Confidence Interval Interpretation

CORRECTION: Although my mistake is beyond the scope of the Step 1 exam, the interpretation of Confidence Interval that I used in the video is incorrect & a bit oversimplified. I stated that for an individual study there is a 95% chance that the true value lies within the 95% CI. However, confidence interval is a type of frequentist inference and the interpretation I gave in the video is really better suited for interpreting statistics of Bayesian Inference (Again please don’t feel like you need this information for the exam). What I should have said is something like “if 100 similarly designed studies use a 95% confidence interval then 95 of these intervals will contain the true value and 5 will not. For more info on this misconception click here https://en.wikipedia.org/wiki/Bayesian_inference

A Confidence Interval (CI) is the range of values the true value in the population is expected to fall within based on the study results. The results we receive in any study do not perfectly mirror the overall population and the confidence interval lets us get a better idea of what the results in the overall population might be. The confidence interval is based on a certain level of confidence. Don’t get this confused with the value of the sample population. If the measured BMI in 100 people in your study population and the mean is 25 than you are very confident that the actual mean BMI in that group is 25. Confidence interval only comes into play when you try to extrapolate your study results to other situations (like to the population overall).

If you have a 95% confidence interval (which is most common) that means there is a 95% chance that the true value lies somewhere in the confidence interval. You can also alter the width of the confidence interval by selecting a different percentage of confidence. 90% & 99% are also commonly used. A 99% confidence interval is wider (has more values) than a 95% confidence interval & 90% confidence interval is the most narrow.

The width of the CI changes with changes in sample size. The width of the confidence interval is larger with small sample sizes. You don’t have enough data to get a clear picture of what is going on so your range of possible values is wider. Imagine your study on a group of 10 individuals shows an average shoe size of 9. If based on the results you are 95% sure that the actual average shoe size for the entire population is somewhere in between 6 and 12, then the 95% CI is 6-12. Based just on your results you don’t really know what the average in the population is, because your study population is a very small sliver of the overall population. Now if you repeat the study with 10,000 individuals and you get an average shoe size of 9 the confidence interval is going to be smaller (something like 8.8 to 9.3). Here you have a much larger sample size and therefore your results give you a much clearer idea of what is going on with the entire population. Therefore, your 95% CI shrinks. The width of the confidence interval decreases with an increasing sample size (n). This is sort of like the standard deviation decreasing with an increased sample size.

Confidence intervals are often applied to RR & OR. For example, the odds ratio might be 1.2, but you aren’t sure how much of an impact chance had on determining that value. Therefore, instead of just reporting the value of 1.2 you also report a range of values where the true value in the population is likely to lie. So we would report something like the odds ratio is 1.2 and we are 95% confident that the true value within the overall population is somewhere between .9 and 1.5.

You can use the confidence interval to determine statistical significance similar to how you use the p-Value. If the 95% confidence interval crosses the line of no difference that is the same things as saying there is a p-value of greater than 5%. This is intuitive because if the confidence interval includes the value of no difference then there is a reasonable chance that there is no difference between the groups. If the confidence interval does not cross the line of no difference than the observed difference is statistically significant, because you know it is highly unlikely that the two groups are the same.

For both relative risk (RR) and odds ratio (OR), the “line of no difference” is 1. So an RR or OR of 1 means there is no difference between the two groups being compared with respect to what you are measuring. This is because RR and OR are ratios and a value divided by itself is 1. If the 95% confidence interval of the RR or OR includes the value 1, that means it is possible the true value is 1 and there is no difference between groups. If that is the case, we say the null hypothesis cannot be rejected or that there is no statistically significant difference shown. This is the same thing as saying the p-value is greater than .05.

If you are comparing the average between groups we apply the confidence interval to the difference between groups (the mean of one group minus the other group). In this case the line of no difference would be 0. So if the confidence interval for the difference between the means crosses 0, the results are not statistically significant.

 

Now that you have finished the last video in the Biostatistics & Epidemiology section you should check out the next section under the umbrella of Behavioral Sciences which covers Medical Ethics and Law.

 

 

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