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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?
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
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?
Chi-Square Test for Goodness-of-Fit
> Nonparametric test when we have one nominal variable
> The six steps of hypothesis testing1. Identify
2. State the hypotheses
3. Characteristics of the comparison distribution
4. Critical values
5. Calculate
6. Decide
> 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
> 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
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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