# 95% CI is Insignificant, P-Value is Significant

#### StatNinja

##### New Member
Suppose you're performing a 2x2 contingency table analysis. You do your Chi Square or Fisher Exact test, as appropriate, then you calculate an odds ratio and get your 95% CI for the OR. Under what circumstances can the P-Value for the ChiSquare and Fisher test be significant (e.g. P < 0.05) but the 95% CI of the OR straddles 1.0?

Is this ever possible using standard statistics techniques?

What about if you're performing complex survey analysis where the survey is stratified, clustered and weighted? I ask because I've been using SAS to process data from a complex survey design and I've run into a situation where the P-Value and 95% CI conflict:

Sample Size = 3,618

Rao-Scott Chi-Square Test
Pearson Chi-Square 4.1614
Design Correction 1.0794
Rao-Scott Chi-Square 3.8551
DF 1
Pr > ChiSq 0.0496 *** significant
F Value 3.8551
Num DF 1
Den DF 1765
Pr > F 0.0498 *** significant

Odds Ratio (Row1/Row2)
Estimate 95% Confidence Limits
Odds Ratio 0.1548 (0.0176-1.3595) *** not significant

#### fed1

##### TS Contributor
Yes this is possible.

It occurs because the chi square (which is just the square of the asymptotic z-test for proportions) cannot be inverted to give the confidence interval for OR that you are using.

In general the deal with p-values and CI that you are thinking of only holds if the hypotheis test and CI are connected by a tautoulogy, excuse spelling.

IE

CI {estimate -se p zquant < parameter < estimate + se* zquant}

cang be reexpressed with the test stat in the middle of the inequality

I would be interested to see exact conditions myself, but that is going to be tedious i think