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.

*F*value. The larger the

*F*value, the more likely it is that the differences the researchers found are not due to chance.

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.**

*Applied Statistics Concepts for Counselors* on AMAZON or GOOGLE

*Creating Surveys*** ****on ****AMAZON **** or ****GOOGLE Worldwide**

IV

DV

75 degrees

Math score

85 degrees

Math score

95 degrees

Math Score

**What is compared?**

**Serious stats help**

**by Andy Field. I've used an earlier edition as a course textbook. It is of course not needed for those who desire only a conceptual understanding. See**

*Discovering Statistics***for more information.**

*Discovering Statistics on AMAZON***Other notes**

*F*in the

*F*value comes from the surname of the British statistician, Sir Ronald Fisher (1890-1962) born in my hometown, London, England.

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