Confidence Intervals

Fundamentals of Social Statistics by Adam J. McKee

In the world of research, there’s a big argument about whether tests that check “how significant” the findings are (we call these “tests of statistical significance”) are really useful. Most researchers think they’re important because they’re used a lot in studies. But, some people say these tests can be tricky because they make things seem more exact than they really are, especially for someone who’s not a researcher. For example, when researchers find an average (or “mean”) from a group they’ve studied, there’s always a bit of error, so it’s not the exact average of everyone in the whole group they’re interested in.

Confidence Intervals: A Better Approach?

To deal with this issue, many researchers suggest using something called “confidence intervals.” This is like saying, “We’re pretty sure the real average is somewhere between these two numbers.” A confidence interval gives a range of values and says how sure we are (like 90%, 95%, or 99%) that this range includes the actual average for the whole group.

How to Create a Confidence Interval

Creating a confidence interval involves three steps:

  1. Estimate the Group’s Average: This is done by finding the average of the group we can study.
  2. Find the Lower Limit: We do this by taking away a little extra (called the “margin of error”) from the average we calculated.
  3. Find the Upper Limit: We add the same margin of error to the average.

The margin of error changes depending on how big our study group is, whether we know the standard deviation (a measure of how spread out the numbers are) of the whole group, and how confident we want to be.

What Does a Confidence Interval Tell Us?

When we say a confidence interval has a certain percentage, like 95%, it means we’re 95% sure that the real average of the whole group is somewhere in that range. Remember, we’re most interested in the average of the whole group (population), not just the group we studied (sample). Each time we pick a new group to study, the average we find will be a little different. If we were to do this 100 times, 95 of those times, the real average of the whole group would fall within our confidence interval. This might sound like a lot, but with computers, we can simulate this to see how it works!

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Last Modified:  11/15/2023


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