Solved – Understanding Bartlett’s test from SAS

heteroscedasticityinterpretationp-valuesas

I am trying interpret the results of Bartlett's test run in SAS. This is the output I get: 

Bartlett's Test for Homogeneity
 of HoursWorked Variance 
Source DF Chi-Square Pr > ChiSq 
Year   1  0.00103    0.9744

My data is comparing the average hours worked between a group of countries between two years. Since the pr is larger than chisq, does that mean there are or aren't equal variances?

Best Answer

It is better to say that Bartlett's test is testing for heteroscedasticity / heterogeneity of variance than to say that it is testing for homogeneity of variance. Homogeneity of variance is the null hypothesis here. The $p$-value gives you information about whether to reject that.

The $p$-value in Bartlett's test mean the same thing as does the $p$-value in any other test. Specifically, it is the probability of getting data as far or further from the null value as your data are, if the null were true. In the context of Bartlett's test, it is: the probability of getting sample variances as far or further from equality as your variances are, if they really were equal. Your $p$-value is very, very high. Your variances should be very close to equal, given the amount of variability in variances that can naturally occur in your data.

Edit: let me clarify a few confusions here.

  1. It makes no sense to say that "P is greater than the chi". The $p$-value and the chi-squared value are different animals. It is not meaningful to compare them. What is printed ("Pr > ChiSq") is shorthand for 'the proportion of the reference chi-squared distribution that is greater than your observed chi-squared test statistic'. Under the null (i.e., equal variances), your test value is distributed as a chi-squared with 1 degree of freedom. Your observed value (0.00103), is 2.56% of the way through the reference distribution (from $0$ to $\infty$); 2.56% is less than that number and 97.44% is greater.
  2. A high $p$-value does not mean you can "accept [the null hypothesis] that there is homogeneity of variance". It may help to read my answer here: Why do statisticians say a non-significant result means “you can't reject the null” as opposed to accepting the null hypothesis?
  3. I suspect you are testing to see if your assumptions are met so that you can run the typical parametric analysis. This is generally not a good strategy. It may help to read this excellent CV thread: A principled method for choosing between t-test or non-parametric e.g. Wilcoxon in small samples.
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