# Weighted t-Test in R

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Although there is a weighted.mean function in R, so far I couldn’t find a implementation of weighted.var and weighted.t.test – here they are (the weighted variance is from Gavin Simpson, found on the R malining list):

^{?}View Code RSPLUS

# weighted variance, inspired by a function from Gavin Simpson on R-Help var.wt <- function(x, w, na.rm = FALSE) { if (na.rm) { w <- w[i <- !is.na(x)] x <- x[i] } sum.w <- sum(w) return((sum(w*x^2) * sum.w - sum(w*x)^2) / (sum.w^2 - sum(w^2))) } weighted.t.test <- function(x, w, mu, conf.level = 0.95, alternative="two.sided", na.rm=TRUE) { if(!missing(conf.level) & (length(conf.level) != 1 || !is.finite(conf.level) || conf.level < 0 || conf.level > 1)) stop("'conf.level' must be a single number between 0 and 1") if (na.rm) { w <- w[i <- !is.na(x)] x <- x[i] } # to achieve consistent behavior in loops, return NA-structure in case of complete missings if (sum(is.na(x)) == length(x)) return(list(estimate=NA, se=NA, conf.int=NA, statistic=NA, df=NA, p.value=NA)) # if only one value is present: this is the best estimate, no significance test provided if (sum(!is.na(x)) == 1) { warning("Warning weighted.t.test: only one value provided; this value is returned without test of significance!", call.=FALSE) return(list(estimate=x[which(!is.na(x))], se=NA, conf.int=NA, statistic=NA, df=NA, p.value=NA)) } x.w <- weighted.mean(x,w, na.rm=na.rm) var.w <- var.wt(x,w, na.rm=na.rm) df <- length(x)-1 t.value <- sqrt(length(x))*((x.w-mu)/sqrt(var.w)) se <- sqrt(var.w)/sqrt(length(x)) if (alternative == "less") { pval <- pt(t.value, df) cint <- c(-Inf, x.w + se*qt(conf.level, df) ) } else if (alternative == "greater") { pval <- pt(t.value, df, lower.tail = FALSE) cint <- c(x.w - se * qt(conf.level, df), Inf) } else { pval <- 2 * pt(-abs(t.value), df) alpha <- 1 - conf.level cint <- x.w + se*qt(1 - alpha/2, df)*c(-1,1) } names(t.value) <- "t" return(list(estimate=x.w, se=se, conf.int=cint, statistic=t.value, df=df, p.value=pval)) } |

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