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KRUSKAL-WALLIS H TEST; FRIEDMAN TEST. NON PARAMETRIC TEST.

KRUSKAL-WALLIS H TEST. The Kruskal-Wallis H test (sometimes also called the "one-way ANOVA on ranks") is a rank-based nonparametric test that can be used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable. It is considered the nonparametric alternative to the one-way ANOVA, and an extension of the Mann-Whitney U test to allow the comparison of more than two independent groups..

ASSUMPTIONS. When you choose to analyse your data using a Kruskal-Wallis H test, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a Kruskal-Wallis H test. You need to do this because it is only appropriate to use a Kruskal-Wallis H test if your data "passes" four assumptions that are required for a Kruskal-Wallis H test to give you a valid result. In practice, checking for these four assumptions just adds a little bit more time to your analysis, requiring you to click a few more buttons in SPSS Statistics when performing your analysis, as well as think a little bit more about your data, but it is not a difficult task..

ASSUMPTION #1. Your dependent variable should be measured at the ordinal or continuous level (i.e., interval or ratio). Examples of ordinal variables include Likert scales (e.g., a 7-point scale from "strongly agree" through to "strongly disagree"), amongst other ways of ranking categories (e.g., a 3-pont scale explaining how much a customer liked a product, ranging from "Not very much", to "It is OK", to "Yes, a lot"). Examples of continuous variables include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth. You can learn more about ordinal and continuous variables in our article: Types of Variable..

ASSUMPTION #3. You should have independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you can test for, but it is an important assumption of the Kruskal-Wallis H test. If your study fails this assumption, you will need to use another statistical test instead of the Kruskal-Wallis H test (e.g., a Friedman test). If you are unsure whether your study meets this assumption, you can use our Statistical Test Selector, which is part of our enhanced content..

In the diagram on the left above, the distribution of scores for the "Caucasian", "African American" and "Hispanic" groups have the same shape. On the other hand, in the diagram on the right above, the distribution of scores for each group are not identical (i.e., they have different shapes and variabilities). If your distributions have the same shape, you can use SPSS Statistics to carry out a Kruskal-Wallis H test to compare the medians of your dependent variable (e.g., "engagement score") for the different groups of the independent variable you are interested in (e.g., the groups, Caucasian, African American and Hispanic, for the independent variable, "ethnicity"). However, if your distributions have a different shape, you can only use the Kruskal-Wallis H test to compare mean ranks. Having similar distributions simply allows you to use medians to represent a shift in location between the groups (as illustrated in the diagram on the left above). As such, it is very important to check this assumption or you can end up interpreting your results incorrectly..

IN THE Test Procedure in SPSS Statistics, we illustrate the SPSS Statistics procedure to perform a Kruskal-Wallis H test assuming that your distributions are not the same shape and you have to interpret mean ranks rather than medians. First, we set out the example we use to explain the Kruskal-Wallis H test procedure in SPSS Statistics..

1. Click Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples... on the top menu as shown below:.

You will be presented with the "Tests for Several Independent Samples" dialogue box, as shown below:.

3. Click on the button. You will be presented with the "Several Independent Samples: Define Range" dialogue box, as shown below:.

5. Click on the button and you will returned to the "Tests for Several Independent Samples" dialogue box, but now with a completed Grouping Variable: box, as highlighted below:.

7. Select the Descriptive checkbox if you want descriptives and/or the Quartiles checkbox if you want medians and quartiles. If you selected the Descriptives option, you will be presented with the following screen:.

You will be presented with the following output (assuming you did not select the Descriptive checkbox in the "Several Independent Samples: Options" dialogue box):.

FRIEDMAN TEST. Unlike Kruskal-Wallis H test the Friedman Test is the non-parametric alternative to the one-way ANOVA with repeated measures. It used to test for difference between groups when the dependent variable being measured is ordinal. It can also be used for continuous data that has violated the assumptions necessary to run the one-way ANOVA with repeated measures (e.g., data that has marked deviations from normality.

ASSUMPTIONS. When you choose to analyse your data using a Friedman test, part of thye process involves checking to make sure that the data you want to analyse can actually be analysed using a Friedman test. Thus your data needs to pass the following assumptions to use the Friedman test..

ASSUMPTION #1. One group that is measured on three or more different occasions...

A researcher wants to examine whether music has an effect on the perceived psychological effort required to perform an exercise session. The dependent variable is "perceived effort to perform exercise" and the independent variable is "music type", which consists of three groups: "no music", "classical music" and "dance music". To test whether music has an effect on the perceived psychological effort required to perform an exercise session, the researcher recruited 12 runners who each ran three times on a treadmill for 30 minutes. For consistency, the treadmill speed was the same for all three runs. In a random order, each subject ran: (a) listening to no music at all; (b) listening to classical music; and (c) listening to dance music. At the end of each run, subjects were asked to record how hard the running session felt on a scale of 1 to 10, with 1 being easy and 10 extremely hard. A Friedman test was then carried out to see if there were differences in perceived effort based on music type..

Friedman Test Procedure in SPSS Statistics The 8 steps below show you how to analyze your data using the Friedman test in SPSS Statistics..

3.Transfer the variables none, classical and dance to the Test Variables: box by using the button or by dragging-and-dropping the variables into the box. You will end up with the following screen:.

6. Tick the Quartiles option:. Note: It is most likely that you will only want to include the Quartiles option as your data is probably unsuitable for Descriptives (i.e., why you are running a non-parametric test). However, SPSS Statistics includes this option anyway..

Reporting the Output of the Friedman Test (without post hoc tests) You can report the Friedman test result as follows: General There was a statistically significant difference in perceived effort depending on which type of music was listened to whilst running, χ2(2) = 7.600, p = 0.022..

• • To examine where the differences actually occur, you need to run separate iMIcoxon siqned-rank tests on the different combinations of related groups. So, in this example, you would compare the following combinations: None to Classical None to Dance- Classical to Dance- You need to use a Bonferroni adjustment on the results you get from the VViIcoxon tests because you are making multiple comparisons, which makes it more likely that you will declare a result significant when you should not (a Type I error). Luckily, the Bonferroni ac%ustment is very easy to calculate; simply take the significance level you were initially using (in this case, 0.05) and divide it by the number of tests you are running. So in this example, we have a new significance level of 0.05/3 = 0.017. This means that if the p value is larger than 0.017, we do not have a statistically significant result- Running these tests (see how with our Wilcoxon siqned-rank test guide) on the results from this example, you get the following result: Test Statistics z Asymp. Sig. (2-tailed) classical - none --061 a .952 dance - none -2.636 008 dance - classical -1 .81 1 a .070 a. Based on positive ranks. b. VVilcoxon Signed Ranks Test.

There was a statistically significant difference in perceived effort depending on which type of music was listened to whilst running, χ2(2) = 7.600, p = 0.022. Post hoc analysis with Wilcoxon signed-rank tests was conducted with a Bonferroni correction applied, resulting in a significance level set at p < 0.017. Median (IQR) perceived effort levels for the no music, classical and dance music running trial were 7.5 (7 to 8), 7.5 (6.25 to 8) and 6.5 (6 to 7), respectively. There were no significant differences between the no music and classical music running trials (Z = -0.061, p = 0.952) or between the classical and dance music running trials (Z = -1.811, p = 0.070), despite an overall reduction in perceived effort in the dance vs classical running trials. However, there was a statistically significant reduction in perceived effort in the dance music vs no music trial (Z = -2.636, p = 0.008)..

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