When talking about a percentage increase in a percentage metric, how can I be clear about what I mean?

It went up by "two percentage points."

~~Not a technical term but people usually understand what you mean.~~ or maybe it is.
So funny this came up here. I recently helped someone with reports she had to make to her bosses and board and we had a whole discussion about this. Company deals with hundreds of millions of dollars and this is actually an issue lol

In the end we decided to present it both ways, enumerating it in addition to the increase, which I think others have suggested. Something like "we saw a 10% increase from 20% to 22%." Helped that there were also charts to visualize the data.

I wouldn't worry about writing it out each time. When you're presenting numbers, you want to be as clear as possible. It's going to sound boring and repetitive sometimes. You're not trying to win a Pulitzer. It's for clarity.
Going from 20% to 22% is “an increase of two points” or “a two point increase”. For example, “average widget efficiency is up two points this week, from 20% to 22%.”
My company requires changes in values to be expressed in percent, but changes in percentages to be expressed in “basis points.” So a change from 8% to 10% is an increase of 200bps.
In business and finance we usually use the term "basis points". A change from 20% to 22% is an increase of 200 basis points.
I think this is always going to have potential for misunderstanding unless you have a particularly numerate audience and you present this information regularly, so they get used to the metric.

You could say "it's a **multiplicative** increase of 10%" (and then add "not an additive increase of 10 percentage points") which should have an unambiguous interpretation if your audience understands it.  (If it's important you will need to "train" your audience so they do understand it).

Edit for further thoughts - or present your info like this:

Last week     Increase      This week
20%             x1.10           22%
25%             x1.12           28%
Percentages are relative an can be misleading, especially when dealing with small numbers or small sample sizes.  For example:

Company A's net annual profits were $1 in 2020, and then$2 in 2021. Net profits increased 100%!

Company B's net annual profits were $1 million in 2020, and then$2 million in 2021. Net profits increased 100%!

Whenever I see a percentage without the base, I get sceptical and ask for the underlying numbers.
You could say "It's an increase of just two percentage points, but going from 20% to 22% is actually a 10% improvement". Wordy, but unambiguous, and it spells it out for anyone who cares enough to think about it.
by
> The change is x% (not pp.)

Or if you're making a report you can state early on that the reader should be mindful to note the difference between a change in percentage and percentage points when the metric involves percentages themselves. Then you're excused to just carry on and only have to mention it once.
State whether it is an absolute improvement or relative improvement. It is often used in the case of error or accuracy percentages. For example, in classification problems, 2% absolute improvement means classification accuracy changed from x % to x+2 %.

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