1.
Exploratory Data Analysis
1.3. EDA Techniques 1.3.5. Quantitative Techniques


Purpose: Test if the variance is equal to a specified value 
A chisquare 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 twosided test or a onesided test. The twosided version tests against the alternative that the true variance is either less than or greater than the specified value. The onesided version only tests in one direction. The choice of a twosided or onesided 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.  
Definition 
The chisquare hypothesis test is defined as:
The formula for the hypothesis test can easily be converted to form an interval estimate for the variance:


ChiSquare Test Example 
A chisquare 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.
H_{0}: σ^{2} = 0.01 H_{a}: σ^{2} ≠ 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. 

Questions 
The chisquare test can be used to answer the following
questions:


Related Techniques 
F Test Bartlett Test Levene Test 

Software  The chisquare 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. 