Normal Probability Plot



Normal Probability Plot

Many statistical inference procedures require a normality assumption. One useful way of assessing the reasonableness of this assumption is by constructing a normal probability plot. If the plotted points fall approximately along a straight line, the normal distribution assumption can be deemed appropriate; if the plotted points deviate significantly and systematically from a straight line, the normal distribution assumption is not appropriate. In example 1 below, the normality assumption would not be deemed appropriate. In example 2, the normality assumption would be deemed appropriate.

Example Consider the following ten observations on bearing lifetime (in hours): [data from “Modified Moment Estimation for the Three-Parameter Lognormal Distribution,” J. Quality Technology, 1985:92-99].

152.7 172.0 172.5 173.3 193.0 204.7 216.5 234.9 262.6 422.6

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Example Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint (“Achieving a Target Value for a Manufacturing process: A Case Study,” J. of Quality Technology, 1992:22-26).

.83 .88 .88 1.04 1.09 1.12 1.29 1.31

1.48 1.49 1.59 1.62 1.65 1.71 1.76 1.83

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