I have an issue with a result I just found.

I ran a sub-population analysis (for 2 age groups) with a complex survey design.

For this purpose I fitted a generalized linear model (family:normal,link:identity), using the function svyglm from the R package survey.

Here is my code for the model:

model=svyglm(score ~ DLA +relevel(sex,2)+raeth+pir+age+educa+(DLA:re‌​level(sex,2)),

DLA is my exposure of interest and was included as categorical (tertiles)

For one of my sub-population analyses (for older age group), my results suggest a significant difference of (-7.50 (95% CI:-14.54, -0.46)) between the third tertile and the first tertile of exposure), but the p-value=0.058 suggested a non significant result.

There is not such a big difference, but I wonder how it could be possible that the confidence interval does not include 0, whereas the p-value suggests a non-significant result.

Thank you very much for your answers

  • 2
    $\begingroup$ Can you clarify the model you fitted please? Its very hard to tell what things we're comparing here. $\endgroup$
    – Glen_b
    Nov 18, 2013 at 20:42
  • $\begingroup$ I fitted a generalized additive model. If you need further informations, please tell me. Here is my code for the model: model=svyglm(score~DLA_tert+relevel(sex,2)+raeth+pir_4+age_yr+educa+(DLA_tert:relevel(sex,2)),design,data=base_imp1) Thank you $\endgroup$
    – You Safe
    Nov 18, 2013 at 20:45
  • $\begingroup$ I can't tell what CI and what test, using which approximations or assumptions, you might be getting. What is the family and link, at least? (What software? What commands?) $\endgroup$
    – Glen_b
    Nov 18, 2013 at 20:47
  • 1
    $\begingroup$ I've never heard of the svyglm function. What package is that in? $\endgroup$
    – Glen_b
    Nov 18, 2013 at 21:55
  • 1
    $\begingroup$ When you edit to include that information, could you remove your name from the question, please? See the help here, under the heading Do not use signature, taglines, or greetings. $\endgroup$
    – Glen_b
    Nov 18, 2013 at 21:58

1 Answer 1


Both should be considered as ''borderline''... this is not so surprising.

Are you familiar with likelihood theory, and the three tests? Assuming it is the case, assume that the confidence interval is a Wald confidence interval, and that the $p$-value is obtained from a score test or a likelihood ratio test. Asymptotically, you will have $p < 0.05$ if, and only if, $0$ is not in the confidence interval, but for small samples you can meet an exception from time.

More generally, the confidence interval and the $p$-value can be obtained by procedures which are not exactly the dual of each other. This example (generated after a few trials) exhibits a similar behavior:

> x <- c(7, 3, 6, 7, 8, 4, 4, 3, 10, 5)
> y <- c(9, 19, 5, 12, 9, 13, 7, 19, 11, 7)
>  fit <- glm(y~x, family=poisson)
> summary(fit)

glm(formula = y ~ x, family = poisson)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-1.92492  -1.15183   0.06332   1.07970   1.31742  

            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  2.88977    0.25941  11.140   <2e-16 ***
x           -0.08786    0.04557  -1.928   0.0539 .  
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

> confint(fit)
                 2.5 %       97.5 %
(Intercept)  2.3732479  3.391536328
x           -0.1791838 -0.000207765
  • $\begingroup$ Thank you ELvis for your response, Do you how to extract the employed method to calculate both p-value and confidence intervals in R. Just to ensure that what you proposed as an explanation is what is happening here. $\endgroup$
    – You Safe
    Nov 19, 2013 at 16:45
  • $\begingroup$ If the documentation (or the package vignette) don’t tell you what procedure is used for the test or for the confidence interval, the only thing to do is to look at the functions code to find it... $\endgroup$
    – Elvis
    Nov 20, 2013 at 10:58

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