When is a variable normally distributed? One way to tell is with the following (from
page 104-105 of ES7):
- Empirical Rule
- If a variable is normally distributed, then:
within one standard deviation of the mean there will be approximately 68% of the data;
within two standard deviations of the mean there will be approximately 95% of the data;
within threestandard deviations of the mean there will be approximately 99.7% of the data.
On pgs. 104-107 in ES7 an empirical rule is given for checking normality. To check a
set of values with this rule, use the NORMRULE template. The template as one data column,
SCORE, and three calculated columns.
The formula for the column ~95% is as follows (and the others are similar).
The formulas calculate 0/1 values according to whether the original variable is within
1, 2, or 3 standard deviations.
Use of Normrule
- Copy the values of the column of interest into the clipboard: Highlight the column, and
- Choose File>Open and select NORMRULE.jmp. (trouble opening this file in JMP?).
- Paste the values on the clipboard into the first column: Change the column name from SCORE
to the original column name from the source dataset. Highlight the first column. Choose Edit>Paste.
- The calculations automatically occur and the results appear in the data table.
To calculate the observed proportions, calculate the mean of these calculated columns.
- Choose Analyze>Distribution of Y.
- Select the columns ~68%, ~95%, ~99.7% (using Shift-click).
The Distribution of Y report displays the proportion of rows with values
of 1 and you can compare these with the expected percentage.
A.M. Best and R.K. Elswick (1996) JMP IN® Companion for Robert Johnson's ELEMENTARY STATISTICS, Seventh Edition. Duxbury
Press. (pp 132-133). ISBN 0-534-24317-7
© Copyright 1996 by Data-Ink. All Rights Reserved.
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imprint of Brooks/Cole Publishing Company, a
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