Why the Standard Deviation in displayed Statistics and Sigma are different in an Individuals and Moving Range chart?

Why the Standard Deviation in displayed Statistics and Sigma are different in an Individuals and Moving Range chart?

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Article ID: KB0074095

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Updated On:

Products Versions
Spotfire Statistica 12.0 and higher

Description

This article uses an example to explain the computation difference in the displayed standard deviation and the sigma in an Individual Moving Range Chart.

Issue/Introduction

Why the Standard Deviation in displayed Statistics and Sigma are different in an Individuals and Moving Range chart?

Environment

Windows

Resolution

1. Open Cover.sta example data from "File | Open Examples" | Datasets folder

2. Select "Statistics | QC Charts | Individuals & moving range" and click "OK"

3. Click "Variables" to select "WIDTH" as Measurements and click "OK"

4. Click "OK" to produce the X and Moving R chart and the X/MR results dialog will be also prompted

5. Under X/MR results dialog, click "Options" to access Options dialog

6. Under "Options | Stats", select "N", "Mean", "Std.dev." (N: number of the observations in the data, Mean: mean of the observations, Std.Dev: Standard deviation of the observations) and click "OK"

7. Return to X/MR results dialog and click "X" to create a compound graph containing an individual (sample size 1) chart plus a histogram of individual observations.

The Std Dev (2.3947) displayed in the top left Statistics text box (requested via Step 6) computes the standard deviation of all observations. To verify the result, select "WIDTH" and obtain its summary statistics via "Statistics | Basic Statistics | Descriptive Statistics". The standard deviation will be the same.

The Sigma (2.1094) in the chart = Averaging moving range (amr) / d2 where d2 differs by sample size. Using average of moving ranges to estimate standard deviation of the example data: sd=amr/d2 = 2.3802/1.128379=2.1094. As such, different computation methods result in different results between Std Dev (2.3947) and Sigma (2.1094).

Note: Click here to learn more computation details of IQC charts in our online help document