# Negative percentages in a table of data

I am writing a paper and I have a table outlining the percentage change of results in different conditions. For example:

Condition A: 5%
Condition B: -7%

Essentially, I want to show that Condition A saw an increase with my method and Condition B saw a decrease. However, my adviser recommended against negative percentages, saying a percentage should always be positive. What is a proper way to format this?

I don't necessarily know that I agree with your advisor's perspective, but the way you could do this is having "baseline" be 100%, and the changes between method A and method B being deviations from 100%.

So for example, rather than 5% and -7% you'd have 105% and 93%. This, to me, seems entirely stylistic in many cases, however may be consistent with things in your field. For example, relative risks in epidemiology implicitly use a scale somewhat like this.

I suspect that your advisor doesn't have much experience with financial markets; there you learn very quickly what negative percentages mean. Jokes aside - I think it's technically correct to write negative percentages to describe changes. It should however be clear what the reference is (the value from which the difference is taken: is it the previous value in a time series, or the initial value...?). This ambiguity (and the value used for the normalization) makes the data prone to misunderstandings.

Therefore I tend to share the opinion of your advisor, as I think that it may be more illustrative to have figures with well-defined limits between 100% and 0% to display percentages as a function of time or number of measurements, rather than their changes in percent. Printing the changes is similar to plotting the derivative of a function. If those changes are expressed in percent values, things are even more complicated - that is similar to taking the derivative of the logarithm of the function. While your data may contain all the relevant information, I suspect that the representation that you have chosen is less intuitive to understand than the function itself (in this case: the percentage in absolute terms).

To give you an example: a change of -50% could be a decline from 60% to 30% as it may be a change from 4% to 2%. The implications and the statistical significance of these two cases could be very different, and by plotting the values rather than the relative differences the situation becomes much clearer.

Long story short: I think that your representation is probably scientifically correct, but I believe that there are good reasons to present the data the way your advisor suggests.

A decrease certainly is a negative percentage, I fail to see your advisor's point. Perhaps you should ask for clarification, and what the preferred way to describe such results is in your specific field.

Please consider that what you get here is the random opinions of people with no stake in your work, which probably have at most a tenuous knowledge of your area, and, most important, know nothing about the preferences of your advisor or the conventions in your research group.

Your advisor appears to have a very unusual perspective. To quote conventional wisdom, in the form of the Wikipedia article on percentages:

While percentage values are often between 0 and 100 there is no restriction and one may, for example, refer to 111% or −35%.

I think that the first thing you need to do is find out more about why your advisor objects, so that you can decide whether they can be persuaded or whether you should look for a workaround instead. If you need to do a workaround, you can simply divide by 100 and call it something like "fraction change of results" instead, i.e. +0.05, -0.07

You can definitely convert all delta numbers to be positive (see below). However, as others said, it is somewhat unusual for treatment effects data. Perhaps, your advisor has some specific reasons for that recommendation - it is better to clarify this issue with the advisor.

Should you decide to follow your advisor's recommendation on that, you can perform conversion by choosing a different anchor point (baseline), which should make sense in the context of your study (if it does not, I would try to politely argue with this recommendation). However, in any case, you would still need to provide the rationale for that decision in your paper.

If your advisor's rationale for positive only percentage values is purely aesthetic, then there is an easy solution to this "problem", especially since you're asking about table format. Just add an "Effect" (or similarly named) column to the table. For original negative delta values, simply indicate that by placing word "Decrease" (or "Negative") into the corresponding cell, while placing the absolute value of the delta into the corresponding column. The effect in the results can also be indicated in writeup, such as "... increased by five percent" and "... decreased by seven percent".