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I observed a very strange behavior while doing logistic regression, univariance analysis and correlation analysis.

I have dependent binary variable and several independent variables that should be included into the model.

When I am running this model the output looks quite strange for variable X (which is in great importance for us):

  1. p-value is 0.003
  2. B is -0.001
  3. exp(B) is 0.999
  4. CI 95% is 0.998 - 1.000

When I am running univariance analysis for variable X from plotted graph I can see that group 1 (the group of the previously mentioned dependent variable that is being compared to the comparison group 2) has higher mean values of the variable X.

When I am running correlation analysis it returns 2-tailed p-value 0.024 and correlation coefficient -0.138. I am interpreting this as, comparison group have to have higher values of the X variable's mean values (which is not true according to the univariance analysis).

Descriptive analysis shows that variable X is more or less symmetric.

I tried to bin variable X in three parts (2 binning points resulting in around 33.33% of values in each bin). This showed that the values of X is increasing from bin to bin fro group 1 which is being compared to group 2.

So, I am basically stuck here. Basic theory shows that if logistic regression has exp(B) value less, than 1, then this means that variable X should have an invert effect on the group being compared to, which is not true in my case. Moreover correlation analysis demonstrates that relation is inverted which again is not true, if I can trust univariance analysis.

So, I have one questions:

  1. How such an unusual behavior (p-value is smaller, than 0.05, but Exp(B) contains 1.0) can be explained?

p.s. If more information needed on this case, then please ask. I will provide it.

Edited:

Logistic regression for bins shows:

  1. 1st bin has p-value 0.059 and Exp(B) is 3.5
  2. 2nd bin has p-value 0.007 and Exp(B) is 5.01

Overall p-value for binned variable X is 0.02

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    $\begingroup$ How can "what" be explained? You probably have an enormous sample size. The upper end of the CI is merely rounded to 1. $p$-values at the usual 0.05 level don't make sense with such large samples. $\endgroup$ – AdamO Sep 24 at 15:14
  • $\begingroup$ Thank you @AdamO for your answer. I edited a question. Now it looks like this "How such an unusual behavior (p-value is smaller, than 0.05, but Exp(B) contains 1.0) can be explained?" $\endgroup$ – user1415536 Sep 24 at 16:00
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    $\begingroup$ As @AdamO explained the value 1.000 is probably due to rounding and is in fact less than 1. Try measuring X in bigger units (so in metres rather than millmetres) to get more interpretable results. $\endgroup$ – mdewey Sep 24 at 16:14
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    $\begingroup$ Thank you, guys! It helped! Dividing by 1000 made it look much better keeping the same value of the p-value. I think, Adam O 's answer should be marked as solution for my question. $\endgroup$ – user1415536 Sep 24 at 16:41
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Based on the answers provided in comments to the original post. I tried several different things. And the best solution in current situation was to normalize variables with Z-score. This improved CI 95%. Now it looks better (No "ones" in the CI 95%). Also, it has an interesting effect on reducing values of unusually huge Exp(B) values of other variables. Descriptive analysis confirmed it.

This is more of summation. Not exactly the answer. @Adam O has provided the answer already.

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