Exploratory Data Analysis
1.3. EDA Techniques
1.3.5. Quantitative Techniques
Test if the variance is equal to a specified value
|A chi-square test ( Snedecor and Cochran, 1983) can be used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value. The one-sided version only tests in one direction. The choice of a two-sided or one-sided test is determined by the problem. For example, if we are testing a new process, we may only be concerned if its variability is greater than the variability of the current process.|
The chi-square hypothesis test is defined as:
The formula for the hypothesis test can easily be converted to form an interval estimate for the variance:
|Chi-Square Test Example||
A chi-square test was performed for the GEAR.DAT
data set. The observed variance for the 100 measurements of
gear diameter is 0.00003969 (the standard deviation is 0.0063).
We will test the null hypothesis that the
true variance is equal to 0.01.
H0: σ2 = 0.01 Ha: σ2 ≠ 0.01The test statistic value of 0.3903 is much smaller than the lower critical value, so we reject the null hypothesis and conclude that the variance is not equal to 0.01.
The chi-square test can be used to answer the following
|Software||The chi-square test for the variance 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 GEAR.DAT data file.|