I have a query which I hope someone can shed some light on:
When comparing 2 groups (paired) with a binary outcome of 0=positive
1=negative, I have calculated the percentage agreement between the 2
groups (i.e. if group1=0 and group2=0 then agree=1, if group1=1 and
group2=1 then agree=1, all other cases agree=0), and calculated the 95%
confidence intervals for this percentage using the basic formula for 95%
confidence intervals for proportions, amended for percentages
(pctagree+/- 1.96*sqrt(pctagree*(100-percent)/N)). However, I have also
seen cases where the exact binomial confidence interval is calculated in
this instance - thus if I have 95 observations that agree out of 95 in
total, I have 100% agreement, and using my formula the CIs are 100,100%.
But the exact binomial CIs (calculated using a software package) are
96.2,100%. Are both approaches correct? I thought exact tests were
mostly used when the sample size was very small?