How to Calculate a Confidence Interval

By Andy Pasquesi
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When analyzing the sample data from an experiment or research study, perhaps one of the most important statistical parameters is the mean: the numerical average of all the data points. However, statistical analysis is ultimately a theoretical model imposed on a set of concrete, physical data. To account for the inherent imprecision of statistical modeling, use confidence intervals to evaluate the reliability of the mean (and other parameters). A confidence interval is a range of values within which a parameter is likely to be found. The larger the interval, the higher the probability of it including the actual parameter.

Calculate The Standard Deviation

Step 1

Add together the value of every data point in the sample.

Step 2

Divide this sum by the total number of data points. This is the mean value for the sample.

Step 3

Subtract the mean from the lowest value of all the data points. For example, in the set of five data points with values of 3, 6, 11, 2 and 4, the mean would be 5.2, or (3+6+11+2+4)/5 = (26)/5 = 5.2. Since "2" is the lowest value, subtract 5.2 from 2 to get -3.2.

Step 4

Square this value and write down the result.

Step 5

Repeat Steps 3 and 4 for every data point in the entire sample.

Step 6

Add together all of the values you wrote down in Step 4.

Step 7

Divide the total from Step 6 by the total number of data points.

Step 8

Find the square root of the result from Step 7. The result will be the standard deviation for the sample.

Step 9

Divide the standard deviation by the square root of the total number of data points. The result is called the standard error of the mean.

Calculating the Confidence Interval

Step 1

Dtermine the critical value or "z" for the specific percentage you want the interval to be. Do this by accessing an online table (see Resources).

Step 2

Scroll down the second calculator on the page and check the box next to "Between."

Step 3

In the text field next to "Area", enter the percentage you want (in decimal form). For example, if you want a 95 percent confidence interval, type 0.95. If you want a 99 percent confidence interval, type 0.99.

Step 4

Write down the number that appears next to "Between." This is the critical value for the interval.

Step 5

Multiply the critical value by the standard error of the mean (calculated in Section 1, Step 9).

Step 6

Subtract the result from the parameter you want to set the confidence interval around (the mean). This is the "lower boundary" of the confidence interval.

Step 7

Add the result from Section 2, Step 5 to the parameter. This is the upper boundary of the confidence interval.

About the Author

A Chicago-based copywriter, Andy Pasquesi has extensive experience writing for automotive (BMW, MINI Cooper, Harley-Davidson), financial services (Ivy Funds, William Blair, T. Rowe Price, CME Group), healthcare (Abbott) and consumer goods (Sony, Motorola, Knoll) clients. He holds a Bachelor of Arts in English from Harvard University but does not care for the Oxford comma.