Chi squared test assumptions not met

#1
I want to perform a univariate analysis to predict if a higher BMI is associated with an increased incidence of complications after surgery. I divided the BMI of patients in 4 categories (<18.5; 18.5-25; 25-30; >30) and complications in 2 categories (yes; no). I tried to use the chi squared test to perform this univariate analysis, but the assumptions were not fulfilled. The expected counts were not higher than 1 in all cells and they were smaller than 5 in more than 20% of the cells. Which test can I use to perform this univariate analysis in a 2x4 table if the assumptions of the chi squared test are not met?
 

Karabiner

TS Contributor
#2
How large is your sample size? "The expected counts were not higher than 1 in all cells" would mean n < 8?!

Moreover, why do you artificially categorize your sample, if you have decent BMI data for use? Categorizing destroys
much information and may cause misleading results. http://biostat.mc.vanderbilt.edu/wiki/Main/CatContinuous
If you really feel a need to categorize, then you can for example still do this after the analysis with the original,
uncategorized data, for descriptive purposes.

With kind regards

Karabiner
 

gianmarco

TS Contributor
#3
Hello,
the issue is tacked e.g. in Spatz's book (LINK) (pages 316 and following).
When saple size (i.e., table's grand total) is large, small expeted frequenciesmight not pose a problem.
Also, I think (but not totally sure) that Fisher's exact test might be carried out in your context.

What is your sample size?
Can you post your actual data?

Best