Beware of percentages

On Saturday, I saw this newspaper clip on the Forum section of Straits Times, where readers write in to comment on issues. I put a copy here, with my own underlined paragraph:

Click on it to enlarge. Taken from ST, 25/01/14 (my own underlined paragraph though)

The author wrote that "total expenditure for social development (...) increased by 54.5% - much faster than the 31.5% increase in tax revenue". I take issue with the fact that using percentages are highly misleading. The reason is that percentage calculations are relative, hence they are always based on something. If the basis of comparison between two computations of percentages are different, there's really nothing to compare. In other words, it could be misleading.


Let me illustrate further. Suppose my salary is $3,000 and I spend $150 on food per month in January.

Let's consider this statement: The amount that I spend on food for February increased by 50% while my salary only increased by 5%.

It's not stated explicitly, but this seems to imply that the increment in salary is unable to cover the increment in food expenses.

This means that:

January: Salary = $3,000, Food = $150
February:  Salary = $3,150, Food =  $225
Absolute increment:  Salary = $150, Food = $75


I can also say: The amount that my salary increases is more than enough to cover the increases in food expenses. Absolute increment shows that is the case, even though relatively speaking, the rise in food is indeed faster than the rise in salary.


Both statements are not wrong, it's just that without digging deeper, it's quite easy to make a hasty conclusion if someone uses that first statement. Hence, when the author uses percentages to compare the increment in expenditure for social development and the corresponding increment in tax revenue, it seems to imply that tax revenue collected are unable to sustain the extra spending.


I didn't check out the actual values in tax revenues and social spending. But it doesn't matter, because no matter what values I put in as the base for 'tax revenue' and 'social spending' in 2008, where the increment is 31.5% for increment in tax revenues and 54.4% for increment in social spending from FY2008 to FY2013, the result is the same. I always end up with more 'Savings' (calculated by subtracting 'social spending' on 'tax revenue') yearly from FY2008 to FY2013.

So...even though more is spent on social spending in percentage terms than tax revenue collected, I still end up with more unused tax revenues year by year that can be used for other stuff? The tax hike doesn't sound so urgent now, it seems.


Note to self: When someone uses percentages, check the base in which the percentage is calculated. The absolute value might be quite a different picture from a relative one.


I know there are other issues involved, but my main point is just to be careful when percentages are used in presentation. There's usually more than meets the eye. Both percentage and absolute values need to be presented to see a clearer picture in case hasty conclusions are drawn. And seriously, I'm not for tax hikes (like most people, I assume).