I have a relatively small data set of 135 subjects. These are categorized in two dichotomous variable, type of health care and sex. I can use a Fisher's Exact test to determine if sex is significantly related to the type of care, but also want to generate a confidence interval for the difference in proportions. In this particular sample, 6 of 85 patients (7%) with good care were female and 11 of 50 (22%) patients with poor care were female. The observed difference in proportions was 15% (22% - 7%). How do I calculate the confidence interval for this difference? A formula would be great. The SPSS tool to get it would be fantastic.
Gary
I am lazy so I would computer generate the appropriate sample stats and put that in the elementary statistics formula. Best wishes, David Booth
The formula here appears pretty common. There's a normality assumption in there dependent on the Central Limit Theorem, but I don't know practically what conditions would be required for this to hold. https://newonlinecourses.science.psu.edu/stat414/node/209/
I can't help pointing out that you are trying to use a spoon to cut bread. Given the nature of your research, you are going to find SPSS tough going. R (free) does it in a trice using the epicalc package, and likewise Stata using the csi command. Given that R will cost you nothing, I'd grab a copy.
thank you all for your thoughtful suggestions. while I hope to start using R soon, for this data set I think I'll stick with good-old Excel for simplicity's sake.
Gary
Here's what I get for the example in the question, using unadjusted Wald.
BTW, you can copy and paste this code into https://rdrr.io/snippets/ .
if(!require(PropCIs)){install.packages("PropCIs")}
library(PropCIs)
wald2ci(6, 85, 11, 50,
conf.level=0.95,
adjust = "Wald")
### 95 percent confidence interval:
### -0.27648985 -0.02233368
###
### sample estimates:
### [1] -0.1494118
x1 = 6
n1 = 85
x2 = 11
n2 = 50
p1 = x1/n1
p2 = x2/n2
Z = qnorm(0.025, lower.tail=FALSE)
CI1 = (p1 - p2) - Z * sqrt(((p1*(1-p1))/n1) + ((p2*(1-p2))/n2))
CI2 = (p1 - p2) + Z * sqrt(((p1*(1-p1))/n1) + ((p2*(1-p2))/n2))
p1-p2
### [1] -0.1494118
CI1
### [1] -0.2764898
CI2
### [1] -0.02233368
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