Regression Analysis Used in Compensation Administration

STANDARD DEVIATION

In compensation analyses, it is often useful to find the standard deviation of a set of salaries. The standard deviation tells you if the differences in salaries in the set of salaries that you are looking at is small or large. If the difference is large, that means there is a lot of variability in that set of salaries, and it may not be reliable to use in comparing salaries.

In statistics, standard deviation is a measure of the average distance of an observation from the mean. Standard deviation is one of several measures of the spread of the sample. In a normal distribution of data:

• 68% of the observations are within 1 standard deviation of the mean
• 95% of the observations are within 2 standard deviations of the mean
• 99.7% of the observations are within 3 standard deviations of the mean

Standard deviation (s) is defined as:

Another way to write the above equation would be:

x1, xn, and xi	observations
	sample mean
n	sample size

Suppose you have the following dataset:

*The numbers used are for illustration purposes only.

What is the standard deviation of the dataset?

The above dataset has a mean of $114,914 and a standard deviation of $32,958. Remember that approximately 95% of the observations in a normal distribution fall within 2 standard deviations of the mean. To find the 95% confidence interval:

$32,958 x 2 = $65,916 (2 standard deviations)

2 standard deviations below $114,914 = $48,998 ($114,914 – $65,916)

2 standard deviations above $114,914 = 180,830 ($114,914 + $65,916)

A standard deviation of $32,958 then, would give you a 95% confidence interval of:

{$48,998 ≤ m≤ $180,830} = 95%

The interpretation of the above confidence interval is that you can be 95% confident that $48,998 and $180,830 include the true value of m (the population mean of all CFO base salaries). The large width of this 95% confidence interval implies that there is too much variability in the dataset and this sample might not be useful in comparing salaries as it is too small.