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Assessing Normality of a Sample
• normal quantile plots can be used to assess whether the data could have
come from a normal distribution
• these plots are also called QQ or normal scores plots
• the sorted values are plotted against the values we would expect to get if
the sample came from a normal distribution
• a straight line in this plot indicates that the data are normally distributed
• outliers show up as values distant from the overall pattern
• curvature indicates departure from normality e.g. skewness
• the NSCORES command in MINITAB can be used to produce the values
to be plotted against the data
For example
MTB > nscores c1 c2
• Manually you can create the normal probability scores using the following
commands
First rank the data from C1 to C3.
Then create the quantile of each observation in column C4
and finally find the point of the normal distribution which gives you the
corresponding quantile.
MTB > rank c1 c3
MTB > let c4=(c3-.375)/(10+.25)
MTB > invcdf c4 c5;
SUBC> normal 0 1.
Comment: 10 is the sample size,
.375 and .25 are constants needed for the estimation of
the quantiles.
• the curvature in the probability plot can reveal the shape of distribution
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• if the distribution is skewed to the right, the probability plot curves down
at both the left and the right
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• if the distribution is skewed to the left, the probability plot curves up at
each end
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• if the distribution has a flatter peak than the normal, the normal scores
plot curves down at the left and up at the right
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• Example: The probability plot for residuals from the data on golf balls is
shown below. Alternatively the residuals can be saved (in C3 for example)
and the plot obtained using the commands
MTB > NSCORE C3 C4
MTB > PLOT C3*C4
• the points are fairly close to a straight line
• there is no evidence of a departure from normality
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• a plot like this can be plotted directly from the pull-down menu for the
One-Way command under the Graphs button.
• Example: For the liver weight data, the probability plot of the residuals is
shown below.
• the normal scores are quite close to the straight line and again there is no
evidence of a departure from normality