## interaction test see http://www.bmj.com/content/326/7382/219.long
#' @title FUNCTION_TITLE
#' @description FUNCTION_DESCRIPTION
#' @param mean1 PARAM_DESCRIPTION
#' @param se1 PARAM_DESCRIPTION
#' @param mean2 PARAM_DESCRIPTION
#' @param se2 PARAM_DESCRIPTION
#' @return OUTPUT_DESCRIPTION
#' @details DETAILS
#' @examples
#' \dontrun{
#' if(interactive()){
#' #EXAMPLE1
#' }
#' }
#' @seealso
#'
#' @rdname interactionTest
#' @export
#' @import data.table
interactionTest = function(mean1, se1, mean2, se2) {
meandiff_se = sqrt(se1^2 + se2^2)
meandiff = mean2 - mean1
meandiff_cilow = meandiff - 1.96*meandiff_se
meandiff_cihigh = meandiff + 1.96*meandiff_se
meandiff_z = meandiff/meandiff_se
meandiff_p = stats::pnorm(abs(meandiff_z), lower.tail = F)*2
if(meandiff_p>1) meandiff_p = 1
data.table::data.table(mean1, se1, mean2, se2, meandiff, meandiff_se, meandiff_cilow, meandiff_cihigh, meandiff_z, meandiff_p)
}
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