Statistical Inference - Simulation of the null distribution
Also recall from the pre-lab, the null and alternative hypotheses for this study:
Ho:
opt-in =
Ha: at least one
To assess the strength of evidence against the null hypothesis, we want to recreate the random assignment process but where the group assignment has no impact on the response variable outcome. For example, we could put each response output (agree to be donor or not) on an index card, shuffle the cards, and deal them out to three groups (sample sizes 55, 50, 56). Then compute the MAD of the shuffled data for each hypothetical random assignment. Keep in mind that this MAD statistic will get larger the more the conditional proportions differ.
- In the applet, check the Show Shuffle Options box.
- Press Shuffle. Notice that the first column hasn't changed, but that the response variable outcomes are now mixed up/re-assgined to those explanatory variable groups.
- Select the Plot radio button.
(b) How does the segmented bar graph for the shuffled data compare to the segmented bar graph for the actual research study? How does the shuffled MAD statistic (in blue below) compare?
(c) Press the Shuffle button 4 more times and watch how the segmented bar graph changes. Do the simulated statistics tend to be larger or smaller than what you calculated for the actual research study?
(d) Now set the number of repetitions to 995 (for 1000 total) and press the Shuffle button. Next, use the applet to determine an estimate for the p-value for this research study by entering an appropriate direction and value in the Count Samples box. Include a screen capture of the null distribution with count output displayed.
