Mood's Median, Kruskal-Wallis, and Friedman

Quick reference

• 00:04 Hello, I'm Ray Sheen.
• 00:06 Non-normal data can sometimes get really.
• 00:10 Fortunately, we have three different tests that we can use when we have various
• 00:15 non-normal data.
• 00:16 Those are the Mood's Median Test, the Kruskal-Walis Test, and
• 00:20 the Friendmann Test.
• 00:23 Once more for the Hypothesis Test Decision Tree.
• 00:26 We're still working with non-normal data, but now we want to consider the test for
• 00:30 the cases where there are two or more samples.
• 00:33 The first test is Mood's Median Test.
• 00:37 Mood's Median considers the quality of the medians form two or more data samples.
• 00:41 The Mood's Median is a quick and simple test, but
• 00:44 also has a few assumptions that must be met.
• 00:46 Mood's Median is most effective when data samples are independent, and
• 00:50 their distributions are roughly the same shape.
• 00:54 One distinctive advantage of Mood's Median Test is that it is robust with respect to
• 00:58 outliers in the data.
• 00:59 The hypothesis are straight forward.
• 01:01 The null hypothesis states that,
• 01:03 the medians of all the sample sets of data are statistically equal.
• 01:07 The alternative hypothesis says that, the medians are not equal.
• 01:11 Since there are multiple data sample sets, there's no designation for larger than or
• 01:15 smaller than, that we would use when there are only two data samples.
• 01:20 So let's look at setting this up on Minitab.
• 01:22 Use the Stat pulldown menu.
• 01:24 Select Nonparametrics, and then Mood's Median, and this panel will appear.
• 01:29 Mood's Median requires that all data from all the samples be in the same column.
• 01:34 However, there is a second column that has the sample designator
• 01:37 that is normally adjacent to the data column.
• 01:40 The easy way to create this column is just to stack the data from each of the samples
• 01:44 one above the other.
• 01:45 Meaning, to actually do this quickly for
• 01:47 you using the stack command under the data pull down menu.
• 01:51 So enter the column name with the data in the response field and
• 01:55 the column name with data sample identifier in the factor entry box.
• 02:01 Now, let's look at the Kruskal-Wallis.
• 02:03 Think of Kruskal-Wallis like it is an advanced version of ANOVA
• 02:07 that works well with non-normal data.
• 02:10 There are some key data sample set characteristics
• 02:13 that must be met when using Kruskal-Wallis.
• 02:15 Again, the data samples should be independent.
• 02:18 The data should be continuous data as compared with discrete data.
• 02:21 However, the data sample sets do not need to have the same shape or distribution.
• 02:26 So in that regard, it has an advantage over Mood's median, but it is sensitive to
• 02:31 outliers so in that characteristic, Mood's median has the advantage.
• 02:35 The hypothesis statements are the same as we had with Mood's median test.
• 02:39 The null hypothesis state that, the medians are statistically equal and
• 02:42 the alternative hypothesis states that they are not equal to each other.
• 02:46 During the Kruskal-Wallis test in Minitab is very similar to that of
• 02:50 the Moods Median Test.
• 02:51 Go to the Stat pulldown menu, select Nonparametrics, and
• 02:54 then select Kruskal-Wallis and this panel will pop up.
• 02:58 And just like with Mood's median, all the data must be in the same column and
• 03:02 the adjacent column should have the factor
• 03:05 that is being used to designate the sample subsets.
• 03:08 Each of these columns are entered into your appropriate field in minitab.
• 03:12 And now for the Friedman test.
• 03:14 The Friedman test is a bit weird,
• 03:16 it works with blocks of paired non normal data groups.
• 03:19 Think of it as a hybrid of ANOVA, paired T-Test and Kruskal-Wallis.
• 03:24 With all of its doing, Friedman need samples with many data points,
• 03:29 a minimum of 30 and more is better.
• 03:31 The Null Hypothesis and
• 03:33 Alternative Hypothesis are the same with Moods Median and Kruskal-Wallis.
• 03:37 The null is that the medians are equal, and
• 03:39 the alternative is that they are not statistically equal.
• 03:43 Minitab is a little bit different.
• 03:45 You still start the same way, go to the Stat pulldown menu, select Nonparametrics,
• 03:49 and then select Friedman, and this is the panel you get.
• 03:53 Once again, all the data is in the same column, but
• 03:56 now you have one column with the sample category data designator or
• 04:01 treatment, and one with the block data designator.
• 04:04 You can probably guess that this test is used primarily with
• 04:07 clinical test of medical treatments and pharmaceuticals.
• 04:10 But you may have a need for it in a Lean Six Sigma project.
• 04:14 If working across multiple locations or
• 04:16 product lines on your project, just designate the appropriate columns.
• 04:21 So let's compare the results of these three tests.
• 04:23 In this case,
• 04:24 I'm using the time trials from the luge event in the 2014 Winter Olympics.
• 04:29 There are four trials and the data is not normally distributed.
• 04:33 Mood's Median shows that the median of each of the four trials
• 04:37 along with the confidence internal on a small scale in the session window.
• 04:41 The P value was 0.001.
• 04:44 Reject the null hypothesis.
• 04:46 Each trial was definitely different.
• 04:47 Kruskal-Wallis shows the median values and average rank.
• 04:52 The ranking clearly shows that the times and samples one and
• 04:55 two are higher than with samples three and four.
• 04:59 Again, the P value is very low, in this case it's zero, so
• 05:02 reject the null hypothesis.
• 05:04 The Friedman Test also shows the median.
• 05:07 Interestingly, and I don't know why, it has an additional significant digit
• 05:11 showing In this test result the sum of ranks which is a ranks measure adjusted
• 05:16 for the Friedman Block characteristic still shows that time trials one and
• 05:20 two are much different than three and four.
• 05:23 And again our P value is 0.
• 05:25 So reject the null, but let me point out
• 05:28 the Friedman Test did the time versus trial and block by the competitor.
• 05:32 In other words, the dominant characteristic is the trial and
• 05:35 competitor blocks were used to minimize the effect of good teams versus bad teams.
• 05:40 But now in this result, I switched the trial and
• 05:43 the competitor between the treatment and block parameters.
• 05:46 We have a very different result.
• 05:47 The data is the same, but in this case there will be a median for
• 05:52 each competitor.
• 05:53 I just left some off the sheet for readability, and there's a rank for
• 05:57 each competitor, notice that the P value is 0.572, so
• 06:01 we will fail to reject the null hypothesis in this case, but that's
• 06:05 because the hypothesis between these two runs of Freedman Test is different.
• 06:10 In the first case the null hypothesis is at the median time in each trial is
• 06:15 the same.
• 06:16 In the second case the null hypothesis is st the median time for
• 06:20 each competitor was the same..
• 06:22 While there is another concern with the compliment test, there are only four data
• 06:26 points for each competitor, and we did say we needed at least 30 points.
• 06:30 So the test should be considered invalid until more trials are conducted, and
• 06:34 the times recorded.
• 06:36 Regardless of the nature of your non-normality,
• 06:39 there will be in a hypothesis test that will work for you.
• 06:43 Look at your data, and then decide whether to use the Mood's Median, Kruskal-Wallis,
• 06:48 or the Friedmann test.

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