# Common Misrepresentations of Percentages

The basic concept of percentages is taught and typically mastered at a young age, but from time to time I find percentages being misused and misinterpreted within the business environment. I will be the first to admit that I am guilty of doing such a thing in the past (nothing to be ashamed of!), but because I don’t have the luxury to incorrectly use percentages in my line of work, the precision I have developed over time has led me to become more aware of common percentage mistakes in articles and reports that I have read. This heightened awareness is what has driven me to compile the following list of the three biggest percentage mistakes I find in business so you can avoid making the same mistakes with your analysis.

## Percentage vs Percentage Point

When discussing performance trends, a common highlight is the difference between two data points, such as the increase between a conversion rate of 24% in period one and a 26% conversion rate in period two. The difference between these two percentages is two, but this should not be classified as a “two percent” increase, but rather a “two **percentage point**” increase or “2**pp**”. Since we are using simple arithmetic to subtract the two values, we need to differentiate it from the relative change associated with the percents. This is done by expressing it as a unit, as opposed to actually 2% of another value. If we were to express the difference in the example as a percentage, then you would really be saying 2% of the original value, 24%, or 2/100 of 24%, which would equate to 24.2%. The results are drastically different and will immediately cause confusion for anyone who lacks access or is unfamiliar with the data being calculated. For this reason of ambiguity, we represent the difference between the two percentages with the use of percentage point or pp.

## Percent Change vs Percent Difference

Percent Change is the go-to formula for computing the differences between two data points in percent format, but what many don’t realize when using this formula is that it isn’t the best formula to use for all data point comparisons. When you are trying to understand the difference between two periods of time, then percent change is perfectly fine to use.

The formula for **percent change** is `((New value - Old value)/Old value)*100`

The first step of the formula is to take the difference between the new and old value.

`New value - Old value`

Then you divide that result by the old value to determine the growth/decline between the two data points in decimal format before multiplying by 100 to convert it to a percentage.

`(Result/Old value)*100`

This formula outputs the relative change from the old value to the new value, which is perfect when analyzing time related performances, but if you are determining the difference in data points without directionality, then this is not the right formula to use.

This is true for cases like that of a funnel progression report, where determining the growth or decline from one step to the next is not helpful in understanding what percentage of the previous step progressed to the next step. This type of question would be best answered using the percent difference formula.

The **percent difference** formula is `((A - B)/((A + B)/2))*100`

and unlike percentage change does not require a strict order of values to generate a proper outcome.

First you take the difference between both values to get a value for the numerator in the calculation.

`A - B`

Then calculate the average between the same two values, which will be the denominator in our calculation.

`(A + B)/2`

Finally, divide the difference by the average and multiply the result by 100.

`(Difference/Average)*100`

As you can see from these two examples, the calculations are very much different and carry completely different meanings despite what many believe. To avoid making the mistake of using the incorrect formula in your analysis, a good rule of thumb is to understand if the variance from your pair of values shows directionality that fits the criteria of “old” or “new” (Percentage Change). If there is no directionality then you will need to use an average of the two values as a standard comparison within your formula (Percentage Difference).

## Fold Change Wording and Relationship to Percentage Growth

A common business reference to demonstrate the scale of growth or decline in two values is the term “-fold”. “**Fold change**” or “-fold” is a measure that describes how much a metric changes from an initial value to its final value. It is calculated by multiplying by a factor of the initial value such as $300 is 3-fold of $100. $100 is the initial value which is multiplied by a factor of three to get the final value of $300. This seems like a pretty straightforward definition, however, when communicating the meaning of this 3-fold increase and its translation in percent format, I have found various interpretations.

Does the 3-fold example above mean it grew by greater than $100 or it is an increase of $100? Connecting this back to the percentage examples presented in the previous sections, is this a 300% return or 200%?

Some may go with the former two answers that the money grew by 3 times and/or 300% of the initial investment, but this is incorrect. In actuality, it is that the final value is three times as much as the initial value and using percentage change, you can see that this is a 200% increase since the initial value is removed from the equation. If you wanted to use grew by, like the example above, then you would actually be saying it doubled or a 200% increase.

While the statements being compared above might appear to be identical to the common reader, the slight variances in word choice deliver very different meanings and if used incorrectly, can result in very misleading interpretations.

## Tying it all together

Percentages, while elementary by nature, are a bit trickier to communicate and interpret than what many are led to believe. A large reason for the incorrect use of percentages is due to poor word choice use in the articulation of percentages and percentage calculations. A few simple words can deliver a definitive statement that does not reflect what the formula computes and the result can severely impact business decisions if not caught quick enough. Your best bet to avoid all of the headaches from making these mistakes is to go back to the basics from time to time to reinforce your understanding of the concept.