# Method table for One-Way ANOVA

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

## 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 (HA) 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.

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