Compute a p-value from a null distribution and observed statistic.

Learn more in vignette("infer").

get_p_value(x, obs_stat, direction)

# S3 method for default
get_p_value(x, obs_stat, direction)

get_pvalue(x, obs_stat, direction)

# S3 method for infer_dist
get_p_value(x, obs_stat, direction)

## Arguments

x A null distribution. For simulation-based inference, a data frame containing a distribution of calculate()d statistics or fit()ted coefficient estimates. This object should have been passed to generate() before being supplied or calculate() to fit(). For theory-based inference, the output of assume(). A data frame containing the observed statistic (in a calculate()-based workflow) or observed fit (in a fit()-based workflow). This object is likely the output of calculate() or fit() and need not to have been passed to generate(). A character string. Options are "less", "greater", or "two-sided". Can also use "left", "right", "both", "two_sided", or "two sided", "two.sided".

## Value

A tibble containing the following columns:

• term: The explanatory variable (or intercept) in question. Only supplied if the input had been previously passed to fit().

• p_value: A value in [0, 1] giving the probability that a statistic/coefficient as or more extreme than the observed statistic/coefficient would occur if the null hypothesis were true.

## Aliases

get_pvalue() is an alias of get_p_value(). p_value is a deprecated alias of get_p_value().

## Zero p-value

Though a true p-value of 0 is impossible, get_p_value() may return 0 in some cases. This is due to the simulation-based nature of the {infer} package; the output of this function is an approximation based on the number of reps chosen in the generate() step. When the observed statistic is very unlikely given the null hypothesis, and only a small number of reps have been generated to form a null distribution, it is possible that the observed statistic will be more extreme than every test statistic generated to form the null distribution, resulting in an approximate p-value of 0. In this case, the true p-value is a small value likely less than 3/reps (based on a poisson approximation).

In the case that a p-value of zero is reported, a warning message will be raised to caution the user against reporting a p-value exactly equal to 0.

Other auxillary functions: get_confidence_interval()

## Examples


# using a simulation-based null distribution ------------------------------

# find the point estimate---mean number of hours worked per week
point_estimate <- gss %>%
specify(response = hours) %>%
calculate(stat = "mean")

# starting with the gss dataset
gss %>%
# ...we're interested in the number of hours worked per week
specify(response = hours) %>%
# hypothesizing that the mean is 40
hypothesize(null = "point", mu = 40) %>%
# generating data points for a null distribution
generate(reps = 1000, type = "bootstrap") %>%
# finding the null distribution
calculate(stat = "mean") %>%
get_p_value(obs_stat = point_estimate, direction = "two-sided")
#> # A tibble: 1 × 1
#>   p_value
#>     <dbl>
#> 1   0.032

# using a theoretical null distribution -----------------------------------

# calculate the observed statistic
obs_stat <- gss %>%
specify(response = hours) %>%
hypothesize(null = "point", mu = 40) %>%
calculate(stat = "t")

# define a null distribution
null_dist <- gss %>%
specify(response = hours) %>%
assume("t")

# calculate a p-value
get_p_value(null_dist, obs_stat, direction = "both")
#> # A tibble: 1 × 1
#>   p_value
#>     <dbl>
#> 1  0.0376

# using a model fitting workflow -----------------------------------------

# fit a linear model predicting number of hours worked per
# week using respondent age and degree status.
observed_fit <- gss %>%
specify(hours ~ age + college) %>%
fit()

observed_fit
#> # A tibble: 3 × 2
#>   term          estimate
#>   <chr>            <dbl>
#> 1 intercept     40.6
#> 2 age            0.00596
#> 3 collegedegree  1.53

# fit 100 models to resamples of the gss dataset, where the response
# hours is permuted in each. note that this code is the same as
# the above except for the addition of the generate step.
null_fits <- gss %>%
specify(hours ~ age + college) %>%
hypothesize(null = "independence") %>%
generate(reps = 100, type = "permute") %>%
fit()

null_fits
#> # A tibble: 300 × 3
#> # Groups:   replicate [100]
#>    replicate term           estimate
#>        <int> <chr>             <dbl>
#>  1         1 intercept     40.7
#>  2         1 age           -0.00753
#>  3         1 collegedegree  2.78
#>  4         2 intercept     41.8
#>  5         2 age           -0.000256
#>  6         2 collegedegree -1.08
#>  7         3 intercept     42.7
#>  8         3 age           -0.0426
#>  9         3 collegedegree  1.23
#> 10         4 intercept     42.6
#> # … with 290 more rows

get_p_value(null_fits, obs_stat = observed_fit, direction = "two-sided")
#> # A tibble: 3 × 2
#>   term          p_value
#>   <chr>           <dbl>
#> 1 age              0.92
#> 2 collegedegree    0.26
#> 3 intercept        0.68

# more in-depth explanation of how to use the infer package
if (FALSE) {
vignette("infer")
}