risk difference ci and chi2 test

[s g]

Hi,

My question is on the interpretation of a 95% CI for a risk difference and the pvalue from a chi2-test.

Sometimes they don't agree and this is because that both methods are based on different assumptions but how would the interpretation go if say the 95% CI includes 0 and the pvalue from a chi2 test is significant?

An example of this is discussed in the statalist post:

https://www.statalist.org/forums/forum/general-stata-discussion/general/1591371-p-value-and-95-ci-don-t-match

Thank you

[David Duffy]

As you say, there are "different assumptions". The point of calculating
confidence intervals is to avoid being hung up on arbitrary thresholds.
One can produce confidence intervals by inverting the chi-square test -
this would remove your dilemma ;). Another point is there are multiple
"chi-squares" (eg Pearson v Gibbs for these kinds of data; Wald, score
and likelihood ratio tests more generally), which also can disagree.
They are all only asymptotically equivalent. This is all aside from
the widely shared distrust of P-values...

[Rich Ulrich]

(applause)

BTW, Pearson vs. Likelihood chisquared tests on (j x k) tables
are NOT asymptotically equivalent with increased N, which some
people imagine to be true. One of the two is more sensitive to
a single very-extreme cell (I forget which), while the other is more
sensitive to several moderate deviations.

I clicked on the statalist discussion cited above. Covered some
points.

If you want more discussion, check out the additional links provided
in the comments there.

--
Rich Ulrich