ContingencyAnalysis Example from Zar (1999)

Biostatistics BI 45, Saint Anselm College

 

Step 1) State the biological question.

Is there a relationship between human hair color and sex in a population or is hair color independent of sex?

 

Step 2) Translate the biological question into statistical hypotheses.

 

 

Step 3) State the alpha level.

 

Step 4) State the statistical test.

 

Because we are comparing distributions of groups with two or more variables and assessing independence among all variables we would use a Chi Square contingency analysis.

 

Step 5) State the assumptions of the test.

 

We assume that the data were obtained from a randomly sampled population and that the categories are mutually exclusive.

 

Step 6) Calculate the observed Chi Square statistic from your data.

 

Sex Black Brown Blond Red Total
Male-obs 32 43 16 9 100
Male-exp 29 36 26.67 8.33  
calculations 100(25)/300  
Female-obs 55 65 64 16 200
Female-exp 58 72 53.33 16.67  
calculations 200(25)/300  
Total 87 108 80 25 300

 

 

Step 7) Find the df and critical value of Chi Square from the table of critical values.

 

 

Step 8) Compare the critical and observed Chi Square values and reject or do not reject the null hypothesis.

 

 

 

Find the actual P value

X2.05,3=7.815<X2obs=8.987<X2.025,3=9.348

0.025<P<0.05

 

Step 9) Interpret the results of the analysis as it relates to the biological question raised in 1).

 

We rejected the null hypothesis in Step 8. There is a relationship between hair color and sex (Chi Square=8.987, df=3, p<0.05).

 

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Trademark and Disclaimers

Copyright © 2001 Jay Pitocchelli. All rights reserved. The contents of this page are the intellectual property of Dr. Jay Pitocchelli for distribution to students enrolled in Biostatistics BI 45 at Saint Anselm College. These pages may not be copied, photocopied, reproduced, translated, or published in any electronic or machine-readable form in whole or in part without prior written approval of Jay Pitocchelli. Students enrolled in Biostatistics BI 45 at Saint Anselm College have permission to print this material for their lecture notes. All formulae and critical values from: Zar, J. H. 1999. Biostatistical Analysis. (4th ed.). New Jersey, Prentice Hall.