Statistics in iPhone article unnecessarily confusing

by bledsoe on February 16, 2008

The Financial Times recently reported that Google “had seen 50 times more searches on Apple’s iPhone than any other mobile handset,” a pretty impressive statistic, and one on which a number of bloggers and tech watchers have commented. One of these is Seth Weintraub, of Computerworld, and while his post adds some interesting comments to the original Financial Times report, his headline ("iPhone users search Google 5,000% more than the nearest competitor.") just makes things unnecessarily confusing by introducing another way of stating the “50 times more” number that doesn’t add any useful information.

"50 times more" and "5,000% more" are just two different ways of saying the same thing, though if you want to be picky about the arithmetic Mr. Weintraub's headline should have read, "iPhone users search Google 4,900% more than the nearest competitor." If you’re a little unclear about how these two numbers are the same, you’re not alone.

To take a simpler example, if I buy 5 shirts and you buy 15 shirts, there are a few different ways that we could compare the number of shirts I bought to the number of shirts that you bought. We could say you bought 10 more shirts than I did (10 = 15 - 5), we could say you bought 3 times as many shirts as I did (15 = 3 x 5) , or we could say you bought 200% more shirts than I did. In this example, it’s a little easier to see where the 200% number came from: you bought 10 more shirts than I did, and I bought 5 shirts, so to calculate the "percentage more" that you bought, you take the "number more" that you bought (10), divide it by the number that I bought (5), and multiply it by 100% to convert it to a percent. The actual formula would look like this:

Percent more (or percent increase) = [ (# you bought - # I bought) / (# I bought) ] x 100%

We don't actually know how many Google searches were performed by iPhone and non-iPhone users over the time period in question, but we don't need to know that to use our formula. We'd calculate it like this:

Percent increase = [ (# iPhone searches - # non-iPhone searches) / (# non-iPhone searches) ] x 100%
Percent increase = [ (50x - x) / x ] x 100%
Percent increase = [49x / x ] x 100%
Percent increase = 49 x 100% = 4900%

So Mr. Weintraub's playing a little fast and loose with his numbers, but that's just being picky. The bigger mistake is that he shouldn't have been expressing this number as a percent in the first place, because using huge percentages in this way just confuses people, and when the original article has already used the much clearer “50 times more” phrase, there’s no need to make up another completely different number to say the same thing.

To say that iPhone users did 50 times as many Google searches as non-iPhone users is immediately clear to even a casual reader, and there's even enough information in that brief statement to gain a fair amount of context. ("Wow, I would have thought 2 or 3 times as many searches would have been a lot, and 10 times as many would have been a WHOLE lot, but 50 times as many? That's impressive.") But a number like 5,000% percent just makes you think, "Wow, that sure is a big number" without giving you any useful context for evaluating it. His headline might just as well have read, "iPhone users search Google a whole whole whole lot more than the nearest competitor."

As technical writers, we owe it to our readers to present numerical information in a way that allows them to make sense out of it, not in a way that attempts to impress or confuse them.

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