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]

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

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]

Post by David Duffy

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

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...

(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.