7. Oneway ANOVA

When to use a Oneway ANOVA

Oneway ANOVA is a generalization of the independent samples t-test. Recall that the independent samples t-test is used to compare the mean values of 2 different groups. A Oneway ANOVA does the same thing, but it has the advantage of allowing comparisons between more than 2 groups. In psychology, for example, we often want to contrast several conditions in an experiment; such as a control, a standard treatment, and a newer “experimental” treatment.

Because Oneway ANOVA is simply a generalization of the independent samples t-test, we use this procedure below to recalculate our previous 2 groups example. Later, we will do an example with more than 2 groups.

Example 7.1

Let’s return to our example of the pizza vs. beer diet. Our research question is: “Is there any weight gain difference between a 1-week exclusive diet of either pizza or beer?”

           X₁

X₂

           1

3

           2

4

           2

4

           2

4

          3

5

2

4

S²_xj= 0.4

0.4

An Oneway-ANOVA is a generalization of the independent samples t-test in which we can specify more than 2 conditions. If we only specify 2 conditions, however, the results will be exactly the same as the t-test. The calculations are somewhat different, but the resulting “p-value” will be the same, and therefore the research conclusion will always be the same.

ANOVA operates on the principle of “partitioning the variance.” There is a total amount of variance in the set of data above. This total variance is found by subtracting each value (e.g., 1,2,2…) from the mean for all 10 people (), squaring the result, summing the squares, and dividing by the number of values (i.e., 10):

, or