# Statistics > Analysis of Variance > One-Way ANOVA

One-way analysis of variance uses one factor to categorize three or more populations. It is used to test hypotheses that three or more population means are equal. The null hypothesis H0 is μ1 = μ2 = ... = μk, where μi is the mean of population i of k populations.

The test statistic F is the ratio of two estimates of the variance common to the k populations:

When the null hypothesis is true, it has an F distribution with degrees of freedom given by

numerator degrees of freedom = k - 1

denominator degrees of freedom = N - k

The test statistics F can be expressed as the ratio MS(treatment) / MS (error). The mean square (MS) and sum of squares (SS) are computed in order to obtain F.

SS(treatment) is a sum of squares representing the variation between the sample means:

where ni is the size of sample i, is the mean of sample i, , and N is the sum of all sample sizes.

SS(error) is a sum of squares representing the variation that is assumed to be common to the populations:

SS(total) is a measure of the total variation in all the sample data:

SS(total) = SS(treatment) = SS(error)

MS(treatment) is the mean square for treatment:

MS(error) is the mean square for error:

To use this utility, you will need to provide sample values for different populations in separate columns and specify the significance level. The SS and MS values are displayed along with the test statistic, critical value, and p-Value.

### Dialog Inputs

To include a column in the analysis, select the column name is the Select the column to be included in the analysis: list and click the Add to list button. The column will be added to the Responses list. To remove a column from the Responses list, select it and click the Remove from list button.

Click the Clear Input List button to clear the input list.

Enter the signicance level (a number between 0 and 1) in the Significance level text box.