Given is the task to determine which odds-ratios are statistically significant for the following data:
Family affluence
Boys (n = 625)
- High: Reference
- Medium, Odds-ratio: 0.53, 95% Confidence-Interval: 0.39,0.74
- Low, Odds-ratio: 0.89, 95% Confidence-Interval: 0.55,1.44
Girls (n = 690)
- High: Reference
- Medium, Odds-ratio: 0.77, 95% Confidence-Interval: 0.46, 1.27
- Low, Odds-ratio: 0.91, 95% Confidence-Interval: 0.52, 1.60
Apparently, significant is only "Medium, Odds-ratio: 0.53, 95% Confidence-Interval: 0.39,0.74" - why is that however? All Odds-ratio values seem to lie within the confidence-interval? Hints very appreciated
I think you misunderstand the meaning of the CI of the OR. The point estimate always lies inside the CI. What determines whether the CI points to a significant result is if the CI contains the value $1$. If it does not, then the OR is statistically significant at level $\alpha$. The only CI for which this is true is the one you pointed out. All the others contain $1$, thus they do not meet the criterion for statistical significance. It is that simple.