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Chi Square Tests Chapter 17

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Nonparametric Statistics >A special class of hypothesis tests >Used when assumptions for parametric tests are not met Review: What are the assumptions for parametric tests?

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When to Use Nonparametric Tests >When the dependent variable is nominal What are ordinal, nominal, interval, and ratio scales of measurement? >Used when either the dependent or independent variable is ordinal >Used when the sample size is small >Used when underlying population is not normal

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Limitations of Nonparametric Tests >Cannot easily use confidence intervals or effect sizes >Have less statistical power than parametric tests >Nominal and ordinal data provide less information >More likely to commit type II error Review: What is type I error? Type II error?

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Chi-Square Test for Goodness- of-Fit >Nonparametric test when we have one nominal variable >The six steps of hypothesis testing 1. Identify 2. State the hypotheses 3. Characteristics of the comparison distribution 4. Critical values 5. Calculate 6. Decide

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Formulae

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Determining the Cutoff for a Chi-Square Statistic

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Making a Decision

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>Evenly divided expected frequencies Can you think of examples where you would expect evenly divided expected frequencies in the population? A more typical Chi-Square

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>Chi-square test for independence Analyzes 2 nominal variables The six steps of hypothesis testing 1. Identify 2. State the hypotheses 3. Characteristics of the comparison distribution 4. Critical values 5. Calculate 6. Decide

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The Cutoff for a Chi-Square Test for Independence

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The Decision

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Cramer’s V (phi) >The effect size for chi-square test for independence

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Graphing Chi-Squared Percentages

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Relative Risk >We can quantify the size of an effect with chi square through relative risk, also called relative likelihood. >By making a ratio of two conditional proportions, we can say, for example, that one group is three times as likely to show some outcome or, conversely, that the other group is one-third as likely to show that outcome.

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Adjusted Standardized Residuals >The difference between the observed frequency and the expected frequency for a cell in a chi-square research design, divided by the standard error; also called adjusted residual.

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