Minitab material on test for Normality
NORMTEST
example
Note
see also
NORMTEST replaces %NORMPLOT.
Stat > Basic Statistics > Normality Test or Graph > Probability Plot
Command Syntax
NORMTEST C
Generates a normal probability plot
PTILES C or K...K
Specifies a set of reference percents
DVALUE K...K
Shows the percents at the reference x-scale positions
PERCENT
Specifies a percent y-scale
PROBABILITY
Specifies a probability y-scale
SCORES
Specifies a percentile y-scale
RJTEST
Specifies the Ryan-Joiner test (similar to Shapiro-Wilk test)
KSTEST
Specifies the Kolmogorov-Smirnov goodness-of-fit test
SPVALUE C
Stores the p-value of test
TITLE "text"
Specifies a graph title
GSAVE "file"
Saves the graph in a Minitab Graphics Format (MGF) file
Generates a normal probability plot. Normal plots use the values in the input column as x-values. The grid
on the graph resembles the grids found on normal probability paper. The horizontal axis is a linear scale.
The line forms an estimate of the cumulative distribution function for the population from which data are
drawn.
By default, an Anderson-Darling test for normality is performed and the numerical results are displayed
with the graph. You can also use a Ryan-Joiner test (similar to a Shapiro-Wilk test) or a KolmogorovSmirnov test.
Subcommands
PTILES C or K...K
DVALUE K...K
Specifies a set of reference percents. The values must be between 0 and 100
when percents are used as the y-scale type or 0 to 1 when probability is the yscale type. Minitab marks each percent in the column with a horizontal
reference line on the plot, and marks each line with the percent value. Minitab
draws a vertical reference line where the horizontal reference line intersects the
line fit to the data, and marks this line with the estimated data value. Use
DVALUE to show the percents at the reference x-scale positions.
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PERCENT
Specifies a percent y-scale.
PROBABILITY
Specifies a probability y-scale.
SCORES
Specifies a percentile y-scale.
RJTEST
There are 3 types of goodness-of-fit test: a chi-square based test, an ECDF
based test, and a correlation based test. By default, Minitab uses the AndersonDarling test, which is an ECDF based test. Use RJTEST to perform a RyanJoiner test, which is a correlation based test; use KSTEST to perform a
Kolmogorov-Smirnov test, which is a chi-square based test.
KSTEST
When your -value is larger than the p-value displayed with the graph, you
should reject the hypothesis of normality. The -value (also known as the
significance level), is the probability that you will reject the hypothesis of
normality when the hypothesis is true.
For example, if you are using an -value of 0.10 and the p-value displayed in
the Graph window is 0.07, then you would reject the hypothesis of normality at
the 0.10 level.
SPVALUE C
Stores the p-value of the test.
TITLE "text"
Use TITLE to specify a title for the graph. When you omit this subcommand,
Minitab displays a default title.
GSAVE "filename"
Use GSAVE to save the graph in a Minitab Graphics Format (MGF) file.
Unless you specify a file extension or use a graphics format subcommand,
Minitab automatically adds the extension MGF to the file name. If you save the
plot, you can view it later with GVIEW and edit the plot with graph editing
tools. See GSAVE for more information on this subcommand.
Use GSAVE to save the graph in a Minitab Graphics Format (MGF) file.
Unless you specify a file extension or use a graphics format subcommand,
Back to top
Minitab automatically adds the extension MGF to the file name. If you save the
plot, you can view it later with GVIEW and edit the plot with graph editing
tools. See GSAVE for more information on this subcommand.
Example of Normality Test
main topic
interpreting results
session command
see also
In an operating engine, parts of the crankshaft move up and down. AtoBDist is the distance (in mm) from
the actual (A) position of a point on the crankshaft to a baseline (B) position. To ensure production quality,
2
a manager took five measurements each working day in a car assembly plant, from September 28 through
October 15, and then ten per day from the 18th through the 25th.
You wish to see if these data follow a normal distribution, so you use Normality test.
1
Open the worksheet CRANKSH.MTW.
2
Choose Stat > Basic Statistics > Normality Test.
3
In Variable, enter AtoBDist. Click OK.
Graph window output -- see below! Thus is a Minitab run on the dataset mentioned above.
Retrieving worksheet from file:
'\\purple2\resource\wminitab14\Data\Cranksh.MTW'
Worksheet was saved on Fri Sep 12 2003
Results for: Cranksh.MTW
MTB > describe c1
Descriptive Statistics: AtoBDist
Variable
AtoBDist
N
125
N*
0
Variable
AtoBDist
Maximum
8.023
Mean
0.442
SE Mean
0.312
StDev
3.491
Minimum
-7.303
Q1
-2.243
Median
0.130
Q3
3.607
MTB > NormTest c1;
SUBC>
KSTest.
Probability Plot of AtoBDist
Probability Plot of AtoBDist
Normal
99.9
Mean
StDev
N
KS
P-Value
99
Percent
95
90
0.4417
3.491
125
0.094
<0.010
80
70
60
50
40
30
20
10
5
1
0.1
-10
-5
0
AtoBDist
5
10
MTB > normtest c1;
SUBC> rjtest.
Probability Plot of AtoBDist
3
Probability Plot of AtoBDist
Normal
99.9
99
Percent
95
90
Mean
StDev
N
RJ
P-Value
0.4417
3.491
125
0.990
0.066
Mean
StDev
N
AD
P-Value
0.4417
3.491
125
0.891
0.022
80
70
60
50
40
30
20
10
5
1
0.1
-10
-5
0
AtoBDist
5
10
MTB > normtest c1
Probability Plot of AtoBDist
Probability Plot of AtoBDist
Normal
99.9
99
Percent
95
90
80
70
60
50
40
30
20
10
5
1
0.1
-10
-5
0
AtoBDist
5
10
4
If your data are perfectly normal, then the data points on the probability plot will form a straight line. The
red line forms an estimate of the cumulative distribution function for the population from which the data are
drawn.
Your text says that if the data are skewed to the left, the plot will rise rapidly at first and then level off,
while if they are skewed to the right the plot will rise slowly at first and fast later.
Interpreting the results
The graphical output is a plot of normal probabilities versus the data. The data depart from the fitted line
most evidently in the extremes, or distribution tails. The Anderson-Darling test's p-value indicates that, at 
levels greater than 0.022, there is evidence that the data do not follow a normal distribution. There is a
slight tendency for these data to be lighter in the tails than a normal distribution because the smallest points
are below the line and the largest point is just above the line. A distribution with heavy tails would show the
opposite pattern at the extremes.
Many statistical procedures assume the data follow a normal distribution. In order to verify this assumption,
you can perform a normality test on your data.
MINITAB provides three normality tests that you can choose from:
·
Anderson-Darling - This test has good power and is especially effective at detecting departure
from normality in the high and low values of a distribution.
·
Ryan-Joiner (similar to Shapiro-Wilk) - This test also has good power. It is based on the
correlation between the sample data and the data one would expect from a normal distribution.
·
Kolmogorov-Smirnov - This is a popular test of normality, but tends to be less powerful than the
other two.
Choosing a normality test
You have a choice of hypothesis tests for testing normality:
 Anderson-Darling test (the default), which is an ECDF (empirical cumulative distribution function)
based test

Ryan-Joiner test [4], [9] (similar to the Shapiro-Wilk test [10], [11]) which is a correlation based test

Kolmogorov-Smirnov test [8], an ECDF based test
The Anderson-Darling and Ryan-Joiner tests have similar power for detecting non-normality. The
Kolmogorov-Smirnov test has lesser powersee [3], [8]and [9] for discussions of these tests for normality.
The common null hypothesis for these three tests is H0: data follow a normal distribution. If the p-value of
the test is less than your  level, reject H0.
The results of each test are accompanied by a normal probability plot that can also help you determine
whether your data follow a normal distribution.
The graphs below are data points generated randomly from a Chi-squared distribution.
Copyright © 2000-2005 Minitab Inc. All rights reserved.
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Probability Plot of C1
Normal
99
95
90
Mean
StDev
N
KS
P-Value
10.20
5.540
20
0.122
>0.150
Mean
StDev
N
RJ
P-Value
10.20
5.540
20
0.970
>0.100
Percent
80
70
60
50
40
30
20
10
5
1
0
5
10
C1
15
20
25
Probability Plot of C1
Normal
99
95
90
Percent
80
70
60
50
40
30
20
10
5
1
0
5
10
C1
15
20
25
6
Probability Plot of C1
Normal
99
Mean
StDev
N
AD
P-Value
95
90
10.20
5.540
20
0.473
0.217
Percent
80
70
60
50
40
30
20
10
5
1
0
5
10
C1
15
20
25
References  Basic Statistics
[1]
S.F. Arnold (1990). Mathematical Statistics. Prentice-Hall.
[2] M.B. Brown and A.B. Forsythe (1974). "Robust Tests for the Equality of Variances," Journal of the
American Statistical Association, 69, 364-367.
[3]
R.B. D'Agostino and M.A. Stephens, Eds. (1986). Goodness-of-Fit Techniques, Marcel Dekker.
[4] J.J. Filliben (1975). "The Probability Plot Correlation Coefficient Test for Normality," Technometrics,
17, 111.
[5] T.P. Hettmansperger and S.J. Sheather (1986). "Confidence Intervals Based on Interpolated Order
Statistics," Statistics and Probability Letters, 4, 75-79.
[6]
N.L. Johnson and S. Kotz (1969). Discrete Distributions, John Wiley & Sons.
[7]
H. Levene (1960). Contributions to Probability and Statistics, Stanford University Press.
[8] H.W. Lilliefors (1967). "On the Kolmogorov
Unknown," Journal of the American Statistical Association, 62, 399-402.
[9] T.A. Ryan, Jr. and B.L. Joiner (1976). "Normal Probability Plots and Tests for Normality," Technical
Report, Statistics Department, The Pennsylvania State University. (Available from Minitab Inc.)
[10] S.S. Shapiro and R.S. Francia (1972). "An Approximate Analysis of Variance Test for Normality,"
Journal of the American Statistical Association, 67, 215-216.
[11] S.S. Shapiro and M.B. Wilk. (1965). "An Analysis of Variance Test for Normality (Complete
Samples)," Biometrika, 52, 591.
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