M now press shuffle four more times does the number

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(m) Now press Shuffle four more times. Does the number of successes vary among the repetitions? (n) Enter 995 for the Number of shuffles . This produces a total of 1000 repetitions of the simulated random assignment process under the null hypothesis (the “null distribution”) . What is the value of the mean of this null distribution? Explain why this center makes intuitive sense. (o) Now we want to compare the observed result from the research study to these “could have been” results under the null hypothesis. x How many improvers were there in the Dolphin therapy group in the actual study? x Based on the resulting dotplot, does it seem like the actual experimental results would be surprising to arise solely from the random assignment process under the null model that dolphin therapy is not effective? Explain. (p) In the Count Samples box, enter the observed statistic from the actual study and press Count to have the applet count the number of repetitions with 10 or more successes in the Dolphin group. In what proportion of your 1000 simulated random assignments were the results as (or more) extreme as the actual study? (q) We said above that it would be equivalent to look at the difference in the conditional proportions. Use the Statistic pull-down menu (on far left side) to select Difference in proportions. How does the null distribution (including the mean) change? Does this make sense? How does the p-value change?
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Chance/Rossman, 2015 ISCAM III Investigation 3.6 214 (r) Interpret the p-value you found [ Hint : Same reasoning as before, but now also focus on the source of randomness that was modelled in the simulation.] (s) Is this empirical p-value small enough to convince you that the experimental data that the researchers obtained provide strong evidence that dolphin therapy is effective (i.e., that the null model is not correct)? (t) Is it reasonable to attribute the observed difference in success proportions to the dolphin therapy alone? Explain. (u) To what population is it reasonable to generalize these results? Justify your answer. Discussion : This procedure of randomly reassigning the response variable outcomes to the explanatory variable groups is often called a “randomization test.” The goal is to assess the chance variability from the random assignment process (as opposed to random sampling), though it is sometimes used to approximate the random chance arising from random sampling as well. Use of this procedure models the two-way table with fixed row and column totals (e.g., people were going to improve or not regardless of which treatment they received).
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Chance/Rossman, 2015 ISCAM III Investigation 3.6 215 Study Conclusions Due to the small p-value (0.01 < p-value < 0.05) from our “randomization test , we have moderately strong evidence that “luck of the draw” of the random assignment process alone is not a reasonable explanation for the higher proportion of subjects who substantially improved in the dolphin therapy group compared to the control group. Thus the researchers have moderate evidence that subjects aged 18
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