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A Repertoire of Hypothesis Tests

Explore a detailed repertoire of hypothesis tests including z-test, t-test, F-test (ANOVA), and Chi-square test. Learn to craft null and alternative hypotheses based on the study design and select the appropriate test statistic. Discover how to decide which test to use based on data type, number of groups, and study design. Dive into summaries of t-tests, ANOVA tests, nonparametric tests, and qualitative tests to conduct accurate statistical analyses. Prepare for your final exam with essential insights on hypothesis testing.

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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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