Interpreting CIs and technical conditions

Foundations of Inference in R

Jo Hardin

Instructor

Creating CIs

# Compare confidence intervals
one_poll_boot %>% summarize(
    lower = p_hat - 2 * 
            sd(prop_yes_boot),
    upper = p_hat + 2 * 
            sd(prop_yes_boot))

# A tibble: 1 × 2
     lower    upper
     <dbl>    <dbl>
1 0.536148 0.863852

# Find 2.5% and 97.5% of p-hat vals
one_poll_boot %>% summarize(
    q025_prop = quantile(prop_yes_boot,
                         p = .025),
    q975_prop = quantile(prop_yes_boot,
                         p = .975))

# A tibble: 1 × 2
  q025_prop q975_prop
      <dbl>     <dbl>
1 0.5333333 0.8333333

Motivating CIs

Goal is to find the parameter when all we know is the statistic
Never know whether the sample you collected actually contains the true parameter

Interpreting the CIs

Bootstrap t-CI: (0.536, 0.864)
Percentile interval: (0.533, 0.833)

We are 95% confident that the true proportion of people planning to vote for candidate X is between 0.536 and 0.864 (or 0.533 and 0.833)

Technical conditions

Sampling distribution of the statistic is reasonably symmetric and bell-shaped
Sample size is reasonably large
Variability of resampled proportions

Let's practice!

Foundations of Inference in R