2 x 2 chi-square
 
  

 


The equation below is the basic equation for the chi square two by two test.

Use the Chi square Webulator to enter your data and compute the Chi square observed score.


Variable 1
Condition 1
 Condition 2
 Row Sums
Variable 2
Condition 1
Variable 2
Condition 2

Sum of
Column 1		 Sum of
Column 2 		Grand
Total

Formula for column 1 Expected Responses
Column 1 		Formula for column 2 Expected Responses
Column 2
(row1 sum × col1 sum)
grand total 		(row1 sum × col2 sum)
grand total
(row2 sum × col1 sum)
grand total 		(row2 sum × col2 sum)
grand total

Chi Square Computations Column 1 Column 2
(observed- expected)2
expected
(observed- expected)2
expected
Chi square formula Chi-Square= 


The computed score is referred to as the chi-square observed. After computing the chi-square for the observed scores we next determine the chi-square critical score which represents the chi-square for the expected population.
The chi-square critical score for a two by two frequency table is determined by computing the “degrees of freedom” for our response set.

The computation of the degrees of freedom is:

degrees of freedom = (number of rows - 1) x (number of columns -1)

degrees of freedom = (2-1) x (2-1)

degrees of freedom = (1) x (1)

degrees of freedom = 1

and the "chi-square critical value” for degrees of freedom of "1”at p<0.05 = 3.84

If the "chi-square observed value” is › the "chi-square critical value of 3.84”, we would reject the null hypothesis and state that the two distributions ARE NOT EQUAL. However, if the "chi-square observed value ” is ‹ the "chi-square critical value of 3.84”, we would ACCEPT the null hypothesis and state that the two distributions ARE EQUAL.


The phi-coefficient provides an estimate of association in a 2 x 2 table and can help us determine the strength of association between the two variables. The phi-coefficient ranges between 0 and 1, typically.

phi2  =  phi  = 
Click here to return to the Webulator Menu Page
For more information, please contact:

Professor William J. Montelpare, Ph.D.,
Margaret and Wallace McCain Chair in Human Development and Health,
Department of Applied Human Sciences, Faculty of Science,
Health Sciences Building, University of Prince Edward Island,
550 Charlottetown, PE, Canada, C1A 4P3
(o) 902 620 5186


Visiting Professor, School of Healthcare, University of Leeds,
Leeds, UK, LS2 9JT
e-mail wmontelpare@upei.ca
Copyright © 2002--ongoing [University of Prince Edward Island]. All rights reserved.