Suppose we are planning a clinical trial and expect a 20% success rate in the active group and a 10% success rate in the placebo group. We expect to enroll 100 participants in each group and are interested in the power of the study. (a) Perform a simulation study, and generate 100 participants from a binomial distribution with p = 0.2 and 100 participants from a binomial distribution with p = 0.1. Test to determine whether the observed sample proportion of successes are significantly different, using a two-sided test with a = 0.05.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose we are planning a clinical trial and expect a 20% success rate in the active group and a 10% success rate in the placebo group. We expect to enroll 100 participants in each group and are interested in the power of the study.
(a) Perform a simulation study, and generate 100 participants from a binomial distribution with p = 0.2 and 100 participants from a binomial distribution with p = 0.1. Test to determine whether the observed sample proportion of successes are significantly different, using a two-sided test with a = 0.05.
(b) Repeat the Problem (a) simulation 1000 times, and compute the proportion of simulations in which a significant difference is found (i.e., an estimate of the power of the study).
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