R/critical.value.ks.test.R

In BoutrosLab.plotting.general: Functions to Create Publication-Quality Plots

# The BoutrosLab.statistics.general package is copyright (c) 2012 Ontario Institute for Cancer Research (OICR)
# This package and its accompanying libraries is free software; you can redistribute it and/or modify it under the terms of the GPL
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critical.value.ks.test <- function(n, conf, alternative = "two.sided") {
	
	if(alternative == "one-sided") conf <- 1- (1-conf)*2;

	# for the small sample size
	
	if (n < 50) {
		# use the exact distribution from the C code in R
		exact.kolmogorov.pdf <- function(x) {
			p <- .Call("pKolmogorov2x", p = as.double(x), as.integer(n), PACKAGE = "BoutrosLab.plotting.general");
			return(p - conf);
		}
		
		critical.value <- uniroot(exact.kolmogorov.pdf, lower = 0, upper = 1)$root;
		}

	# if the sample size is large(>50), under the null hypothesis, the absolute value of the difference
	# of the empirical cdf and the theoretical cdf should follow a kolmogorov distribution
	
	if (n >= 50) {
		# pdf of the kolmogorov distribution minus the confidence level
		kolmogorov.pdf <- function(x) { 
			i <- 1:10^4;
			sqrt(2*pi) / x * sum(exp(-(2*i - 1)^2*pi^2/(8*x^2))) - conf;	
			}

		# the root of the function above
		# is the critical value for a specific confidence level multiplied by sqrt(n);
		critical.value <- uniroot(kolmogorov.pdf , lower = 10^(-6), upper = 3)$root / sqrt(n);
		}

	return(critical.value);
	}