Exploratory Data Analysis
1.3. EDA Techniques
1.3.5. Quantitative Techniques
Test if variances from two populations are equal
|An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal. The one-tailed version only tests in one direction, that is the variance from the first population is either greater than or less than (but not both) the second population variance. The choice is determined by the problem. For example, if we are testing a new process, we may only be interested in knowing if the new process is less variable than the old process.|
The F hypothesis test is defined as:
|F Test Example||
The following F-test was generated for the
AUTO83B.DAT data set. The data set
contains 480 ceramic strength measurements for two batches
of material. The summary statistics for each batch are
BATCH 1: NUMBER OF OBSERVATIONS = 240 MEAN = 688.9987 STANDARD DEVIATION = 65.54909 BATCH 2: NUMBER OF OBSERVATIONS = 240 MEAN = 611.1559 STANDARD DEVIATION = 61.85425We are testing the null hypothesis that the variances for the two batches are equal.
H0: σ12 = σ22 Ha: σ12 ≠ σ22The F test indicates that there is not enough evidence to reject the null hypothesis that the two batch variancess are equal at the 0.05 significance level.
The F-test can be used to answer the following
|Case Study||Ceramic strength data.|
|Software||The F-test for equality of two variances is available in many general purpose statistical software programs. Both Dataplot code and R code can be used to generate the analyses in this section. These scripts use the AUTO83B.DAT data file.|