Method table for One-Way ANOVA

Find definitions and interpretations for every statistic in the Method table.

In This Topic

Null hypothesis and Alternative hypothesis
Significance level
Equal variances

Null hypothesis and Alternative hypothesis

One-way ANOVA is a hypothesis test that evaluates two mutually exclusive statements about two or more population means. These two statements are called the null hypothesis and the alternative hypotheses. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

For one-way ANOVA, the hypotheses for the test are the following:

The null hypothesis (H₀) is that the group means are all equal.
The alternative hypothesis (H_A) is that not all group means are equal.

Interpretation

Compare the p-value to the significance level to determine whether to reject the null hypothesis.

Significance level

The significance level (denoted by alpha or α) is the maximum acceptable level of risk for rejecting the null hypothesis when the null hypothesis is true (type I error).

Interpretation

Use the significance level to decide whether to reject or fail to reject the null hypothesis (H₀). When the p-value is less than the significance level, the usual interpretation is that the results are statistically significant, and you reject H₀.

For one-way ANOVA, you reject the null hypothesis when there is sufficient evidence to conclude that not all of the means are equal.

Equal variances

The Method table indicates whether Minitab assumes that the population variances for all groups are equal.

Interpretation

Look in the standard deviation (StDev) column of the one-way ANOVA output to determine whether the standard deviations are approximately equal.

If you cannot assume equal variances, deselect Assume equal variances in the Options sub-dialog box for One-Way ANOVA. In this case, Minitab performs Welch's test, which performs well when the variances are not equal.