Mood’s Median, Kruskal-Wallis, Friedman Tests

Quick reference

• 00:04 Hello, I'm Ray Sheen.
• 00:05 Non-normal data sets can sometimes get really squirrely.
• 00:09 Fortunately, we have three tests for use with multiple non-normal data sets,
• 00:15 and different ones apply to different squirrely conditions.
• 00:19 Those tests are the Mood's Median test, Kruskal-Wallis test and Friedman's test.
• 00:27 >> Once more for the hypothesis test decision tree,
• 00:30 we are still working with non-normal data.
• 00:33 And now we want to consider the tests for cases when there are two or more samples.
• 00:39 The first test to discuss is Mood's median test.
• 00:42 Mood's median considers the equality of the medians from two or more data samples.
• 00:48 The Mood's median is a quick and simple test, but
• 00:51 it also has a few assumptions that must be met.
• 00:55 Mood's median is most effective when data samples are independent and
• 00:58 the distributions are roughly the same shape.
• 01:02 One distinct advantage of the Mood's median test is that it is robust with
• 01:06 respect to outliers in the data.
• 01:09 The hypotheses are straightforward.
• 01:11 The null hypothesis states that the medians of all
• 01:14 the sample sets are statistically equal.
• 01:18 The alternative states that one or more of the medians are not equal.
• 01:22 Since there are multiple data samples, there's no designation of larger than or
• 01:26 smaller than that we use when there are only two data samples.
• 01:29 So let's look at setting this up on our Minitab.
• 01:32 Use the stat pull-down menu, select Non-parametric and then Mood's median, and
• 01:37 this panel will appear.
• 01:39 Mood's median requires that the data from all the samples be in the same column.
• 01:44 However, there is a second column that has the sample designator that is
• 01:49 normally adjacent to the data column.
• 01:52 The easy way to create this column is to just stack your data from one sample below
• 01:57 the previous sample.
• 01:59 Minitab will actually do this quickly for
• 02:02 you using the stack command under the data pulldown menu.
• 02:06 So under the column name with the data, in the response field and
• 02:10 the column name with the data sample identifier and the factor entry box.
• 02:16 Now let's look at Kruskal-Wallis.
• 02:18 Think of Kruskal Wallis like it is an advanced version of
• 02:21 ANOVA that works well with non-normal data.
• 02:24 There are some key data sample set characteristics that must be met when
• 02:27 using Kruskal-Wallis.
• 02:29 Again the data samples should be independent,
• 02:32 the data should be continuous data as compared to discrete data.
• 02:36 However, the data sample sets do not need to have the same shape or distribution.
• 02:41 So in that regard, they have an advantage over Mood's median.
• 02:45 But it is sensitive to outliers, so in that way Mood's median has the advantage.
• 02:51 The hypothesis statements are the same as with Mood's median test.
• 02:55 The null hypothesis states that the medians are statistically equal and
• 02:59 the alternative hypothesis states that they are not equal to each other.
• 03:04 Doing the Kruskal Wallis in Minitab is very similar to Mood's median test.
• 03:08 Go to the stat pulldown menu, select Nonparametric, and
• 03:12 then select Kruskal-Wallis, and this panel will pop up.
• 03:15 Just like with the Mood's median, all the data must be in the same column and
• 03:20 adjacent column should have the factor that is being used to designate the sample
• 03:25 subsets.
• 03:26 Each of these columns are entered into the appropriate field in Minitab.
• 03:31 And now for the Friedman test.
• 03:33 The Friedman test is a bit weird.
• 03:35 It works with blocks of paired non-normal data groups.
• 03:39 Think of it as hybrid of ANOVA, paired t-test and Kruskal-Wallis.
• 03:44 With all that it's doing, Friedman needs samples with many data points,
• 03:49 a minimum of 30 and more is better.
• 03:51 The null hypothesis and
• 03:53 alternative hypothesis are the same as with Mood's median and Kruskal-Wallis.
• 03:58 The null is that the medians are equal, and
• 04:00 the alternative is that they are statistically not equal.
• 04:04 Minitab is a bit different.
• 04:06 You start at the same, go to the stat pull down menu, select Nonparametric,
• 04:10 and then select Friedman, and this is the panel you get.
• 04:13 Once again, all the data is in the same column, but
• 04:16 now you have one adjacent column with the sample category designator or
• 04:21 treatment, and one with the block designator.
• 04:23 You can probably guess this test is often used with clinical trials of medical
• 04:28 treatments and pharmaceuticals, but you may have a need for
• 04:32 it in Lean Six Sigma projects if working across multiple locations or
• 04:36 product lines on your project.
• 04:38 Just designate all the appropriate columns.
• 04:42 So let's consider the result of these three tests.
• 04:46 In this case,
• 04:47 I'm going to be using time trials from the luge event at the 2014 Winter Olympics.
• 04:52 There are four trials and the data is not normally distributed.
• 04:56 Mood's median shows the median of each of the four trials along with a confidence
• 05:01 interval on a small scale in the session window.
• 05:04 The P value was 0.001, reject the null hypothesis.
• 05:09 Each trial was definitely different.
• 05:11 Kruskal-Wallis also shows the median values and an average rank.
• 05:16 The ranking clearly shows that the times in samples 1 and
• 05:20 2 are higher than with samples 3 and 4.
• 05:23 Again, P value is very low, in this case it's 0.
• 05:26 So reject the null hypothesis.
• 05:29 The Friedman's test also shows the median value, and
• 05:32 I don't know why it has an additional significant digit showing.
• 05:36 In this test result, the sum of ranks, which is a ranks measure adjusted for
• 05:41 the Friedman block characteristics, still shows the time trials 1 and
• 05:46 2 were much different from 3 and 4, and again, the P value is 0.
• 05:50 So reject the null hypothesis.
• 05:53 But let me point out that this Friedman test divided time versus trial and
• 05:57 block by competitor.
• 05:59 In other words, the dominant characteristic is the trial and competitor
• 06:05 blocks were used to minimize the effects of good teams versus bad teams.
• 06:10 In this result, I switch trial and competitor between the treatment and
• 06:14 block parameter.
• 06:15 We have a very different result.
• 06:18 In this case, there will be a median for each competitor.
• 06:22 I just left some off the sheet for readability, and there is a rank for
• 06:26 each competitor.
• 06:28 Notice that the P value is 0.572.
• 06:31 So we would fail to reject the null hypothesis in this case.
• 06:34 But that's because the hypotheses between these two runs of the Friedman test is
• 06:39 different.
• 06:41 In the first one,
• 06:42 the null hypothesis is that the median time in each trial is the same.
• 06:47 In the second case, the null hypothesis is that the median time for
• 06:52 each competitor is the same.
• 06:55 There's another concern with the second Friedman test.
• 06:58 There are only four data points for each competitor, and
• 07:01 we said that we needed at least 30 points.
• 07:04 So this version of the test should be considered invalid until more time
• 07:09 trials are conducted and the times recorded.
• 07:13 >> Regardless of the nature of your non-normality,
• 07:16 there will be a hypothesis test that will work.
• 07:19 Look at your data, and then select either Mood's median, Kruskal-Wallis, or
• 07:23 Friedman's tests.

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