Standardized effect inference

In comparing my reaction times with those of my son Steven, we are interested in the regression model

$$ Time = \beta_0 + \beta_1 * Person $$

The parameter beta1 measures the change (from me to Steven) in mean reaction time and the parameter

delta = beta1 / S

represents the standardized change (in standard deviation units).

This exercise is part of the course

Beginning Bayes in R

Exercise instructions

Perform a regression fit of Time using Person as a covariate.
Simulate 1000 draws from the joint posterior distribution using the sim() function.
Extract the simulated values of (beta0, beta1) and S (functions coef() and sigma.hat()).
Compute the simulated values of the standardized change delta.
Find a 90% interval estimate for delta.

Hands-on interactive exercise

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

# Perform a regression fit of Time with Person as a covariate: fit
fit <- lm(Time ~ Person, data = dd)

# Simulate 1000 values from the posterior distribution: sim_fit
sim_fit <- sim(fit, n.sims = 1000)

# Extract simulated draws of beta and S:  beta_sim, s_sim
beta_sim <- ___
s_sim <- ___

# Compute simulated values of the standardized change: s_delta


# Find 90% interval estimate for s_delta

Edit and Run Code

This exercise is part of the course

Beginning Bayes in R

BeginnerSkill Level

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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 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

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