Validity conditions or how large does n need to be

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VALIDITY CONDITIONS OR "HOW LARGE DOES N NEED TO BE?“ (ACCORDING TO THIS BOOK) Validity conditions: A rule of thumb is there needs to be at least 10 successes and 10 failures in the sample. St. George Example 10 heart transplants # of successes? (i.e. patient died) # of failures? (i.e. patient lived) Are the validity conditions met? 8 resulted in death of patient
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SUMMARY If you want to use Theory Based approach Need a sample size large enough , in order to say the null will follow the Normal Distribution Applet – Normal approximation button Will calculate the p-value for us Can calculate Standardized statistic by hand Doesn’t always work If the sample size is small … null distribution will not be approximately bell-shaped and the resulting normal approximation p-value and standardized statistics are not accurate Simulation ALWAYS works
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HUSKERS EXAMPLE Hypotheses Variable of Interest: Football or Volleyball (Categorical) Parameter & Symbol: The long run proportion of husker fans who prefer football. () Statistic & Symbol: = Can theory based method be used? (i.e. validity conditions met?) Yes because successes (selecting football)and failures (selecting volleyball) Research Question: Do husker fans show a preference for football over volleyball? Researchers took a sample of 283 husker fans and found that 148 preferred to go to a football game over a volleyball game.
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HUSKERS EXAMPLE Find the standardized statistic using theory-based and simulation approach. Theory Standard Deviation of the Null = = 0.0297 Standardized Statistic = Simulation Standardized Statistic = Do we have evidence that husker fans have preference for football? No, we do not have evidence to conclude that the long-run proportion of husker fans who select football is greater than 0.5.
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