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[Audio] KRUSKAL-WALLIS H TEST; FRIEDMAN TEST NON PARAMETRIC TEST VANISA C. INTELIGANDO.

[Audio] 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. We will discuss the Kruskal-Wallis H Test, a nonparametric test used to evaluate the difference between two or more groups. This test can determine if there is any statistically significant variation in a continuous or ordinal dependent variable when the independent variables are not known. It is the nonparametric alternative to the one-way ANOVA and is an extension of the Mann-Whitney U test, allowing comparison of more than two independent groups..

[Audio] 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. Kruskal-Wallis H test is a significant non-parametric test that permits us to evaluate multiple groups of data. Before using this test, we must make sure that our data fulfills four assumptions. These assessments are vital to guarantee that our results are legitimate. By taking the extra exertion to audit these assumptions, we can be certain that our data is being analysed accurately..

[Audio] ASSUMPTION #1 ASSUMPTION #2 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. Your independent variable should consist of two or more categorical, independent groups. Typically, a Kruskal-Wallis H test is used when you have three or more categorical, independent groups, but it can be used for just two groups (i.e., a Mann-Whitney U test is more commonly used for two groups). Example independent variables that meet this criterion include ethnicity (e.g., three groups: Caucasian, African American and Hispanic), physical activity level (e.g., four groups: sedentary, low, moderate and high), profession (e.g., five groups: surgeon, doctor, nurse, dentist, therapist), and so forth. The Kruskal-Wallis H Test and the Friedman Test are non-parametric tests used to compare the median differences between two or more independent groups. To be valid, these tests require that the dependent variable is measured at the ordinal or continuous level, such as a Likert scale or customer satisfaction with a product, and the independent variable consist of two or more categorical, independent groups, such as ethnicity, physical activity level and profession..

[Audio] ASSUMPTION #3 ASSUMPTION #4 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 order to know how to interpret the results from a Kruskal-Wallis H test, you have to determine whether the distributions in each group (i.e., the distribution of scores for each group of the independent variable) have the same shape (which also means the same variability). To understand what this means, take a look at the diagram below: The Kruskal-Wallis H test requires that observations used in the test come from independent sources and are collected from the same population. This is a study design issue rather than a statistical assumption that can be tested for, and if not met, a Friedman test should be used instead. To interpret the results of the Kruskal-Wallis test, it is essential to assess if the distributions of each group have the same shape and variability..

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[Audio] 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 previous slide, we discussed how the Kruskal-Wallis H test and Friedman test can be used to compare the medians or mean ranks depending on the shape of the distributions for the groups being compared. The next slide will discuss an inspiring example of never settling for less than one's best and believing in oneself even when the odds are stacked against them..

[Audio] 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. A medical researcher has heard anecdotal evidence that certain anti-depressive drugs can have the positive side-effect of lowering neurological pain in those individuals with chronic, neurological back pain, when administered in doses lower than those prescribed for depression. The medical researcher would like to investigate this anecdotal evidence with a study. The researcher identifies 3 well-known, anti-depressive drugs which might have this positive side effect, and labels them Drug A, Drug B and Drug C. The researcher then recruits a group of 60 individuals with a similar level of back pain and randomly assigns them to one of three groups – Drug A, Drug B or Drug C treatment groups – and prescribes the relevant drug for a 4 week period. At the end of the 4 week period, the researcher asks the participants to rate their back pain on a scale of 1 to 10, with 10 indicating the greatest level of pain. The researcher wants to compare the levels of pain experienced by the different groups at the end of the drug treatment period. The researcher runs a Kruskal-Wallis H test to compare this ordinal, dependent measure (Pain_Score) between the three drug treatments (i.e., the independent variable, Drug_Treatment_Group, is the type of drug with more than two groups). For this slide, I will be discussing the Kruskal-Wallis H test, a non-parametric test often used to compare ordinal data among various independent groups. This test was used in a study by a medical researcher who wanted to investigate the anecdotal evidence that certain anti-depressant drugs could help lower neurological pain in those individuals with chronic, neurological back pain. The researcher recruited 60 individuals with similar levels of back pain and randomly assigned them to one of the three drug treatments. They then rated their back pain on a scale of 1 to 10. To compare the levels of pain, the researcher ran a Kruskal-Wallis H test. This test helped the researcher compare the pain scores between the three drug treatments and determine which drug was most effective..

[Audio] Test Procedure in SPSS Statistics The eight steps below show you how to analyze your data using the Kruskal-Wallis H test in SPSS Statistics. 1. Click Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples... on the top menu as shown below: Kruskal-Wallis H Test, also known as Kruskal-Wallis one-way analysis of variance by ranks, is a nonparametric technique used to detect differences between several independent groups. It works by comparing the ranks of the groups to determine if there is a significant difference between them. This is particularly useful in cases where the assumptions of parametric tests are not viable. This slide provides an overview of how to analyze data using Kruskal-Wallis H Test in SPSS Statistics, which includes eight steps, beginning with clicking on Analyze, and Nonparametric Tests, Legacy Dialogs and K Independent Samples. Following these steps will lead you to successfully complete the analysis..

[Audio] button. You will end up with a screen similar to the one below: 2. Transfer the dependent variable, Pain_Score , into the Test Variable List: box and the independent variable, Drug_Treatment_Group, into the Grouping Variable: box. You can transfer these variables by either drag-and-dropping each variable into the appropriate boxes or by highlighting (i.e., clicking on) each variable and using the appropriate button. You will end up with a screen similar to the one below: You will be presented with the "Tests for Several Independent Samples" dialogue box, as shown below: Note: The Kruskal-Wallis H checkbox in the –Test Type– area should be selected by default, but if it is not, make sure to check this option. This option instructs SPSS Statistics to run a Kruskal-Wallis H test on the variables you are going to transfer in the next step of this procedure. Today I will discuss how to use the Kruskal-Wallis H Test and the Friedman Test. These two tests are Non-Parametric Tests, known for their reliance on qualitative data, rather than quantitative. These tests are used to compare the means of several independent samples, and can be conducted with the Assistance of the SPSS Statistics software. The first step is to open the Tests for Several Independent Samples Dialogue Box. In this dialogue box, you must then transfer the dependent variable, such as Pain Score, into the Test Variable List box and the independent variable such as Drug Treatment Group, into the Grouping Variable box. After making these transfers, you are ready to run the Non-Parametric Test of your choice..

[Audio] 3. Click on the button. You will be presented with the "Several Independent Samples: Define Range" dialogue box, as shown below: 4. Enter "1" into the Minimum: box and "3" into the Maximum box. These values represent the range of codes you gave the groups of the independent variable, Drug_Treatment_Group (i.e., Drug A was coded "1" through to Drug C which was coded "3"). You will end up with a screen similar to below: Note: If the button is not active (i.e., it looks faded like this ) ) make sure that the Drug_Treatment_Group variable is highlighted in yellow (as shown above in step 2) by clicking on it. This will activate the button. Note: If you had four groups (e.g., Drug A through Drug D) and only wanted to analyse Drug B through Drug D, you could enter "2" and "4" into the Minimum: and Maximum boxes, respectively (assuming you ordered the groups numerically). When looking at non-parametric tests, the Kruskal-Wallis H Test and Friedman Test are two important tests to consider. The Kruskal-Wallis H Test is used when there are multiple groups with two or more measurements associated with each, whereas the Friedman Test is used when you have one measurement associated with multiple groups. Both of these tests should only be used if the assumptions of parametric tests cannot be met, typically due to the data not being normally distributed. Using the SPSS software, it is necessary to set the range of codes within the independent variable in order to perform either test..

[Audio] 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: 6. Click on the button. You will be presented with the "Several Independent Samples: Options" dialogue box, as shown below: Discussing Kruskal-Wallis H Test, Friedman Test, and Non Parametric Tests, SPSS provides a Tests for Several Independent Samples dialogue box to enter the chosen Grouping Variable. This is followed by the Several Independent Samples: Options dialogue box, from which the options for the test can be selected..

[Audio] 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: 8. Click on the button. You will be returned to the “Test for Several Independent Samples" dialogue box 9. Click on the button. This will generate the results. For data that is not normally distributed, such as ordinal data, we should use a Nonparametric Test instead of a Parametric Test. For the Kruskal-Wallis H Test and the Friedman Test, we first need to select the Descriptive checkbox if we want descriptives and/or the Quartiles checkbox if we want medians and quartiles. Then click on the Define button. Afterwards, click on the Continue button to generate the results..

[Audio] You will be presented with the following output (assuming you did not select the Descriptive checkbox in the "Several Independent Samples: Options" dialogue box): The mean rank (i.e., the "Mean Rank" column in the Ranks table) of the Pain_Score for each drug treatment group can be used to compare the effect of the different drug treatments. Whether these drug treatment groups have different pain scores can be assessed using the Test Statistics table which presents the result of the Kruskal-Wallis H test. That is, the chi-squared statistic (the "Chi-Square" row), the degrees of freedom (the "df" row) of the test and the statistical significance of the test (the "Asymp. Sig." row). A Kruskal-Wallis H test showed that there was a statistically significant difference in pain score between the different drug treatments, χ2(2) = 8.520, p = 0.014, with a mean rank pain score of 35.33 for Drug A, 34.83 for Drug B and 21.35 for Drug C. We will discuss nonparametric tests for several independent samples, focusing on the Kruskal-Wallis H Test and Friedman Test. When interpreting the results in SPSS, we look at the Ranks Test Statistics table – this includes the chi-squared statistic, degrees of freedom and statistical significance of the test. To illustrate, consider an example with three drug treatments, A, B and C, and their effect on pain score. The Kruskal-Wallis H test showed a statistically significant difference in pain score between the treatments, with a mean rank pain score of 35.33 for Drug A, 34.83 for Drug B and 21.35 for Drug C. This example demonstrates the usefulness of the nonparametric tests on independent samples when assessing differences in dependent variables..

[Audio] 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 We are now discussing the Friedman Test, a non-parametric alternative to the one-way ANOVA with repeated measures. This test is useful when the data being measured is at an ordinal level, or when the data has deviated from normality and does not meet the criteria of the one-way ANOVA with repeated measures. The Friedman Test can provide powerful insights if traditional methods of analysis do not apply. Let's explore how this test can help..

[Audio] 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. Discussing the Kruskal-Wallis h-test and Friedman Test, two non-parametric tests used to compare two or more related groups, is the topic for today. To use these tests, it is vital to ensure that the data meets their assumptions - it must be ordinal, the samples must come from different populations and all the samples must be independent of each other. The distributions of the data and the sample sizes can be different..

[Audio] ASSUMPTION #2 ASSUMPTION #1 One group that is measured on three or more different occasions.. Group is a random sample from the population. ASSUMPTION #2 ASSUMPTION #4 Your dependent variable should be measured at the ordinal or continuous level. 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 5-point scale explaining how much a customer liked a product, ranging from "Not very much" 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. Samples do NOT need to be normally distributed. Without greetings, beginning with Today, or thanks: The KRUSKAL-WALLIS H Test and the Friedman Test are both non-parametric tests and the assumptions for them are similar. The first assumption is that groups measured on three or more occasions are random samples from a population. The second is that the dependent variable should be measured on the ordinal or continuous level. Examples of ordinal variables are Likert scales, while continuous variables include revision time, intelligence, exam performance, and weight. Samples do not need to be normally distributed..

[Audio] Example 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. Examining the effect of music on perceived psychological effort required to perform an exercise session, twelve runners were recruited to run three times on a treadmill each for 30 minutes at a consistent speed. Various music types, such as no music, classical music, and dance music, were used to measure the perceived effort as recorded on a scale of 1 to 10. The data from the experiment was used to carry out a Friedman test to determine whether there were any differences in perceived effort based on the type of music..

[Audio] Friedman Test Procedure in SPSS Statistics The 8 steps below show you how to analyze your data using the Friedman test in SPSS Statistics. 2. You will be presented with the Tests for Several Related Samples dialogue box, as shown below: 1. Click Analyze > Nonparametric Tests > Legacy Dialogs > K Related Samples... on the top menu, as shown below: From the top menu, select Analyze > Nonparametric Tests > Legacy Dialogs > K Related Samples. This will open the Tests for Several Related Samples dialogue box, enabling us to assess the differences between three or more independent groups. After opening the dialogue box, you will be guided through the 8 steps necessary to analyze data using the Friedman Test Procedure in SPSS Statistics..

[Audio] 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: 4. Make sure that Friedman is selected in the –Test Type– area. 5. Click on the button. You will be presented with the following Several Related Samples: Statistics dialogue box, as shown below: Transfer the variables none, classical, and dance to the Test Variables: box either by using the button or by dragging and dropping the variables. In the Test Type area, make sure that Friedman is selected. These are the third and fourth steps of carrying out a Friedman test on SPSS..

[Audio] 6. Tick the Quartiles option: 7. Click on the button. This will return you back to the Tests for Several Related Samples dialogue box, as shown below: 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. 8. Click on the button to run the Friedman test. We will be discussing the Kruskal-Wallis H Test, Friedman Test, and Vanisa C. Inteligando. To use this test in SPSS Statistics, the Quartiles option must be ticked. This is likely the only option needed due to the test's non-parametric nature. After ticking the option, press the Continue button, followed by OK to run the test..

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