Workshop on Data Analysis and Result Interpretation in Social Science Research Day 03-non-parametric tests-presentation
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This document defines and provides examples of several non-parametric tests: Mann-Whitney U test, Kruskal-Wallis H test, Mood's median test, and Friedman test. The Mann-Whitney U test compares two independent groups on a continuous or ordinal dependent variable. The Kruskal-Wallis H test compares three or more independent groups. Mood's median test compares the medians of two independent groups. The Friedman test compares three or more related groups on a continuous or ordinal dependent variable. Examples of using each test are also provided.
Workshop on Data Analysis and Result Interpretation in Social Science Research Day 03-non-parametric tests-presentation
- 1. NON-PARAMETRIC TEST (a)Mann Whitney U test (b) Median Test ( c) Kruskal Wallis H Test (d) Friedman Test
- 2. Non-parametric tests • Non-parametric tests are used when continuous data are not normally distributed or when dealing with discrete variables. • Most widely used are chi-squared, Fisher's exact tests, Wilcoxon's matched pairs, Mann–Whitney U-tests, Kruskal–Wallis tests and Spearman rank correlation.
- 5. Appropriate data • Two-sample data. That is data with two groups only • Dependent variable is ordinal, interval, or ratio •Independent variable is a factor with two levels. That is two groups •Observations between groups are independent. That is not paired or repeated measures data
- 6. Hypotheses • Null hypothesis: The two groups are sampled from populations with identical distributions. Typically, that the sampled populations show stochastic equality. • Alternative hypothesis (two-sided): The two groups are sampled from populations with different distributions. Typically, that one sampled population exhibits stochastic dominance.
- 7. Interpretation Significant results can be reported as e.g. “Values for group A were significantly different from those for group B.” Other notes and alternative tests The Mann–Whitney U test can be considered equivalent to the Kruskal–Wallis test with only two groups.
- 8. Two-sample Mann–Whitney U test- example • Are B.Ed.-General scores significantly different from those of B.Ed.-Special? • The Mann–Whitney U test is conducted with the wilcox.test function, which produces a p- value for the hypothesis.
- 9. Kruskal-Wallis Test • A collection of data samples are independent if they come from unrelated populations and the samples do not affect each other. • Using the Kruskal-Wallis Test, we can decide whether the population distributions are identical without assuming them to follow the normal distribution. Example • The daily air quality measurements in Delhi, November to March, are recorded. The ozone density are presented in the data frame column Ozone.
- 10. Mood’s Median Test • Mood’s median test is used to compare the medians for two samples drawn from different populations to find out if they are different. • For example- you might want to compare the median number of positive calls to a hotline vs. the median number of negative comment calls to find out if you’re getting significantly more negative comments than positive comments (or vice versa).
- 11. Population 1 Population 2 Sample-1 Sample-2
- 12. Continue- • This test is the nonparametric. - Nonparametric means that you don’t have to know what distribution your sample came from (i.e. a normal distribution) before running the test. • Samples should have been drawn from distributions with the same shape. • The null hypothesis for this test is that the medians are the same for both groups. • The alternate hypothesis for the test is that the medians are different for both groups.
- 13. Results for The Test • Like most hypothesis tests, your results will include a p-value and an alpha level (usually 5% or 0.05). • If your p-value is less than or equal to alpha, the medians are different and you can reject the null hypothesis that they are the same.
- 14. Friedman test • The Friedman test is the non-parametric alternative to the one-way ANOVA with repeated measures. • It is used to test for differences 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).
- 15. Assumptions • One group that is measured on three or more different occasions. • Group is a random sample from the population.
- 16. • 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. • Samples do NOT need to be normally distributed.
- 17. 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.