Calculating Intervals

Calculating Quick & Dirty Confidence Intervels with Excel

The Descriptive Statistics tool in Excel's Data Analysis add-in provides a very useful number with a very misleading label. What Excel calls "confidence level" is in fact the margin of error for a two sided confidence interval for the mean of the sample's parent population. If the specified confidence level is 90%,

we can be 95% confident that the population mean is above the lower bound found by subtracting the margin of error from the sample mean, or
we can be 95% confident that the population mean is below the upper bound found by adding the margin of error to the sample mean, or
we can be 90% confident that the population mean is between the two numbers referred to above.

The reason the confidence is lower for the two sided interval is that there's a 5% possibility of error on the low side and also a 5% possibility of error on the high side so the confidence is only 90%. If you specify an 95% (two sided) confidence level to the Descriptive Statistics tool thecorresponding one sided confidence intervals will be at 97.5% confidence.

The margin of error given by Excel's Descriptive Statistics tool (under the misnomer "confidence level") is only strictly accurate if the parent population is normally distributed. Statistics textbooks detail specific ways to construct confidence intervals in many specific circumstances, but using the margin of error from Excel's Descriptive Statistics tool will very often be good enough for business decision making.