I agree. When somebody uses this sort of second order percentage, it is confusing.
When a car's top speed increases from 105mph to 120mph, after you modified the engine, you say it increased 15mph ... or, perhaps you could say it increased 14.3%.
Using this paradigm, when a conversion rate increases from 14.5% to 18.6%, you would say it increased by 4.1% ... or, perhaps you could say it increased 28.28%
Woops! We have a problem. We just expressed the same increase, in the same units, using two very different numbers.
This is obviously a problem. The reader doesn't know what you're talking about.
It's perfectly valid to say the car increased by 15mph, so it must be perfectly valid to say the conversion rate increased by 4.1%. In fact, I think that when most people read something like this, this is what they assume, that the delta between the old conversion and the new conversion is that percentage. At first blush, saying the conversion rate increased by 28.28% should be OK, but it's not OK, because the whole point is to convey information, and you have failed to do so. Now you have to use context, to figure out what the hell they meant. This is unacceptable, especially when talking about mathematics, we should not need context to sort out what's going on.
What's the answer? I don't know. But there's definitely a problem here.
>Using this paradigm, when a conversion rate increases from 14.5% to 18.6%, you would say it increased by 4.1%
No you cannot say it increased by 4.1% and that's because you are talking about per cent. I don't know why you would ever use 4.1% in this context. It is simply wrong.
May be you can say 4.1 percentage points but I don't see a need for it when you can say (and be right) that it increased by 28%.
To be sure, the fact that we are talking about percent changes something, which is what I spent several paragraphs exploring.
To say that subtraction of percentages is against the rules, (while perfectly valid and often used in other units) but percentages of percentages is not against the rules, requires a bit more than "It is simply wrong", don't you think?
Sure, you're "right", when you say it increased by 28%. The point is, perhaps you shouldn't be "right", and what is "right", anyway, if nobody knows what the hell you're really saying?
We see this when talking about tax changes. If somebody wants to minimize the sticker shock of a tax increase, they use the delta. So, if the rate rises from 3% to 4.5%, they say they increased the rate 1.5%. If you want to maximize the sticker shock, you say that the tax rate was increased 50%. Either side can say they are doing the math "right".
Those who care about actually conveying the information, rather than produce sticker shock of either sort, always have to spell it out carefully, by actually saying, "the tax rose from a rate of 3% to a rate of 4.5%" This is a bit longer, but it's necessary, given this weird unit.
Why not? It makes perfect sense and conveys the relevant information. You should talk about percent changes whenever the important bit is the ratio between the new and old value.
Comments
Can we not talk about percent changes of percentages?
I agree. When somebody uses this sort of second order percentage, it is confusing.
When a car's top speed increases from 105mph to 120mph, after you modified the engine, you say it increased 15mph ... or, perhaps you could say it increased 14.3%.
Using this paradigm, when a conversion rate increases from 14.5% to 18.6%, you would say it increased by 4.1% ... or, perhaps you could say it increased 28.28%
Woops! We have a problem. We just expressed the same increase, in the same units, using two very different numbers.
This is obviously a problem. The reader doesn't know what you're talking about.
It's perfectly valid to say the car increased by 15mph, so it must be perfectly valid to say the conversion rate increased by 4.1%. In fact, I think that when most people read something like this, this is what they assume, that the delta between the old conversion and the new conversion is that percentage. At first blush, saying the conversion rate increased by 28.28% should be OK, but it's not OK, because the whole point is to convey information, and you have failed to do so. Now you have to use context, to figure out what the hell they meant. This is unacceptable, especially when talking about mathematics, we should not need context to sort out what's going on.
What's the answer? I don't know. But there's definitely a problem here.
>Using this paradigm, when a conversion rate increases from 14.5% to 18.6%, you would say it increased by 4.1%
No you cannot say it increased by 4.1% and that's because you are talking about per cent. I don't know why you would ever use 4.1% in this context. It is simply wrong.
May be you can say 4.1 percentage points but I don't see a need for it when you can say (and be right) that it increased by 28%.
I believe your logic is backwards.
To be sure, the fact that we are talking about percent changes something, which is what I spent several paragraphs exploring.
To say that subtraction of percentages is against the rules, (while perfectly valid and often used in other units) but percentages of percentages is not against the rules, requires a bit more than "It is simply wrong", don't you think?
Sure, you're "right", when you say it increased by 28%. The point is, perhaps you shouldn't be "right", and what is "right", anyway, if nobody knows what the hell you're really saying?
We see this when talking about tax changes. If somebody wants to minimize the sticker shock of a tax increase, they use the delta. So, if the rate rises from 3% to 4.5%, they say they increased the rate 1.5%. If you want to maximize the sticker shock, you say that the tax rate was increased 50%. Either side can say they are doing the math "right".
Those who care about actually conveying the information, rather than produce sticker shock of either sort, always have to spell it out carefully, by actually saying, "the tax rose from a rate of 3% to a rate of 4.5%" This is a bit longer, but it's necessary, given this weird unit.
Why not? It makes perfect sense and conveys the relevant information. You should talk about percent changes whenever the important bit is the ratio between the new and old value.
Not sure I got your point. Can you clarify?