In the excellent Practical Statistics for Medical Research Douglas Altman writes in page 235: "Because the standard error used for calculating the confidence interval differs from that used in hypothesis testing it can occasionally happen[...] that the confidence interval excludes the value specified under the null hypothesis when the hypothesis gives a non-significant result"
Could someone comment why the SE's are different in hypothesis testing than in confidence intervals construction and which formulas are appropriate in each case?
10.3 Proportions in two independent groupswith
10.3.1 Confidence interval,
10.3.2 Hypothesis testand
10.3.3 Continuity correction. The passage appears as a general conclusion of
10.3. Chapter 10 is about
Comparing groups - categorical data$\endgroup$