Goodness of Fit Test (k=4)


The following Webulator is a chi-square -- Goodness of Fit Webulator for k= 4 responses

Enter the response data into the webulator below for each of your four options and then click the button labelled Compute expected frequencies. This will produce the sum of the four values that you entered and compute the expected frequency for the values in the table.

Response Options Input Column
option 1
option 2
option 3
option 4
Total Frequency Sum =
expected frequency = sum frequency × 0.25

Now scroll down and click on the button labelled Compute chi square scores. Notice each of the cells in this table will present the values of the original scores minus the corresponding expected score, squared, divided by the corresponding expected score.
The chi-square computed value is simply the sum of these individual cell values.

expected value =
(observed- expected)2
(observed- expected)2
(observed- expected)2
(observed- expected)2
Sum of (observed- expected)2

The important value from this Webulator is the computed chi-square score. The computed score is referred to as the chi-square observed. After computing the chi-square observed value, determine the chi-square critical score from a table of chi square values. The chi-square critical score represents what we should expect to observe for a distribution with "k" responses. The critical value is determined by computing the “degrees of freedom” for our response set.

The computation of the degrees of freedom is:

degrees of freedom = “k” possible responses -1

degrees of freedom = 4-1

degrees of freedom = 3

and the “chi-square critical value” for degrees of freedom of “3”

at p<0.05 = 7.815

If the “chi-square observed value ” is the “chi-square critical value of 7.815”, we must reject the null hypothesis and state that the distribution of responses across the response categories IS NOT EQUAL.

Computations for Chi Square are discussed in several texts including:

Fleiss, J., (1981). Statistical methods for rates and proportions, (2nd ed). Toronto: John Wiley and Sons.

Freedman, D., Pisani, R., Purves, R., Adhikari, A., (1991). Statistics. New York: Norton and Company.

Freund, J.E., and Simon, G.A., Statistics A First Course, New Jersey, Prentice Hall, page 66-67,1991.

Saunders, D.H., Statistics A Fresh Approach,Toronto, MGraw-Hill Publishing Company, 1990.

Hirsch, R.P., and Riegelman, R.K., Statistical First Aid: Interpretation of Health Research Data, Boston, Blackwell Scientific Publications, page 73-75,1992.

Knapp R.G., and Miller, M.C., Clinical Epidemiology and Biostatistics , Baltimore, Williams and Wilkins, 1992.

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
Copyright © 2002--ongoing [University of Prince Edward Island]. All rights reserved.