Odds ratio with 95% confidence interval
The width and direction of the confidence interval is the primary inference with an odds ratio
If the confidence interval of an odds ratio crosses over 1.0, the event is just as likely to occur as not occur, then researchers have a non-significant association between the variables.
If the odds ratio and confidence interval are both entirely above 1.0, then the outcome is MORE LIKELY to occur as a result of the treatment or exposure.
If the odds ratio and confidence interval are both entirely below 1.0, then the outcome is LESS LIKELY to occur as a result of treatment or exposure, denoting a "protective" effect.
Confidence intervals of odds ratios and sample size
An important concept to understand is that the width of the confidence interval for an odds ratio is 100% COMPLETELY DEPENDENT upon your sample size. Look at the example below:
For purposes of presenting the reasoning of interdependency between sample size and confidence intervals, all that was done was to add a "0" to each of the frequencies in the above cross-tabulation table. The frequency of 10 in (A) became 100, 4 in (B) became 40, 2 in (C) became 20, and 8 in (D) became 80, for a new sample size of 240. With these new values, you find the EXACT same odds ratio of 10.0 as before, but look at the width of the confidence interval. It has constricted substantially and now you have more confidence that the true effect lies in the interval, 95% CI 5.42 - 18.44. This example shows that when conducting studies with categorical outcomes, a larger sample size is needed to yield precise measures of treatment effects.
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