SITEMAP UPDATES ABOUT
MiC Quality

SIX SIGMA GLOSSARY

  PROCESS IMPROVEMENT AND SIX SIGMA
ONLINE COURSES FREE TRIAL SIX SIGMA FAQ BROCHURES LICENSES ENROLL
GLOSSARY
:: Online Courses
:: Free Trial
:: Six Sigma
>> Glossary
>> Calculators
>> Reference Tables
>> Book Reviews
>> Black Belt ASQ
:: FAQ
:: Brochures
:: Licenses
:: Discounts
 
Welcome to MiC Quality Six Sigma Resources
Online Course Instructor
Glen Netherwood
MiC Quality
Online Learning
:: Home ::Six Sigma ::SIX SIGMA GLOSSARY :: CURRENT STUDENTS LOGIN

[SIX SIGMA GLOSSARY ALPHABETICAL INDEX] [SIX SIGMA GLOSSARY INDEX OF TOPICS]

Chi Square Tests

Chi Square Tests are covered in the MiC Quality online course Advanced Statistics.

Try out our courses by taking the first module of the Primer in Statistics free of charge.

  Enroll Now
Overview of the Chi Square Test

Chi Square tests, and contingency tables, are used to test whether counts, or proportions, are consistent with some specified population distribution. They can be used to answer questions such as:

  • are people who have seen an advertisement more likely to purchase a product
  • are people of a particular type under, or over represented, in a group

In both these examples the tests would discover whether the differences could be explained by chance, or whether they indicate that the factor being investigated did affect the result.

Chi Square Test

The Chi-Square 'Goodness of Fit' test is used to test whether a sample is drawn from a population that conforms to a specified distribution.

The hypothesis is:

H0 the sample conforms to the specified distribution
H1 the sample does not conform to the distribution

The test is illustrated by example. An organization has three categories of employees, 'A', 'B' and 'C'. It collects the following data:

Category
# Employees
Days Sick
A
100
10
B
60
12
C
40
14
Total
200
36

From this we form the table. Expected for 'Days Well' is calculated from:

Category
# Employees
Days Well
Expected
Chi-Square Contribution
Days Sick
Expected
Chi-Square Contribution
A
100
90
82.0
0.78
10
18.0
3.56
B
60
48
49.2
0.03
12
10.8
0.13
C
40
26
32.8
1.41
14
7.2
6.42
Total
200
164
164
2.22
36
36
10.11

If the sample conformed exactly to the distribution, the days well and days sick would be shared out as shown in the expected column. The chi-square statistic is calculated by summing the chi-square contributions from each category:

Where:

Ai actual value for category 'i'
Ei expected value for category 'i'

There are two degrees of freedom (if two of the 'days sick' data values are known the third can be calculated from the totals).

The critical p-value can be obtained from tables, or the p-value can be calculated using eg. Excel:

=CHIDIST(12.33,2) gives 0.0021

Contingency Tables

Contingency tables are an application of the chi-square test used when the relationship is between two variables. For example, the organization decides to investigate whether there is a relationship between employers who take sick leave, and who take their full entitlement of annual leave. The hypothesis is:

H0 there is no relationship between taking leave and propensity for sickness
H1 there is a relationship between taking leave and sickness

The data are as follows:

 
Sick
Not Sick
Total
Take Leave
65
55
120
Don't take leave
50
30
80
Total
115
85
200

The expected values for the individual cells are found from:

The chi-square contributions for each cell are calculate from:

The expected values and the chi-square contribution are

 
Sick
Not Sick
Total
Take Leave
69 (0.23)
51 (0.31)
120
Don't take leave
46 (0.35)
34 (0.47)
80
Total
115
85
200


The total chi-square value is 1.36. The number of degrees of freedom can be calculated from:

(rows - 1) x (column - 1)

This gives one degree of freedom. The number of degrees of freedom may also be obtained by considering that given any cell and the totals, the values in the remaining cells can be calculated.

From Excel =CHIDIST(1.36,1) the p-value is 0.24; this would not be accepted at the 0.05 level of significance.

[SIX SIGMA GLOSSARY ALPHABETICAL INDEX] [SIX SIGMA GLOSSARY INDEX OF TOPICS]
FREE eLearning
Primer in Statistics
First Module
"Introduction to Statistics"

PDF

Primer in Statistics
Reference Booklet

Excel Primer

MiC Quality Courses
   
:: Six Sigma Primer
:: Primer in Statistics
:: Advanced Statistics
:: Statistical Process Control SPC
:: Advanced SPC
:: Design of Experiments
:: Advanced DOE
:: Measurement Systems Analysis MSA/ Gage R&R
   
Learn More


Links & Copyright
If you want to link to this glossary you are welcome but please let us know.

This glossary is copyright. We will take action against anybody who downloads, copies or otherwise breaches the copyright law.


 
Copyright 1998-2008 MiC Quality Legal Notices and Privacy Policy