Comparison of proportions

Recall that when comparing two drugs with the use of a uniform prior, the posterior distributions for the two proportions were independent with pS as \(beta(13, 9)\) and pN as \(beta(18, 4)\).

Suppose a vector of differences d_NS = pN - pS is computed. A histogram of the posterior density of d_NS is displayed on the right with a 90 percent probability interval marked by vertical lines.

Now you will look at the posterior of the ratio of proportions r_NS = pN / pS.

This exercise is part of the course

Beginning Bayes in R

Exercise instructions

Use the code provided in the editor to simulate 1000 draws from the posterior of (pS, pN).
For each pair of simulated proportions, compute the ratio of proportions r_NS.
Construct a histogram of the simulated values of r_NS.
Find the probability r_NS is larger than 1.
Find an 80% probability interval for r_NS.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Simulate 1000 draws from the posterior: sim_pS, sim_pN
sim_pS <- rbeta(1000, 13, 9)
sim_pN <- rbeta(1000, 18, 4)

# For each pair of proportions, compute the ratio: r_NS


# Plot a histogram of the values in r_NS


# Find the probability r_NS is larger than 1


# Find a 80% probability interval for r_NS

Edit and Run Code

This exercise is part of the course

Beginning Bayes in R

BeginnerSkill Level

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Exercise 1: Discrete probability distributions Exercise 2: Most likely spin?Exercise 3: Chance of spinning an even number?Exercise 4: Constructing a spinner Exercise 5: Simulating spinner data Exercise 6: Bayes' rule Exercise 7: The prior Exercise 8: The likelihoods Exercise 9: The posterior Exercise 10: Interpreting the posterior Exercise 11: Sequential Bayes Exercise 12: Bayes with another spin

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Exercise 1: Bayes with discrete models Exercise 2: Constructing a discrete prior Exercise 3: Updating by Bayes' rule Exercise 4: Continuous prior Exercise 5: Working with a beta curve Exercise 6: Constructing a beta prior Exercise 7: Updating the beta prior Exercise 8: Bayesian updating Exercise 9: Testing a claim Exercise 10: Bayesian inference Exercise 11: Interval estimates Exercise 12: Compare with classical methods Exercise 13: Bayesian probability interval Exercise 14: Posterior simulation Exercise 15: Simulating from a beta curve Exercise 16: Why simulate?

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Exercise 1: Normal sampling model Exercise 2: Reaction times Exercise 3: Updating by Bayes' rule Exercise 4: Bayes with a continuous prior Exercise 5: A continuous prior Exercise 6: Comparing normal priors Exercise 7: Updating the normal prior Exercise 8: The normal posterior Exercise 9: Compare with classical interval Exercise 10: Is Jim slow?Exercise 11: Simulation Exercise 12: Posterior simulation Exercise 13: Predictive simulation Exercise 14: Prediction vs. inference

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Exercise 1: Comparing two proportions Exercise 2: A discrete prior Exercise 3: Discrete posterior Exercise 4: Proportions with continuous priors Exercise 5: Independent beta priors Exercise 6: Posterior of proportions Exercise 7: Comparison of proportions

Current Exercise

Exercise 8: Normal model inference Exercise 9: Uniform prior Exercise 10: Learning about a percentile Exercise 11: Bayesian regression Exercise 12: Two group model Exercise 13: Standardized effect inference Exercise 14: Wrap-up and review