Confidence Intervals: The basics

Disclaimer: This article is in response to a question I received recently. However, the article is of a general nature and may be of benefit to others as well.

Background Information:

Often, researchers want to find the value of a particular measure in a specific population. It could be the average height, or mean haemoglobin, etc. This measure is referred to as the population parameter. One could get an accurate measure of the population parameter by measuring all eligible individuals in the population for the measure of interest. Thus, if we are interested in the mean haemoglobin of adults in a population, we measure the haemoglobin of every adult in the population. Unless one is dealing with small populations, one is unlikely to be able to obtain measurements from every member of that population- even if every member consents to participate in the research.

Since it is not possible obtain measurement from everyone in a population, we obtain samples from the population. If the samples are large enough and representative of the population, we should be able to obtain a reasonable estimate of the population parameter from the samples. One could either strive to obtain a single value (point estimate), or a range (interval estimate) that estimates the population parameter. In the above example, the mean haemoglobin of the sample would be a point estimate. On the other hand, the confidence interval would be an interval estimate.

Usually, one obtains a point estimate and determines the p value to decide statistical significance (Null Hypothesis Significance Testing). There is a problem with stating a point estimate of the population parameter- we do not know the population parameter and can never be absolutely certain of it using inferential statistics. At best, we can obtain an estimate of the population parameter. This means there is always uncertainty surrounding the sample estimate. Therefore, stating a precise point estimate despite the uncertainty inherent in the value is counterintuitive. Confidence intervals are an improvement over point estimates in this aspect as they express the uncertainty inherent in such estimation.

The overemphasis on p-values and significance testing has lead to a profusion of articles wherein the results are simply declared as ‘significant’ or ‘non-significant’ based on P values. In medical research, investigators are generally interested in determining the size of difference of an outcome between groups. Confidence intervals present a range of values (based on the sample data) in which the population value may lie. P values convey nothing about the sizes of the differences between study groups and are not very helpful. Moreover, statistically non-significant p-values may reflect other issues like a small sample size, for instance.

A confidence interval produces a shift from a single value estimate (like the sample mean, difference between sample means, etc.) to a range of values that are considered plausible for the population.

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