means for groups 1 and 3 were different

which type of test should be used if levene's stastistics is not significant but ANOVA is significant?

tukey post hoc test

which type of test should be used if levene's stastistics is significant and ANOVA is significant?

bonferroni correction post hoc test

which type of test should be used if levene's stastistics is/is not significant but ANOVA is not significant?

no post hoc test is necessary

what is the kruskal wallis test?

a nonparametric test to compare group means

when is kruskal wallis indicated?

- dependent variable is measured on an ordinal scale

- sample size is small; dependent variable is not normally distributed in each group

- variances in each group are different so the groups are not equal; data is not normal

what does it mean if the kruskal wallis test is significant?

null hypothesis is rejected; rank order means are not all equal