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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?

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    $\begingroup$ The problem seems self-inflicted. A logit regression of (yes, no) for complications on BMI data as they arrive avoids the unnecessary and arbitrary categorisation. You may need a more nuanced approach to the data on complications as well. There is much literature that BMI is a crude measure any way and that using thresholds like 25 can confuse as much as it clarifies. $\endgroup$ – Nick Cox Apr 18 at 10:12
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I would do away with the BMI grouping altogether and, at least as a start, run logistic regression on the BMI values. Then you can test the coefficient on BMI to get your p-value for BMI’s effect on rate of complications.

Grouping BMI puts you in the position of saying that 24.9 and 25.1 are as different as 18.5 and 30, which you probably do not believe.

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