Normal Probabilities PlotSection 7.6
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Normal Plots
A normal probability plot is a scatter plot of the (normal score*, observation) pairs.
A substantially linear pattern in a normal probability plot suggests that population normality is plausible.
A systematic departure from a straight-line pattern (such as curvature in the plot) casts doubt on the legitimacy of assuming a normal population distribution.
*There are different techniques for determining the normal scores. Typically, we use a statistical package such as a graphing calculator or Excel to create a normal probability plot.
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Normal Probability Plot Example
Ten randomly selected shut-ins were each asked to list how many hours of television they watched per week. The results are
82 66 90 84 7588 80 94 110 91
Minitab obtained the normal probability plot on the following slide.
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Normal Probability Plot Example
P-Value: 0.753A-Squared: 0.226
Anderson-Darling Normality Test
N: 10StDev: 11.8415Average: 86
110100908070
.999
.99
.95
.80
.50
.20
.05
.01
.001
Pro
bab
ility
Hours of TV
Normal Probability Plot
Notice that the points all fall nearly on a line so it is reasonable to assume that the population of hours of tv watched by shut-ins is normally distributed.
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Normal Probability Plot Example
A sample of times of 15 telephone solicitation calls (in seconds) was obtained and is given below. 5 10 7 12 35
65 145 14 3 22011 6 85 6 16
Minitab obtained the normal probability plot on the next slide
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Normal Probability Plot Example
P-Value: 0.000A-Squared: 2.087
Anderson-Darling Normality Test
N: 15StDev: 63.1129Average: 42.6667
2001000
.999
.99
.95
.80
.50
.20
.05
.01
.001
Pro
bab
ility
Length of Ca
Normal Probability Plot
Clearly the points do not fall nearly on a line. Specifically the pattern has a distinct nonlinear appearance. It is not reasonable to assume that the population of hours of tv watched by shut-ins is normally distributed.
One would most assuredly say that the distribution of lengths of calls is not normal.