Bartlett's Test
Many statistical tests (like a one-way ANOVA) assume that variances are equal across samples. Bartlett’s test can be used to verify that assumption.
- You want to do a one-way ANOVA and need to verify that the variances are equal across samples.
Many statistical tests (like a one-way ANOVA) assume that variances are equal across samples. Bartlett’s test can be used to verify that assumption.
The test uses the following hypotheses:
H0: The variance of each group is equal.
H1: At least one group has a variance that is not equal to the rest.
An online calculator can be found HERE.
Worked Example
A researcher wants to know whether different advertising campaigns impact people’s views on recycling. She recruits 30 individuals and randomly splits them up into three groups to view either no advertising, Advertisement 1 or Advertisement 2.
After viewing, each individual completes a short survey asking questions about their views on recycling. The survey uses a 5-point Likert scale from “strongly disagree” (1) to “strongly agree” (5). Questions are worded such that “strongly agree” always indicates a positive attitude towards recycling.
Once all the surveys are completed each person’s total score is calculated, with a possible maximum of 25. You then have the following data:
No advertisement: 23, 12, 16, 9, 14, 8, 14, 5, 18, 13
Advertisement 1: 13, 22, 21, 19, 24, 6, 17, 15, 20, 19
Advertisement 2: 23, 22, 12, 9, 27, 16, 24, 5, 12, 9
Test whether the variances can be assumed to be equal across the three groups.
| Using an online calculator we get a p-value of 0.413. Since this is more than our level of significance (α = 5%) we cannot reject our H0 and must conclude that the variances of the three groups are not statistically different. Therefore, we can go on to do a one-way ANOVA. |
You want to compare four different fertilisers and their effect on crop yields. You find five farmers who are willing to test each brand of fertiliser and measure their crop yields (kg/ha).
You then have the following data:
Brand A: 8750, 9125, 7980, 7950, 8150
Brand B: 9225, 8765, 8945, 7490, 8450
Brand C: 7950, 8750, 8960, 8940, 8760
Brand D: 8970, 9990, 9850, 9560, 9760
You want to do a one-way ANOVA on this data, but first you need to verify that it is reasonable to assume that the variances are equal across samples. We will use a Bartlett's Test to confirm this.
What will our null and alternative hypotheses be for this test?
We will use the online calculator HERE to do the Bartlett's Test.
In this case, the data corresponding to "Sample 1" is...
We have four "samples" corresponding to the four brands we are comparing.
After we run the test, which of the following statements are correct?
Since the p-value is greater than the significance level, we should fail to reject the null hypothesis.
The rule of thumb is "If p is low, H0 must go" ... so in this case H0 must stay!
Because Bartlett's Test tells us it is reasonable to assume that the variances are equal across samples we can now do a one-way ANOVA.