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 (see p76-77). 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
Probability Plot of lifetime
Normal
99
Mean
StDev
N
AD
P-Value
95
90
220.5
78.41
10
0.975
0.008
Percent
80
70
60
50
40
30
20
10
5
1
0
100
200
lifetime
300
400
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
1.48
.88
1.49
.88
1.59
1.04
1.62
1.09
1.65
1.12
1.71
1.29
1.76
1.31
1.83
Probability Plot of thickness
Normal
99
Mean
StDev
N
AD
P-Value
95
90
Percent
80
70
60
50
40
30
20
10
5
1
0.50
0.75
1.00
1.25
1.50
thickness
1.75
2.00
2.25
1.348
0.3385
16
0.422
0.283