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A Repertoire of Hypothesis Tests

A Repertoire of Hypothesis Tests. z-test – for use with normal distributions and large samples. t-test – for use with small samples and when the pop std deviation is unknown. F-test (ANOVA) – for comparing means for multiple groups. Chi-square test – for use with qualitative data.

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A Repertoire of Hypothesis Tests

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  1. A Repertoire of Hypothesis Tests • z-test – for use with normal distributions and large samples. • t-test – for use with small samples and when the pop std deviation is unknown. • F-test (ANOVA) – for comparing means for multiple groups. • Chi-square test – for use with qualitative data.

  2. 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, chi-square, U, T, H). • This will be on the final exam.

  3. 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?

  4. Summary of t-tests • Single group t-test for one sample compared to a population mean. • Independent sample t-test – for comparing two groups in a between-subject design. • Paired (matched) sample t-test – for comparing two groups in a within-subject design.

  5. Summary of ANOVA Tests • One-way ANOVA – for one IV, independent samples • Repeated Measures ANOVA – for one or more IVs where samples are repeated, matched or paired. • Two-way (factorial) ANOVA – for two or more IVs, independent samples. • Mixed ANOVA – for two or more IVs, between and within subjects.

  6. 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.

  7. Summary of Qualitative Tests • Chi Square (c2) – 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.

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