Compare with classical interval

In our example, if \(\bar y\) and \(se\) are the respective sample mean and standard error, then a standard 90 percent confidence interval for M is given by

$$ (\bar y - 1.645 \times se, \bar y + 1.645 \times se). $$

For my data, we have ybar = 275.9, and se = 6.32, so my confidence interval is given by

c(275.9 - 1.645 * 6.32, 275.9 + 1.645 * 6.32)

Recall that Kathy's posterior curve was normal with mean 271.35 and standard deviation 5.34.

Now you can compare the 90% confidence interval with Kathy's probability interval for M!

This exercise is part of the course

Beginning Bayes in R

Exercise instructions

Compute a vector C_Interval containing the 90% confidence interval. This is the interval obtained by using the frequentist method.
Find the length of the confidence interval using the diff() function.
Define a vector Posterior with the mean and standard deviation of Kathy's posterior.
Use the normal_interval() function to display a 90% probability interval.
Use qnorm() to compute the 90% Bayesian probability interval. Assign the result to B_Interval.
Compute the length of the Bayesian interval using diff() once more.

Hands-on interactive exercise

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

# Define mean and standard error: Data
Data <- c(275.9, 6.32)

# Compute 90% confidence interval: C_Interval


# Find the length of the confidence interval


# Define mean and standard deviation of posterior: Posterior


# Display a 90% probability interval


# Compute the 90% probability interval: B_Interval
B_Interval <- qnorm(c(___, ___), mean = ___, sd = ___)

# Compute the length of the Bayesian interval

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

Current Exercise

Exercise 10: Is Jim slow?Exercise 11: Simulation Exercise 12: Posterior simulation Exercise 13: Predictive simulation Exercise 14: Prediction vs. inference

Suppose you're interested in comparing proportions from two populations. You take a random sample from each population and you want to learn about the difference in proportions. This chapter will illustrate the use of discrete and continuous priors to do this kind of inference. You'll use a Bayesian regression approach to learn about a mean or the difference in means when the sampling standard deviation is unknown.

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 Exercise 14: Wrap-up and review