There are several types of ANOVA procedures. The term ANOVA refers to Analysis of Variance. Variance is a statistical term we will review later. Variance refers to differences, so the ANOVA procedures examine differences in scores among groups of people who complete a survey, a test, or produce a scorable response.
There may be several independent variables in a project. The effect of each variable is tested with an F test. When there are two or more variables, researchers also test for possible interaction effects, which results in additional F tests for each interaction. Interactions refer to the possibility that two or more variables combine to produce a change in the dependent variable. As with t tests, researchers include a probability (p) value with each F test. A common effect size associated with F tests is partial eta squared. An ANOVA is used when there are one or more independent variables but only one dependent variable.
Independent or grouping Variable = 1 or more IV
Dependent or criterion Variable = 1 DV
Dependent Measure = DM = a test score or quantitative measure of the DV
IV Groups or levels = 2 or more. An IV may have many levels (e.g., temperature, dosages) or groups (e.g., therapy groups, learning groups, work groups).
Overall tests are used to determine significant effects or differences among the groups or levels of the IVs.
An F test indicates significance overall and for specific effects or relationships.
A commonly reported measure of effect size is eta squared. In psychology, researchers have been encouraged to focus on effect sizes rather than p values when analyzing and reporting research results.
A p value reveals the probability of a significant relationship-- one that is not due to chance factors. The level of significance is set by the researchers. A common level is p is .05. F values yielding a probability below 0.05 are commonly considered significant in psychology and education.
The concept or idea is that a difference between means yields a large F value that would only occur 95 times out of a hundred due to chance. When researchers analyze the differences, they are analyzing variance hence, ANOVA.
If the overall F test is significant, then researchers may compare group means two at a time to determine possible significant differences between pairs of groups. There are many tests of pairs. For example t tests, Tukey HSD, Bonferroni, Neuman-Keuls. These tests are called post hoc tests because they are used only if the overall F test is significant.
Read more about ANOVA and data analyses in the following books.
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