Performing Bartlett’s test in R

Bartlett’s test

Bartlett’s test allows you to compare the variance of two or more samples to determine whether they are drawn from populations with equal variance. It is suitable for normally distributed data. The test has the null hypothesis that the variances are equal and the alterntive hypothesis that they are not equal.1

This test is useful for checking the assumptions of an analysis of variance.

You can perform Bartlett’s test with the bartlett.test function. If your data is in stacked form (with the values for both samples stored in one variable), use the command:

> bartlett.test(values~groups, dataset)

where values is the name of the variable containing the data values and groups is the name of the variable that specifies which sample each value belongs too.

If your data is in unstacked form (with the samples stored in separate variables) nest the variable names inside the list function as shown below.

> bartlett.test(list(dataset$sample1, dataset$sample2, dataset$sample3))

If you are unsure whether your data is in stacked or unstacked form, see the article Stacking a dataset in R for examples of data in both forms.

Example 10.10. Bartlett’s test using the PlantGrowth data

Consider the PlantGrowth dataset (included with R), which gives the dried weight of three groups of ten batches of plants, where each group of ten batches received a different treatment. The weight variable gives the weight of the batch and the groups variable gives the treatment received (either ctrl, trt1 or trt2). To view more information about the dataset, enter help(PlantGrowth). To view the data, enter the dataset name:

> PlantGrowth
   weight group
1    4.17  ctrl
2    5.58  ctrl
3    5.18  ctrl
4    6.11  ctrl
5    4.50  ctrl
6    4.61  ctrl
7    5.17  ctrl
8    4.53  ctrl
9    5.33  ctrl
10   5.14  ctrl
11   4.81  trt1
12   4.17  trt1
13   ...

30   5.26  trt2

Suppose you want to use Bartlett’s test to determine whether the the variance in weight is the same for all treatment groups. A significance level of 0.05 will be used.

To perform the test, use the command:

> bartlett.test(weight~group, PlantGrowth)

This gives the output:

        Bartlett test of homogeneity of variances

data:  weight by group 
Bartlett's K-squared = 2.8786, df = 2, p-value = 0.2371

From the output we can see that the p-value of 0.2371 is not less than the significance level of 0.05. This means we cannot reject the null hypothesis that the variance is the same for all treatment groups. This means that there is no evidence to suggest that the variance in plant growth is different for the three treatment groups.

[1] Montgomery, D.C. and Runger, G.C., 2007. Applied Statistics and Probability for Engineers, 4th ed. John Wiley & Sons.

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