The following four statistics are commonly used to communicate how a value changes over time:
- Variance -- the actual change from one period to the next, either positive or negative.
- Percent Variance -- the percentage change from one period to the next, either positive or negative.
- Absolute Variance -- the actual change between periods, expressed as a positive number or zero.
- Absolute Percent Variance -- the percentage change between periods, expressed as a positive number or zero.
For example, if the price of a gallon of gasoline was $3.50 last week but is only $3.00 today, the variance is -50 cents, the percent variance is -14 percent, the absolute variance is 50 cents and the absolute percent variance is 14 percent.
The absolute percent variance is the percent variance expressed as a positive number or zero. The formula is:
| (new value - old value) / old value * 100 |
For example, the gallon of gas that went from $3.50 to $3.00 changed by -50 cents. Divide -50 cents by $3.50 and then multiply by 100 to get a percentage change of -14 percent. Take the absolute value of -14 percent, which is 14 percent.
Another way to express the absolute percent variance in a formula is:
| new value / old value - 1 | * 100
Communicating Change Using Percentages
If you knew that a gallon of gas decreased by 50 cents per gallon, but you didn't know what the price of gas was at the beginning or the end of the period, it's difficult to determine whether the 50 cent decrease is significant. However, when you communicate that the price of gasoline decreased by 14 percent, the person interpreting the change can determine how significant the change was without knowing the starting or ending values.
Using Absolute Values
The variance and percent variance are commonly used when communicating change in a tabular format, without text, while their absolute counterparts are typically used in an explanation that characterizes the change as either positive or negative. For example, in the following table, the numbers in parentheses indicate negative values:
- Beginning Price: $3.50
- Ending Price: $3.00
- Change ($0.50)
- Pct. Change: (14%)
It's important to show the change as either a positive or a negative number when displaying it in a tabular format, without text. However, when you discuss the change in a commentary, the words you use to describe the change already communicate whether the change was positive or negative, so you use the absolute value instead of the actual value. For example, you wouldn't say tha a gallon of gas decreased by -14 percent; you would say that a gallon of gas decreased by 14 percent. The word "decreased" already communicates whether the value is positive or negative, so you use the absolute percent variance in your commentary.
Steve McDonnell's experience running businesses and launching companies complements his technical expertise in information, technology and human resources. He earned a degree in computer science from Dartmouth College, served on the WorldatWork editorial board, blogged for the Spotfire Business Intelligence blog and has published books and book chapters for International Human Resource Information Management and Westlaw.