Bit More About 1-Way ANOVA

Essentially, a 1-Way ANOVA is an overgrown t-test. A t-test compares two means. A 1-Way ANOVA lets you test the differences between more than two means. Like a t-test, there is only one independent variable (hence the “1-way”). It is an ANOVA because it analyzes the variance in the scores. The acrostic ANOVA stands for ANalysis Of VAriance.

In general, you can design experiments where people are re-used (within-subjects designs) or used only once (between-subjects design). The difference is all about time.

 Within-Subjects Designs

Sometimes we want to take repeated measures of the same people over time. These specialized studies are called within-subjects or repeated measures designs. Conceptually, they are extensions of the correlated t-test; the means are compared over time.

Like correlated t-tests, the advantages are that subjects act as their own controls, eliminating the difficulty of matching subjects on similar backgrounds, skills, experience, etc. Also, within-subject designs have more power (require less people to find a significant difference) and consequently are cheaper to run (assuming you’re paying your subjects).

They also suffer from the same disadvantages. There is no way of knowing if the effects of trial one wear off before the subjects get trial 2. The more trials in a study the larger the potential problem. In a multi-trial study, the treatment conditions could be impossibly confounded.

A more detailed investigation of within-subject designs is beyond the score of this discussion. For now, realize that it is possible, and sometimes desirable, to construct designs with repeated measures on the same subjects. But it is not a straight-forward proposition and requires more than an elementary understanding of statistics. So we’re going to focus on between-subjects designs.

Between-Subjects Designs

In a between-subject design, subjects are randomly assgined to groups. The groups vary along one independent variable. It doesn’t matter if you have 3 groups (high, medium and low) or ten groups or 100 groups…as long as they only vary on one dimension. Three types of cars is one independent variable (cars) with 3 groups. Ten types of ice cream can also be one independent variable: flavor.

Like an Analysis of Regression, an Analysis of Variance uses a F test. If F is equal to or larger than the value in the standard table, the F is considered significant, and the results are unlikely to be due to chance.

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    Day9: 1-Way ANOVA
    Bit More About 1-Way ANOVA
    Even More About 1-Way ANOVA
    Calculate 1-Way ANOVA
    Practice Problems
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    Word Problems
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    Vocabulary
    Formulas
    Quiz 9
    Summary