Q 591. What is the purpose of a 2 Variance Test? What inferences can be drawn if the test shows that 2 data sets have different variances? Support your answer with an example.

 

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2 Variance test also known as F-test compares variances between two sample groups or data sets which come from the same population assuming data follows normal distribution. The distribution follows F distribution with two different degrees of freedom. Instead of means, it compares variances between two groups.

 

Purpose is to use this test to compare variances between two groups in different fields and domains. Example – Grading % of the exams between two sections – A & B can be compared for a particular class to check if there is any variation in the score.

 

Following are the inferences drawn if the data sets have different variances –

• Variance between the two data sets are different. One might have a higher or lower variance when compared to the other data set.
• Data spread are statistically different from one another though the values are independent to each other.

Test Name	2 Variance Test
Purpose	Two variances test helps us to determine whether the variances of two populations are the same. It uses in case variance of a process is of more important to compare than the process mean
Test shows that 2 data sets have different variances :  inferences	In Two variances test the hypothesis are Null hypothesis is Ho:  s1² = s2² means two populations have equal variances Alternate Hypothesis Ha :  s1² ≠ s2²  or s1² < s2²  or s1² > s2² , means two populations variance not equal If the test shows that 2 data sets have different variances, means the test statistic F which is the ratio s1²/s2² is deviates from 1, which shows the stronger evidence for unequal population variances. Means Null hypothesis that the two variances are same is rejected.
Example :	We need to find out whether there is difference between the mathematics exam grades as per the way the exams are conducted. Suppose each got the grade based on the same set of 20 exams, one of the teacher grades has the variance of 40 and another teacher got 25. Means this test will show that the first teacher’s variance is higher compared to 2nd teacher. Which is not expected for such exams.

The published answers are correct, however, there is no winner for this question.

 

The respondents have only highlighted one of the purposes - compare two variances. Another purpose is to determine the assumption for a 2 sample T test (variations are the same or variations are different).

 

Some of the not so common uses of 2 variance test

- confirm pre vs post improvement after a variation reduction project

- determine which data set is giving a smaller variation and hence a better performance (provided mean of both data sets is same)