I was checking a paper , they reported Beta= 1.77, 95% CI = .96, 2.58 it as a significant association? Why is that so? Isn't that a non-significant association? Isn't there a rule if 0 comes in the CI then it is non-significant?
If anyone could explain this?
Thanks
Jochen Wilhelm so if the value of confidence interval is let's say -0.9 to 2.58, would it be considered significant then?
Answer regarding the confidence interval (-0.9, 2.58): If beta = 0 is the tested hypothesis, the interval is a 95% confidence interval and the significance level is 5%, then: no, it would not be considered significant.
If your confidence interval for a regression (assuming that your null hypothesis is beta = 0) does not include zero, which is the case [0.96 , 2.59], it means that there is a good chance of finding association in your data, therefore, you can considered it significant.
It may be worth noting that the correspondence between the CI and p value of a test only holds exactly if the CI and test are formulated using the same statistical approach. For example if you use a Wald-style test and Wald CI the they should match and for NHSTs if the Ci doesn't contain the null value (usually zero) then p < alpha.
However, its not that uncommon for the test and CI to be constructed using different statistical approaches e.g., likelihood ratio test and Wald CI in a logistic regression. In these cases the two could and often do differ (though typically only slightly). Its more elegant to use the same approach ...
Beta is Type II error that should not be more than 0.20(Probability), A 95% confidence level indicates that the normal deviate is 1.96, if you consider the normal deviation as 2.58 means it is 99% CI, this are statistically significant. level. For beta 80% normal deviate will be 0.84 and for 90% its 1.64