Applicability of chi-square test if many cells have frequencies less than 5

To find association between peer’s support (independent variable) and work satisfaction (dependent variable) I wish to apply chi-square test. Peer’s support is categories in four groups according to the extent of support: 1=very less extent, 2=to some extent, 3=to great extent and 4=to very great extent. Work satisfaction is categories into two: 0=not satisfied and 1=satisfied.

The SPSS output says than 37.5 percent cell frequencies are less than 5. My sample size is 101 and I don’t want to reduce categories in independent variable into lesser number. In this situation is there any other test that can be applied to test this association?


Conover (1999:202) suggested that the expected values can be “as small as 0.5, as long as most are greater than 1.0, without endangering the validity of the test.”

He also provides a “rule of thumb” from Cochran (1952) which suggested that if expected values are less than 1 or if more than 20% are less than 5, the test may perform poorly. However, Conover (1999) provides some evidence that Cochran’s “rule of thumb” is overly conservative.


Cochran, W. G. 1952. The χ2 test of goodness of fit. Annals of Mathematical Statistics 23:315-345.

Conover, W. J. 1999. Practical nonparametric statistics. Third Edition. John Wiley & Sons, Inc., New York, New York, USA.

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