Let the ordered sample observations be denoted byy1, y2, ,

Chapter 4, Problem 96

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Let the ordered sample observations be denoted by y1, y2, , yn (y1 being the smallest and yn the largest). Our Suggested check for normality is to plot the \(\left(\Phi^{-1}((i-.5) / n), y_{i}\right)\) pairs. Suppose we believe that the observations come from a distribution with mean 0, and let w1,..., wn be the ordered absolute values of the xi’s. A half-normal plot is a probability plot of the wi’s. More specifically, since \(P(|Z| \leq w)=P(-w \leq Z \leq w)=2 \Phi(w)-1\), a half-normal plot is a plot of the \(\left(\Phi^{-1} /\{[(i-.5) / n+1] / 2\}, w_{i}\right)\) pairs. The virtue of this plot is that small or large outliers in the original sample willnow appear only at the upper end of the plot rather than at both ends. Construct a half-normal plot for the following sample of measurement errors, and comment: 23.78, 21.27, 1.44,2.39, 12.38, 243.40, 1.15, 23.96, 22.34, 30.84