BECAUSE OF THE ASSUMPTION THAT THE POPULATION VARIANCES ARE EQUAL, WHEN YOU DO A ANALYSIS OF VARIANCE.
You use ANOVA when you want to analyze the effects of several independent variables at once.
When you perform an analysis of variance (ANOVA), one of the assumptions is that the population variances across the different groups being compared are equal. This assumption is known as the assumption of equal variances or homogeneity of variances.
It is important to check this assumption before conducting an ANOVA because violation of this assumption can lead to incorrect conclusions and affect the validity of the analysis.
To test for equality of variances, you can use a statistical test called the Levene's test or the Bartlett's test. These tests compare the variances of the groups and check if they are significantly different from each other.
Here is how you can carry out the assumption of equal variances test using Levene's test:
1. State your null and alternative hypotheses:
Null hypothesis (H0): The variances of the groups are equal (homogeneity of variances).
Alternative hypothesis (HA): The variances of the groups are not equal (heterogeneity of variances).
2. Gather your data: Collect the data from each group you are comparing. Ensure that the data is continuous and collected independently.
3. Calculate the mean absolute deviation (MAD) for each group: MAD is the sum of the absolute deviations from the group mean divided by the number of data points. Calculate MAD for each group separately.
4. Calculate the test statistic: The test statistic for Levene's test is based on the absolute deviations. It compares the variability between groups against the variability within each group.
5. Conduct the hypothesis test: The test statistic follows an F-distribution. You can use statistical software or online calculators to find the p-value associated with the test statistic. Compare the p-value to your chosen significance level (e.g., α = 0.05) to determine if you reject or fail to reject the null hypothesis.
If the p-value is below your significance level, you reject the null hypothesis, indicating that the variances are significantly different between groups. If the p-value is above your significance level, you fail to reject the null hypothesis, suggesting that there is no significant evidence to conclude that the variances are different.
It is important to note that if the assumption of equal variances is violated, there are alternative statistical tests available, such as Welch's ANOVA or non-parametric tests like the Kruskal-Wallis test, that can be used instead of the traditional ANOVA.