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Normal Probability Plot - normal probability plotter


Normal Probability Plot-normal probability plotter

STATGRAPHICS - Rev. 11/7/2013
Normal Probability Plot
Summary ......................................................................................................................................... 1
Data Input........................................................................................................................................ 2
Analysis Summary .......................................................................................................................... 2
Normal Probability Plot .................................................................................................................. 3
Summary
The Normal Probability Plot is used to help judge whether or not a sample of numeric data
comes from a normal distribution. If it does not, you can often determine the type of departure
from normality by examining the way in which the data deviate from the normal reference line.
Sample StatFolio: probplot.sgp
Sample Data
The file bottles.sgd contains the measured bursting strength of n = 100 glass bottles, similar to a
dataset contained in Montgomery (2005). The table below shows a partial list of the data from
that file:
strength
255
232
282
260
255
233
240
255
254
259
235
262
2013 by StatPoint Technologies, Inc. Normal Probability Plot - 1
STATGRAPHICS - Rev. 11/7/2013
Data Input
The data to be analyzed consist of a single numeric column containing n = 2 or more
observations.
Data: numeric column containing the data to be summarized.
Select: subset selection.
Analysis Summary
The Analysis Summary shows the number of observations in the data column.
Probability Plot - strength
Data variable: strength
100 values ranging from 225.0 to 282.0
Also displayed are the largest and smallest values.
2013 by StatPoint Technologies, Inc. Normal Probability Plot - 2
STATGRAPHICS - Rev. 11/7/2013
Normal Probability Plot
This pane displays the probability plot.
Normal Probability Plot
99.9
n:100
99 Median:255.0
95
Sigma:8.14815
W:0.97781
80 P:0.4162
50
20
5
1
0.1
220 240 260 280 300
stre ngth
The plot is constructed in the following manner:
The data are sorted from smallest to largest and the order statistics are determined. By
definition, the j-th order statistic is the j-th smallest observation in the sample, denoted by
x(j).
The data are then plotted at the positions
x( j) , 1 j 0.375
n 0.25 (1)

where 1(u) indicates the inverse standard normal distribution evaluated at u.
If desired, a straight line is fit to the data and added to the plot.
The normal probability plot is created in such a way that, if the data are random samples from a
normal distribution, they should lie approximately along a straight line. In the above plot, the
deviation of the values from the reference line at both ends indicates that the data may come
from a distribution with relatively longer tails than a normal distribution.
2013 by StatPoint Technologies, Inc. Normal Probability Plot - 3
percentage