Levene's Test & Mann-Whitney Test

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About this lesson

These tests are used when comparing two non-normal data samples. The Levene's Test checks for the variance and the Mann-Whitney checks the Medians. These tests are both standard tests in Minitab and the lesson will illustrate how to conduct them.

Quick reference

Levene's Test & Mann-Whitney Test

Levene’s Test and Mann-Whitney Test are hypothesis tests used for testing two non-normal data samples.  Levene’s Test checks the variance of the data sample and the Mann-Whitney Test checks the medians.

When to use

These tests are used for non-normal data sets.  They are appropriate for comparing the two sets to determine if there are statistically significant differences.  This helps to identify root cause factors for problems and to demonstrate the impact of implemented solutions.

Instructions

Levene’s Test

Levene’s Test is similar to the F Test or Bartlett’s Test that is used with normal data.  The variance, or spread, of two sets of sample data are compared to determine if they are statistically different.  The test can be set to check equality, greater than or less than relationships.

  • Minitab:
    1. Stat > Basic Statistics > 2 Variances
    2. Select the columns with the data, the order matters if doing a greater than or less than relationship.
    3. Use the Option button to change the type of relationship to be tested – default is equal/not equal. 
    4. Use the Option button to ensure that the normality box is not checked (checking the box will result in an F Test instead of Levene’s Test).

Mann-Whitney Test

The Mann-Whitney Test is similar to the Two-Sample T Test used with normal data.  The primary difference is that Mann-Whitney uses the median value since it is the preferred measure for central tendency with non-normal data.  The test can be to check for equal medians or to check whether one is greater than or less than the other.

  • Minitab:
    1. Stat > Nonparametrics > Mann Whitney
    2. Select the format of the data
    3. Select the columns with the data
    4. Select the relationship to be tested (equals, greater than, less than)
    5. The results are shown in the Session Window.  Minitab states the “the test is significant at .XXX”  This is the P Value for the test.

Hints & tips

  • The Levene’s Test provides a box plot that makes the differences between the data samples very clear.
  • Check your data for normality first.  If normal, use the F Test and Two-Sample T Test, if non-normal, use these tests. 
  • A small number of data points has a tendency to result in variances and medians with large confidence intervals.  This makes it more difficult to identify true differences.
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  • 00:05 Hi I'm Ray Sheen.
  • 00:06 Well, sticking non-normal data,
  • 00:08 now let's look at what we should do when we have two datasets.
  • 00:13 The Levene's test and
  • 00:14 the Mann-Whitney test can tell us if they are truly different.
  • 00:19 Going back into the hypothesis test decision tree,
  • 00:22 we see that when the data samples are non-normal and there are two of them,
  • 00:26 the best approach is to use the Levene's test, followed by the Mann-Whitney test.
  • 00:31 The Levene's test is for variances.
  • 00:34 Levene's test is similar to the F test or Bartlett's test, except that it's less
  • 00:38 sensitive and therefore is better suited for non-normal data.
  • 00:42 Levene's test will determine if the variances for
  • 00:45 two non-normal datasets are statistically equal or statistically different.
  • 00:49 Minitab will do this test at the same time that it does an F test for normal data.
  • 00:53 You may recall that the way we did this was to select the Stat pull-down menu,
  • 00:58 then select Basic Statistics and then select 2 variances.
  • 01:02 Be sure that the box for normal data in the option panel is not checked.
  • 01:07 That is the default value but if you've been doing F test and
  • 01:11 checking it, the box may still be checked when you attempt to do this test.
  • 01:15 The hypothesis are similar to the F test and Bartlett's test.
  • 01:19 The null hypothesis is that the variance for each sample are equal and
  • 01:22 the alternative hypothesis is that the variances are not equal.
  • 01:26 If your Lean Six Sigma problem was to reduce variation in a process with
  • 01:30 non-normal results, then the Levene's test is the most appropriate test to use.
  • 01:36 Now let's consider Mann-Whitney.
  • 01:37 The Mann-Whitney test is a non-parametric test that considers whether the medians
  • 01:42 from two samples are statistically different.
  • 01:45 The samples do not need to be normally distributed, nor
  • 01:48 do they need to have equal variances.
  • 01:51 This test is similar to the 2 Sample T-Test for normal data.
  • 01:54 Only that the T-Test uses the mean values, and this test uses the median values,
  • 01:59 since that is the more appropriate measure for non-normal data.
  • 02:03 A common use of this test is to determine
  • 02:05 if the median value of a non-normal process parameter has changed
  • 02:09 following the implementation of an improvement in the process.
  • 02:13 It can also be used to analyze problems in the same way a T-Test is used to determine
  • 02:18 when two samples should be considered to be from the same population or
  • 02:22 when they are statistically different.
  • 02:24 The null hypothesis is that the median for the two sample statistics are equal, and
  • 02:29 the alternative hypothesis is normally that one is greater than or
  • 02:33 less than the other.
  • 02:35 The Mann-Whitney test in Minitab is easy to conduct but
  • 02:38 there is a minor point of difference in the results that are presented.
  • 02:42 Conducting the test in Minitab follows our normal process.
  • 02:45 Select the Stat pull-down menu, then select Nonparametrics and
  • 02:49 select Mann-Whitney, this panel will appear.
  • 02:52 Then enter your data column and enter the alternative hypothesis operator.
  • 02:57 One point to note,
  • 02:58 you don't need to tell Mann-Whitney whether the variances are equal or not.
  • 03:01 From our standpoint in hypothesis testing, Levine's test is a standalone test for
  • 03:06 variance and Mann-Whitney is a standalone test for medium.
  • 03:10 Minitab will provide results in the session window.
  • 03:13 But here's a point that is a little bit squirrely.
  • 03:16 Minitab does not state a P value,
  • 03:18 instead, it says that the test is significant at a calculated value.
  • 03:23 For our purposes,
  • 03:24 we will use the calculated value in the same way as a P value.
  • 03:28 So in this case,
  • 03:30 the value is 0.4968 and we will fail to reject the null hypothesis.
  • 03:34 The median values from time 1 and time 2 are statistically equal.
  • 03:39 However, when we look at the median values from times 1 and
  • 03:42 time 3, we get a different answer.
  • 03:44 In this case, the test is significant at 0.0010.
  • 03:48 That is far below our P value threshold of 0.05.
  • 03:51 So we reject the null for this case.
  • 03:54 The median for time 1 and time 3 are not statistically equal.
  • 04:00 The Levene's test and the Mann-Whitney test do for
  • 04:02 non-normal data what the F test and the T test did for normal data.
  • 04:07 If you have no non-normal data, you'll be using these two tests.

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