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An overview of statistical tests for ranked data and non-normal distributions, including transformations and rank order tests. It covers the pros and cons of using nonparametric tests and discusses specific tests such as the mann-whitney u test and the wilcoxon t test. It also includes examples of calculating u and interpreting the results.

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2011/2012

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Download Choosing the Right Test for Non-normal Distributions in Behavioral Sciences and more Slides Behavioural Science in PDF only on Docsity! Statistics for the Behavioral Sciences Tests for Ranked Data, Choosing Statistical Tests Docsity.com What To Do with Non-normal Distributions Tranformations (pg 382): The shape of the distribution can be changed by applying a math operation to all observations in the data set. Square roots, logs, normalization (standardization). Rank order tests (pg 387): Use a nonparametric statistic that has different assumptions about the shape of the underlying distribution. Docsity.com When to Use Nonparametric Tests When the distribution is known to be non-normal. When a small sample (n < 10) contains extreme values. When two or more small samples have unequal variances. When the original data consists of ranks instead of values. Docsity.com Mann-Whitney Test (U Test) The nonparametric equivalent of the independent group t-test. Hypotheses: H0: Pop. Dist. 1 = Pop. Dist. 2 H1: Pop. Dist. 1 ≠ Pop. Dist. 2 The nature of the inequality is unspecified (e.g., central tendency, variability, shape). Docsity.com Calculating the U-Test Convert data in both samples to ranks. With ties, rank all values then give all equal values the mean rank. Add the ranks for the two groups. Substitute into the formula for U. U is the smaller of U1 and U2. Look up U in the U table. Docsity.com Testing U H0: Population distribution 1 = population distribution 2 H1: Population distribution 1 ≠ population distribution 2 Look up critical values in U Table. Instead of degrees of freedom, use n’s for the two groups to find the cutoff. Since 20 is larger than 10, retain the null (not reject). Docsity.com Interpretation of U U represents the number of times individual ranks in the lower group exceed those in the higher group. When all values in one group exceed those in the other, U will be 0. Reject the null (equal groups) when U is less than the critical U in the table. Docsity.com Directional U-Test Similar variance is required in order to do a directional U-test. The directional hypothesis states which group will exceed which: H0: Pop Dist 1 ≥ Pop Dist 2 H1: Pop Dist 1 < Pop Dist 2 In addition to calculating U, verify that the differences in mean ranks are in the predicted direction. Docsity.com A Repertoire of Hypothesis Tests z-test – for use with normal distributions when σ is known. t-test – for use with one or two groups, when σ is unknown. F-test (ANOVA) – for comparing means for multiple groups. Chi-square test – for use with qualitative data. Docsity.com Null and Alternative Hypotheses How you write the null and alternative hypothesis varies with the design of the study – so does the type of statistic. Which table you use to find the critical value depends on the test statistic (t, F, χ2, U, T, H). t and z tests can be directional. Docsity.com Deciding Which Test to Use Is data qualitative or quantitative? If qualitative use Chi-square. How many groups are there? If two, use t-tests, if more use ANOVA Is the design within or between subjects? How many independent variables (IVs or factors) are there? Docsity.com Summary of Nonparametric Tests Two samples, independent groups – Mann-Whitney (U). Like an independent sample t-test. Two samples, paired, matched or repeated measures – Wilcoxon (T). Like a paired sample t-test. Three or more samples, independent groups – Kruskal-Wallis (H). Like a one-way ANOVA. Docsity.com Summary of Qualitative Tests Chi Square (χ2) – one variable. Tests whether frequencies are equally distributed across the possible categories. Two-way Chi Square – two variables. Tests whether there is an interaction (relationship) between the two variables. Docsity.com