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?
 A: The $\chi^2$-test was originally devised by Pearson as an approximation to the log-likelihood ratio, due to the fact that log-likelihoods were too computationally intensive for the time.
Pearson's G is defined as $G = 2\sum_{ij}O_{ij}\ln(O_{ij}/E_{ij})$. It follows the same distribution as the corresponding $\chi^2$-test. 
(Forgot to mention originally: G is much less sensitive to expected cell counts < 5).
A: 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.
References
Cochran, W. G. 1952. The $\chi^2$ 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.
