NORMRULE

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; and
within threestandard deviations of the mean there will be approximately 99.7% of the data.

Keywords

normal distribution

Description

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.

NORMRULE

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 Edit>Copy.
• 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.
• Reference

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