- Complete a randomization test involving a difference in proportions
Simulation-based Hypothesis Tests
All simulation-based hypothesis tests follow the same general steps:
- Set up the null and alternative hypotheses based on the research question.
- Simulate a large number of samples (usually [latex]1,000[/latex] or more) under the assumption of the null hypothesis, calculating a sample statistic for each simulated sample.
- Plot the simulated sample statistics with a histogram and compare the original observed statistic to the plot.
- The proportion of simulated statistics as or more extreme than observed is the estimated P-value.
Let’s simulate a large number of samples under the assumption of the null hypothesis using the statistical tool below.
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- Select “Contingency Table” under “Enter Data.”
- Type “Peanut” for the row variable, with “Avoiders” and “Eaters” for the category labels.
- Type “Conditions” for the column variable, with “Allergic” and “Not allergic” as the category labels.
- Enter the table below:
| Allergic | Not allergic | |
| Peanut avoiders | 35 | 220 |
| Peanut eaters | 5 | 240 |
Step 2: Now select “Permutation Distribution” in the top right. You should see the contingency table you entered as the “Observed Contingency Table.” Check “Conditions” under “Permutate Labels of” and then generate a [latex]1000[/latex] permutation of the data.
Step 3: The plot of the simulated differences in proportion can be found at the bottom of the “Permutation Distribution” tab. This plot is called a simulated null distribution of differences in sample proportions.
Optional: You may use the “Change binwidth of histogram” and adjust the sliders to create a more detailed histogram by selecting a smaller binwidth.