# Data series comparison using Akaike weight This function is used as a replacement of t.test() to not use p-value. ```r series.compare(..., criterion = c("BIC", "AIC", "AICc"), var.equal = TRUE) ``` ## Arguments - `...`: Series of data (at least two or data are in a table with series in different rows) - `criterion`: Which criterion is used for model selection. can be AIC, AICc or BIC - `var.equal`: Should the variances of all series being equal? Default TRUE ## Returns The probability that a single proportion model is sufficient to explain the data ## Details series.compare compares series of data using Akaike weight. ## Examples ```r ## Not run: library("HelpersMG") A <- rnorm(100, 10, 2) B <- rnorm(100, 11.1, 2) series.compare(A, B, criterion = "BIC", var.equal=TRUE) B <- B[1:10] series.compare(A, B, criterion = "BIC", var.equal=TRUE) A <- rnorm(100, 10, 2) B <- rnorm(100, 10.1, 2) C <- rnorm(100, 10.5, 2) series.compare(A, B, C, criterion = "BIC", var.equal=TRUE) B <- B[1:10] series.compare(A, B, criterion = "BIC", var.equal=TRUE) t.test(A, B, var.equal=TRUE) # Example with a data.frame series.compare(t(data.frame(A=c(10, 27, 19, 20, NA), B=c(10, 20, NA, NA, NA)))) # Test in the context of big data A <- rnorm(10000, 10, 2) B <- rnorm(10000, 10.1, 2) series.compare(A, B, criterion = "BIC", var.equal=TRUE) t.test(A, B, var.equal=TRUE) ########################### w <- NULL p <- NULL for (i in 1:1000) { A <- rnorm(50000, 10, 2) B <- rnorm(50000, 10.01, 2) w <- c(w, unname(series.compare(A, B, criterion = "BIC", var.equal=TRUE)[1])) p <- c(p, t.test(A, B, var.equal=TRUE)$p.value) } layout(mat = 1:2) par(mar=c(4, 4, 1, 1)+0.4) hist(p, main="", xlim=c(0, 1), las=1, breaks = (0:20)/20, freq=FALSE, xlab = expression(italic("p")*"-value")) hist(w, main="", xlim=c(0, 1), las=1, breaks = (0:20)/20, freq=FALSE, xlab = expression(italic("w")*"-value")) ########################### x <- seq(from=8, to=13, by=0.1) pv <- NULL aw <- NULL A <- rnorm(100, mean=10, sd=2) B <- A-2 for (meanB in x) { pv <- c(pv, t.test(A, B, var.equal = FALSE)$p.value) aw <- c(aw, series.compare(A, B, criterion="BIC", var.equal = FALSE)[1]) B <- B + 0.1 } par(mar=c(4, 4, 2, 1)+0.4) y <- pv plot(x=x, y=y, type="l", lwd=2, bty="n", las=1, xlab="Mean B value (SD = 4)", ylab="Probability", ylim=c(0,1), main="") y2 <- aw lines(x=x, y=y2, type="l", col="red", lwd=2) l1 <- which(aw>0.05)[1] l2 <- max(which(aw>0.05)) aw[l1] pv[l1] aw[l2] pv[l2] l1 <- which(pv>0.05)[1] l2 <- max(which(pv>0.05)) aw[l1] pv[l1] aw[l2] pv[l2] par(xpd=TRUE) segments(x0=10-1.96*2/10, x1=10+1.96*2/10, y0=1.1, y1=1.1, lwd=2) segments(x0=10, x1=10, y0=1.15, y1=1.05, lwd=2) par(xpd=TRUE) text(x=10.5, y=1.1, labels = "Mean A = 10, SD = 2", pos=4) v1 <- c(expression(italic("p")*"-value"), expression("based on "*italic("t")*"-test")) v2 <- c(expression(italic("w")*"-value for A"), expression("and B identical models")) legend("topright", legend=c(v1, v2), y.intersp = 1, col=c("black", "black", "red", "red"), bty="n", lty=c(1, 0, 1, 0)) segments(x0=min(x), x1=max(x), y0=0.05, y1=0.05, lty=2) par(xpd = TRUE) text(x=13.05, y=0.05, labels = "0.05", pos=4) ## End(Not run) ``` ## References Girondot, M., Guillon, J.-M., 2018. The w-value: An alternative to t- and X2 tests. Journal of Biostatistics & Biometrics 1, 1-4. ## See Also Other w-value functions: `compare()`, `contingencyTable.compare()` ## Author(s) Marc Girondot marc.girondot@gmail.com

series.compare function