Calculate Empirical P-Value

Computes an empirical p-value by comparing an observed test statistic against a null distribution. This is the standard approach in MOSAIC for calibrating differential connectivity significance: run the DC pipeline on real labels and on shuffled labels, then compare F-statistics.

Usage

calculate_empirical_pvalue(test_value, data_list, alternative = "greater")

Arguments

test_value

Numeric scalar. The observed test statistic (e.g. a PERMANOVA F-statistic from run_DC_test).

data_list

Numeric vector of null distribution values (e.g. all F-statistics from a label-shuffled run).

alternative

Character string specifying the alternative hypothesis:

"greater"

(Default) Tests whether test_value is unusually large. P-value = proportion of null values >= test_value.

"less"

Tests whether test_value is unusually small. P-value = proportion of null values <= test_value.

"two.sided"

Tests whether test_value is extreme in either direction. P-value = 2 * one-sided p-value, capped at 1.

Value

A numeric p-value between 0 and 1.

See also

run_DC_test which produces the F-statistics to be tested.

Examples

# Simulate a null distribution and test an observed value
set.seed(42)
null_distribution <- rnorm(10000, mean = 0, sd = 1)
observed <- 2.5

# One-sided test (is the observed value unusually large?)
calculate_empirical_pvalue(observed, null_distribution, alternative = "greater")
#> [1] 0.0058

# Two-sided test
calculate_empirical_pvalue(observed, null_distribution, alternative = "two.sided")
#> [1] 0.0116

# Typical MOSAIC usage:
# pval <- calculate_empirical_pvalue(F_observed, F_null_vector)