Sample size for ordinal logistic regression (or at least ordinal)

#1
Sample size for ordinal logistic regression (or at least logistic regression)

I am trying to determine the sample size I need for my dissertation and I have no clue where to begin. I have been unable to find a sample size calculator for ordinal logistic regression and was told by my chair to just find the sample size for logistic regression and multiply it by 1.5. That would work for me except I don't know how to do that either. I have downloaded G*Power 3 and SPSS Sample Power. When I try to use GPower I go to z tests> a priori > logistic regression but I don't know what to put in the fields (namely odds ratio, Pr(Y=1|X=1), R square other X, X parm u, or x parm theta). How do you determine this? I am using a power level of .80 and alpha level .05. I have tried looking at previous research to no avail. This is my research question: "Controlling, for income and education, is there a relationship between perceived body image and current weight stage of change?". Both perceived body image and weight stage of change are ordinal variables with body image being underweight, normal weight, overweight, and obese and stage of change being pre-contemplation, contemplation, preparation, action, and maintenance. Any insight would be greatly appreciated.
 
Last edited:

ted00

New Member
#2
Even expensive clinical studies are often powered on less information than what I think you're considering. Using a basic test, like the z-test you found, is going to typically be either a very good guess or slightly more conservative (larger sample size) than what you need. Keep in mind what all is being approximated here -- assuming your data is generated by a random physical process that can be modeled with a simple mathematical probability function, that you've accounted for the appropriate confounders, etc, etc. On top of that, nearly all power/sample size calculations use asymptotic results, i.e. they lean on large-sample theory/CLT to eventually take us to the Normal. This includes testing proportions in a logistic regression. You will need to know/guess some informatino a priori, *but*, luckily, you can also assess how sensitive your power or sample size is to those inputs. For example, say I "guess" the background rate might actually be 0.5, or 50%, and I want to see if my data suggests the rate is significantly different from 30%, I get sample size of 49 for Type I/II error 5%/20% using the usual z-test approximation (http://powerandsamplesize.com/Calculators/Test-1-Proportion/1-Sample-Equality) ... that's just for one sample, or in your case one strata ... point is, it's easier than I think you realize to build up that way, i.e. realize that significant confounders will only improve things, and first just consider the overall test of the primary study question. This http://powerandsamplesize.com/Calculators/ is a good place to do what i'm saying and assess how sensitive your input values are to your required sample sizes.