2.15. Statistical tables for the normal- and t-distribution

../_images/Statistical-tables.png

If interested, here is the code used to generate these figures

# The source code used to generate the # *normal distribution* section: q <- c(seq(-3.0, -2.0, 0.25), c(-1.8, -1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, 1.8), seq(2.0, 3.0, 0.25)) cumulative.quantile = pnorm(q) p <- c(0.001, 0.0025, 0.005, 0.010, 0.025, 0.05, 0.075, 0.10, 0.3, 0.5, 0.7, 0.9, 0.925, 0.950, 0.975, 0.99, 0.995, 0.9975, 0.999) cumulative.probability = qnorm(p) layout(matrix(c(1,2), 1, 2)) par(mar = c(4.2, 4.2, 0.2, 1)) plot(q, cumulative.quantile, type = "b", main = "", xlab = "z", ylab = "q = cumulative area under the normal distribution", cex.lab = 1.4, cex.main = 1.8, lwd = 4, cex.sub = 1.8, cex.axis = 1.8, ylim = c(0, 1)) grid(col="gray30") a1 = -0.6 arrows(a1, y = -0.2, x1 = a1, y1 = pnorm(a1), code = 0, lwd = 2) arrows(a1, y = pnorm(a1), x1 = -3, y1 = pnorm(a1), code = 2, lwd = 2) text(-2, pnorm(a1) + 0.05, "pnorm(z)", cex = 1.5) plot(cumulative.probability, p, type = "b", main = "", xlab = "z", ylab = "q = cumulative area under the normal distribution", cex.lab = 1.4, cex.main = 1.8, lwd = 4, cex.sub = 1.8, cex.axis = 1.8, ylim = c(0, 1)) grid(col = "gray30") a1 = qnorm(0.65) arrows(a1, y = 0, x1 = a1, y1 = pnorm(a1), code = 1, lwd = 2) arrows(a1, y=pnorm(a1), x1 = -5, y1 = pnorm(a1), code = 0, lwd = 2) text(-2, pnorm(a1)+0.05, "qnorm(q)", cex = 1.5) # The source code used to generate the t-distribution section: dof <- c(1, 2, 3, 4, 5, 10, 15, 20, 30, 60, Inf) tail.area.oneside <- c(0.4, 0.25, 0.1, 0.05, 0.025, 0.01, 0.005) n.dof <- length(dof) n.tails <- length(tail.area.oneside) values <- matrix(0, nrow=n.dof, ncol=n.tails) k = 0 for (entry in tail.area.oneside){ k = k + 1 values[ , k] <- abs(qt(entry, dof)) } round(values,3) par(mar=c(4.2, 4.2, 0.2, 1)) z <- seq(-5, 5, 0.01) probabilty <- dt(z, df=5) plot(z, probabilty, type = "l", main = "", xlab = "z", ylab = "Probabilities from the t-distribution", cex.lab = 1.4, cex.main = 1.8, lwd = 4, cex.sub = 1.8, cex.axis = 1.8) abline(h = 0) z = 1.5 abline(v = z) abline(v = 0)