Confidence intervals which contain 1 but the z test and p value are significant

I calculated the confidence intervals for the regression coefficients using the formula: SE X 1.96. I then took this value away from the regression coefficient to get the lower confidence level and added it to the regression coefficient to get the upper confidence level. However, for those z tests and associated p values which are significant I am getting confidence intervals which include 1.

For instance:

Predictor variable 1:

Coefficient   = 1.08
SE            = 0.47
Z test        = 2.3
p value       = 2.2e-02

Confidence interval calculation:
SE X 1.96   = 0.47 X 1.96 = 0.92
1.08 - 0.92 = 0.16
1.08 + 0.92 = 2

Lower and upper confidence levels = (0.16, 2)

I'm just wondering why this may be the case?

Thanks so much!

• The Z test you've calculated is probably a Z test of the null hypothesis that the true value is 0?
– jona
Aug 20 '14 at 11:47

The main thing that's going on here is that here:

Coefficient = 1.08
SE              = 0.47
Z test          = 2.3
p value         = 2.2 e-02

You're testing the null that the population coefficient is zero against the alternative that it's non-zero. Something can be significantly different from zero and not significantly different from 1.

So your confidence interval can easily include 1.

Perhaps should provide us with info on what type of regression your dealing with.

The statement that confidence limits including "1.0" are non significant applies to situations when the coefficient is estimating a relative figure, often a "relative risk". This could for example be Cox regression, logistic regression (when exponentiating the coefficients). In these cases, coefficients including 1 are non significant.

But if your dealing with linear regression and model, for example, blood pressure as dependent variable and obtain a coefficient on 0.9 for blacks vs whites and a confidence limit landing on 0.8 to 1.0 then this might be extremely significant in terms on p-values; one group has higher blood pressure. In that case, passing 0.0 would imply non significance.

• Hi, thanks for replying. I'm using multinomial logistic regression Aug 20 '14 at 20:31