Variance Tests

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:06 While many of the hypothesis tests will focus on the mean of the data
• 00:10 sets being investigated, the variance can also be important.
• 00:14 Differences in variances can lead to a different hypothesis tests.
• 00:19 The test introduced in this lesson will analyze the variance when
• 00:23 using the data that is normal.
• 00:25 Once again, we start with the hypothesis test decision tree.
• 00:29 We have normal data and we have a combination of discrete and
• 00:32 continuous aspects of the data.
• 00:34 You can see that if there's more than one sample, the first thing we
• 00:38 want to do is to check the variance using the F Test or Bartlett's Test.
• 00:42 Let's spend a moment to discuss testing for variance.
• 00:46 When comparing data from different samples or sets of data,
• 00:49 there are normally two attributes we consider, the mean and the variance.
• 00:54 The mean is a measure of the average value.
• 00:56 Since we're talking about normal data,
• 00:59 it will be near the center of the distribution.
• 01:01 The variance is a measure of the spread or width of the data in the data sample.
• 01:06 The variance is clearly related to the standard deviation for that distribution.
• 01:11 In fact, the standard deviation is a square root of the variance.
• 01:15 Don't try to picture variance on the typical distribution plot like you would
• 01:20 picture a standard deviation.
• 01:21 Variance is in the units of standard deviation squared so
• 01:25 it really can't be placed on a single axis.
• 01:28 There are two tests used with normal data to check for variance.
• 01:31 The F test is commonly used when there are two sample sets of data.
• 01:35 And the Bartlett's test is when there are more than two sample sets.
• 01:40 The null hypothesis is that the variance of all the samples are the same.
• 01:44 There is nothing unique about any of the data.
• 01:46 The alternative hypothesis is that the variances are statistically different.
• 01:51 They are not equal.
• 01:53 Let's take a moment to consider equal and unequal variances.
• 01:57 Unequal variances may be a very good thing.
• 02:00 Depending upon your hypothesis, you may want to demonstrate unequal variances.
• 02:05 If you've put an improvement in a process that's supposed to reduce the variability
• 02:10 and uncertainty in the output, you would expect to see a reduction in variance,
• 02:14 although there may not be any impact on the mean or average value.
• 02:18 Unequal variance does not mean we can't continue on to test for
• 02:21 differences in the mean values of the data.
• 02:24 However, the two primary tests that we will be using, the T test and ANOVA,
• 02:28 require that we make an assumption about the equality and the variance because
• 02:33 the calculation is different depending upon whether the variances are equal.
• 02:38 This applies with both the XL and Minitab testing.
• 02:42 Generally speaking, we use the F-test when we will then go on to use the T-test for
• 02:46 the means.
• 02:47 And we use the Bartlett's test when we're going to be using the ANOVA test.
• 02:51 However, it's worth noting that Minitab will calculate both for you,
• 02:55 the result will be slightly different.
• 02:57 When in doubt, use a test for unequal variances.
• 03:01 Granted, the math is a little more difficult, but
• 03:03 it turns out the computer really isn't bothered by difficulty in algebra.
• 03:08 So let's start with the F test.
• 03:10 This test determines if the difference between the variance from two samples
• 03:14 are statistically significant.
• 03:15 The F statistic is the ratio of the two variances.
• 03:19 Excel does the F test by going to the Data Analysis menu on the data ribbon and
• 03:24 selecting the function F Test Two Sample for Variance.
• 03:28 Enter the data range for each of the two data sets.
• 03:31 You should enter the data range so that the sample that has the largest variance
• 03:36 is variable one, and the smaller variance is variable two.
• 03:40 Then compare the F ratio to the F critical value that is calculated based
• 03:45 upon the sample size.
• 03:46 If the F ratio is greater than F critical, then reject the null hypothesis.
• 03:51 This is similar to a P value of less than 0.05.
• 03:55 Minitab doesn't call the test the F test, rather,
• 03:58 it uses what it is doing for the title.
• 04:01 Go to the Stat pulldown menu, select Basic Statistics,
• 04:05 then select 2 variances which is about two-thirds way down the menu.
• 04:09 Select the format of your data in the data columns in the same manner that
• 04:13 we have been doing that with other tests.
• 04:15 Then use the Option button to bring up the second panel.
• 04:18 Ensure the hypothesis ratio is 1 and you can change your alternate
• 04:23 hypothesis to be greater than or less than instead of equal to.
• 04:27 Finally, check the box for normal data.
• 04:29 You'll get a P value and graphs that show the confidence interval for your variance.
• 04:34 Now let's consider the Bartlett's test.
• 04:37 Bartlett's test will compare the variance of two or
• 04:40 more sample data sets to determine if the variances are statistically different.
• 04:45 Excel does not perform the Bartlett's test, although you can do a similar
• 04:49 analysis by doing multiple F tests with each pair or combination of data sets.
• 04:54 So that if there are four data sets, you would do an F test with one and two,
• 04:59 one and three, one and four, then two and three, two and four, and
• 05:03 finally three and four.
• 05:04 The Bartlett's test in Minitab is very easy.
• 05:07 Select Stat, then ANOVA, and then select Test for Equal Variance.
• 05:13 Select the format of your data and
• 05:15 the data columns just as we had done on the other tests.
• 05:19 Again, use the option button to bring up the option form and check the box for
• 05:24 normal distribution.
• 05:25 The result is a p value and a plot showing the variance and the confidence interval.
• 05:33 In this example, the confidence interval for sample set three does not even come
• 05:37 close to overlapping with the other sample variances.
• 05:41 Therefore, the p value is zero and
• 05:44 we reject the null hypothesis of equal variances.
• 05:48 F test and Bartlett's test seldom provide the entire answer for hypothesis testing,
• 05:54 but they may be essential to know how best to complete the hypothesis testing.

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