infer R Package

The infer package uses an expressive, verb-based grammar to perform statistical inference (both hypothesis testing and confidence interval construction) following tidyverse principles. Instead of calling specific test functions (like a t-test), you build a pipeline using four main verbs that abstract the underlying statistical process.

Hypothesis Testing Workflow

To test if an effect is real or due to chance, follow this pipeline:

1. specify(): Define the variable or relationship of interest.
2. hypothesize(): Declare the null hypothesis (e.g., that there is no difference).
3. generate(): Create a null distribution by simulating data that reflects the null hypothesis (randomization) or by using bootstrapping.
4. calculate(): Compute summary statistics from both the observed data and the generated null data to form the test statistic and the null distribution.

Confidence Interval Workflow

To construct confidence intervals via bootstrapping, use a similar pipeline but omit the hypothesize() step:

1. specify()
2. generate() (using bootstrap)
3. calculate()

Visualizing and Extracting Results

Once the pipeline is complete, use these utilities to interpret the output:

• For Hypothesis Testing:
  • visualize(): Plots the null distribution.
  • shade_p_value(): Shades the region of the distribution as extreme or more extreme than the observed statistic.
  • get_p_value(): Calculates the p-value by comparing the observed statistic to the null distribution.
• For Confidence Intervals:
  • visualize(): Plots the bootstrap distribution.
  • shade_confidence_interval(): Situates the confidence interval region within the distribution.
  • get_confidence_interval(): Calculates the specific bounds of the interval.

The infer package uses a statistical grammar centered around four main verbs to perform randomization-based inference. This workflow follows a specific sequence:

1. specify(): Define the variable or relationship (e.g., using a formula like y ~ x) that you are interested in.
2. hypothesize(): Declare the null hypothesis (e.g., null = "independence").
3. generate(): Create data that reflects the null hypothesis (e.g., using type = "permute" and specifying the number of reps).
4. calculate(): Compute a distribution of statistics from the generated data to form the null distribution.

This process can be visualized to compare the observed statistic against the generated null distribution.

# Example of the full pipeline logic
F_hat <- gss |> 
  specify(age ~ partyid) |
  calculate(stat = "F")

null_dist <- gss |> 
   specify(age ~ partyid) |
   hypothesize(null = "independence") |
   generate(reps = 1000, type = "permute") |
   calculate(stat = "F")

A typical inference workflow involves calculating an observed statistic, generating a null distribution, and then comparing the two to visualize or calculate a p-value. infer supports both formula interfaces (e.g., y ~ x) and non-formula interfaces (e.g., response = y, explanatory = x).

Example: Testing if age is independent of partyid using an ANOVA (F-statistic) approach:

1. Calculate observed statistic: Use specify() and calculate().
2. Generate null distribution: Use specify(), hypothesize(), generate(), and calculate().
3. Visualize: Use visualize() combined with shade_p_value().
4. Calculate p-value: Use get_p_value().

library(infer)
data(gss)

# 1. Calculate the observed statistic
F_hat <- gss |> 
  specify(age ~ partyid) |> 
  calculate(stat = "F")

# 2. Generate the null distribution
null_dist <- gss |> 
   specify(age ~ partyid) |> 
   hypothesize(null = "independence") |> 
   generate(reps = 1000, type = "permute") |> 
   calculate(stat = "F")

# 3. Visualize the observed statistic alongside the null distribution
visualize(null_dist) +
  shade_p_value(obs_stat = F_hat, direction = "greater")

# 4. Calculate the p-value
null_dist |> 
  get_p_value(obs_stat = F_hat, direction = "greater")

To test if a variable (e.g., age) is independent of a categorical variable (e.g., partyid), follow these steps using the gss dataset:

1. Calculate the observed statistic: Use specify() with a formula and calculate(stat = "F").
2. Generate the null distribution: Use hypothesize(null = "independence") followed by generate(reps = 1000, type = "permute") and calculate(stat = "F").
3. Visualize: Use visualize() combined with shade_p_value() to see the observed statistic relative to the null distribution.
4. Calculate p-value: Use get_p_value() on the null distribution object.

Note: You can use either formula notation (y ~ x) or non-formula notation (response = y, explanatory = x). Formula notation is recommended if you plan to use modeling functions like lm() or glm() later.

# 1. Calculate observed statistic
F_hat <- gss |> 
  specify(age ~ partyid) |
  calculate(stat = "F")

# 2. Generate null distribution
null_dist <- gss |> 
   specify(age ~ partyid) |
   hypothesize(null = "independence") |
   generate(reps = 1000, type = "permute") |
   calculate(stat = "F")

# 3. Visualize
visualize(null_dist) +
  shade_p_value(obs_stat = F_hat, direction = "greater")

# 4. Get p-value
null_dist |> 
  get_p_value(obs_stat = F_hat, direction = "greater")