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

confidence intervalp-valuestatistical significance

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!

Best Answer

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.

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