What is an "evidence based" teaching statement?
I think the verbage &quot;evidence-based&quot; is often a little misleading to a STEM researcher. When we hear &quot;evidence&quot;, we think of proofs or scientific experiments with significant sample sizes and controlling of confounders. Clearly, such hard data is not usually available in your teaching statement. However, it's also not really what people are asking for when the want to see &quot;evidence&quot; - normally, plausible anecdotal data is entirely sufficient.
More generally, what people often mean when they ask for evidence is that the current text is simply not sufficiently convincing, often because it &quot;tells&quot; rather than &quot;demonstrates&quot;. It's not so different to how we tell PhD applicants to write their Letters of Motivation - everybody can write that they love teaching (by itself this is a meaningless, empty statement), it's better to explain what you do that shows that you love teaching.
I can give an example from my own teaching statement for promotion to Associate Professor a while back. The initial version had a paragraph that read something like this:

I redesigned course XYZ and improved student success as well as student evaluations.

I received the fair criticism that I should be providing more evidence, because the current statement isn't particularly convincing. So my final version instead read something like this:

I redesigned course XYZ [explain changes]. After implementing these changes in 2017, the percentage of failing students dropped from an average of 20% to 13%, despite a technically more challenging exam design. Additionally, the course evaluation improved from an average of 3.2 to 4.4. This leads me to believe that my changes were effective, both in terms of student learning and student motivation.

This is clearly not hard proof that my course is now indeed better - maybe my exam wasn't actually harder, or maybe I just got a smarter class this year. But it's a whole lot more convincing than simply writing &quot;I did well&quot;.