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 Glen Netherwood MiC Quality Online Learning
 :: Home ::Six Sigma ::SIX SIGMA GLOSSARY: Contingency Tables :: CURRENT STUDENTS LOGIN

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

Contingency Tables

Contingency tables are an application of the chi-square test used to test the relationship between two variables. For example, an organization decides to investigate whether there is a relationship between employees who experience sickness 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.

 Analytical and descriptive statistics are covered in the MiC Quality online course Primer in Statistics. Try out our courses by taking the first module of the Primer in Statistics free of charge.
[SIX SIGMA GLOSSARY ALPHABETICAL INDEX] [SIX SIGMA GLOSSARY INDEX OF TOPICS] [Top]

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 Primer in Statistics FREE First Module "Introduction to Statistics" Primer in Statistics FREE Reference Booklet FREE Excel Primer