How to perform an ANOVA test?

To perform an ANOVA test, first gather data from multiple groups and calculate their means and variances.

ANOVA, or analysis of variance, is a statistical test used to compare the means of three or more groups. To perform an ANOVA test, you must first gather data from each group and calculate their means and variances.

Next, calculate the overall mean of all the groups combined. This is done by adding up all the individual means and dividing by the total number of groups.

Then, calculate the sum of squares between groups (SSB) by subtracting the overall mean from each group mean, squaring the result, and multiplying by the number of observations in each group. Add up the SSB for all groups.

Calculate the sum of squares within groups (SSW) by subtracting each individual observation from its respective group mean, squaring the result, and adding up all the values for each group.

Calculate the degrees of freedom for SSB by subtracting 1 from the number of groups. Calculate the degrees of freedom for SSW by subtracting the total number of observations from the number of groups.

Calculate the mean square between groups (MSB) by dividing SSB by its degrees of freedom. Calculate the mean square within groups (MSW) by dividing SSW by its degrees of freedom.

Calculate the F-statistic by dividing MSB by MSW. Compare the F-statistic to the critical value from an F-distribution table with degrees of freedom for SSB and SSW. If the F-statistic is greater than the critical value, reject the null hypothesis and conclude that there is a significant difference between the means of the groups.