provides can be relatively unhelpful. While dropping to a 90 percent CI would reduce the range and
sample size needed, having only 90 percent confidence that the true value is in the range is also not
very helpful. This may be why there seems to be an industry standard to use the 95 percent confidence
level when calculating and reporting CIs.
The confidence level is sometimes abbreviated CL, just like the confidence limit, which can
be confusing. Fortunately, the distinction is usually clear from the context in which CL appears.
When it’s not clear, we spell out what CL stands for.
FEEL CONFIDENT: DON’T LIVE ON AN ISLAND!
Imagine that you enroll a sample of participants from some defined population in a study and obtain a sample statistic. As an
example, you calculate a mean blood glucose level from a sample of 50 adult diabetics representing the background
population of all adult diabetics. Assume you calculate a 95 percent CI around this statistic, and then you assert that you are
95 percent confident that your CI contains the true population value. But what does that even mean? How can anyone be 95
percent confident? What does that feel like?
There is a popular simulation to illustrate the interpretation of CIs and help learners understand what it is like to be 95 percent
confident. Imagine that you have a Microsoft Excel spreadsheet, and you make up an entire population of 100 adult diabetics
(maybe they live on an island?). You make up a blood glucose measurement for each of them and type it into the
spreadsheet. Then, when you take the average of this entire column, you get the true population parameter (in our
simulation). Next, randomly choose a sample of 50 measurements from your population of 100, and calculate a sample
mean and a 95 percent CI. Your sample mean will probably be different than the population parameter, but that’s okay —
that’s just sampling error.
Here's where the simulation gets hard. You actually have to take 100 samples of 50. For each sample, you need to calculate
the mean and 95 percent CI. You may find yourself making a list of the means and CIs from your 100 samples on a different
tab in the spreadsheet. Once you are done with that part, go back and refresh your memory as to what the original population
parameter really is. Get that number, then review all 100 CIs you calculated from all 100 samples of 50 you took from your
imaginary population. Because you made 95 percent CIs, 95 out of your 100 CIs will contain the true population parameter
(and 5 of them won’t)! This simulation is a way of demonstrating a proof of the central limit theorem (CLT), and helps learners
understand what it means to be 95 percent confident about their CI.
Taking sides with confidence intervals
As demonstrated in the simulation described in the sidebar “Feel Confident: Don’t Live on an Island!”,
95 percent CIs contain the true population value 95 percent of the time, and fail to contain the true
value the other 5 percent of the time. Usually, 95 percent confidence limits are calculated to be
balanced, so that the 5 percent failures are split evenly. This means that the true population parameter
is actually less than the lower confidence limit 2.5 percent of the time, and it is actually greater than
the upper confidence limit 2.5 percent of the time. This is called a two-sided, balanced CI.
In some situations, you may want all the failures to be on one side. In other words, you want a one-
sided confidence limit. Cars that run on gasoline may have a declaration by their manufacturer that they
go an average distance of at least 40 miles per gallon (mpg). If you were to test this by keeping track of
distance traveled and gas usage on a sample of car trips, you may only be concerned if the average
was below the lower confidence limit, but not care if it was above the upper confidence limit. This
makes the boundary on one side infinite (which would really save you money on gas!). For example,
from the results of your study, you could have an observed value of 45 mpg, with a one-sided