The confidence interval marks the limits of uncertainty for the estimation of a population parameter from a sample.
The confidence interval is one of those tools that allow us to conserve one of our most persistent vices: we always want to draw conclusions about many from data obtained from a few.
When we want to know something about a particular group of patients it is often not possible to reach all the subjects that we are interested in, so we have to settle selecting a sample from the population and measure the variable that we consider appropriate in sampled subjects. The problem in that case is clear: we’ll know what the value in our sample is but, what is the value in the overall population? Is there any way to find it out without studying the entire population?.
The bad news is that the only way to know the exact value of the variable in the population is measuring it in all subjects. The good news is that we can estimate the population’s value from the value obtained from the sample, although within certain limits of uncertainty. These limits define the confidence interval.
Thus, the confidence interval calculated from the results of the sample tell us the limits within which the variable is in the global population, but we always have some degree of error or uncertainty. By agreement, this level of error is usually located at 95%.
In practice, the confidence interval with a probability of 95% (the most commonly used) is calculated as follows:
CI 95% = V ± 1,96 SE
In this formula, V represents the measured variable (the mean, a ratio, etc.), corresponding ±1,96 to the range around the value that includes 95% of the population in a standard normal distribution. SE stands for standard error, a term rather more unfriendly to explain, with is the equivalent to the standard deviation of the variable values distribution that we’ll obtain if we do the measure many times. But you don’t have to worry about all this nonsense, statistical software do it all effortless. The only thing that we have to know is that the confidence interval includes the true variable value in the population with the specified probability (the truth is a bit more complex, but leaves it at that by now).
One final thought before closing this topic. In addition to the degree of uncertainty, the confidence interval informs us about the study precision. The smaller the interval, the more precision we’ll have achieved. On the other hand, if the interval is too wide it is possible that the result might not be of worth for nothing, even if statistically significant. This information is not provided by p. So, what good is p?. p is useful for other things. But that’s another story…