Comparing randomization inference and t-inference

When technical conditions (see next chapter) hold, the inference from the randomization test and the t-distribution test should give equivalent conclusions. They will not provide the exact same answer because they are based on different methods. But they should give p-values and confidence intervals that are reasonably close.

This exercise is part of the course

Inference for Linear Regression in R

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Exercise instructions

Calculate the absolute value of the observed slope, obs_slope.
Add a column to perm_slope of the absolute value of the slope in each permuted replicate. The slope column is called stat.
In the call to summarize(), calculate the p-value as the proportion of absolute estimates of slope that are at least as extreme as the absolute observed estimate of slope.

Hands-on interactive exercise

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

# The slope in the observed data and each permutation replicate
obs_slope
perm_slope

# Calculate the absolute value of the observed slope
abs_obs_slope <- ___

# Find the p-value
perm_slope %>%
  # Add a column for the absolute value of stat
  ___ %>%
  summarize(
    # Calculate prop'n permuted values at least as extreme as observed
    p_value = ___
  )

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