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Statistically (at least as a frequentist), it is more correct to say "we do not find significant evidence of a difference between group A and B" than "we find evidence that groups A and B are the same". I would even pick " no evidence of a difference" over claiming a null result is evidence for the null (without additional work).

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It's worth being very careful about these constructions.

"no evidence of a difference" is fine so long as it's proceeded with "This study found", which when studies are translated to press reports often gets dropped, especially in headlines.

> when studies are translated to press reports

On this particular issue, even the original studies often screw things up unfortunately. Frequentist statistics works very differently from people's natural intuition, and the attraction of a binary decision tool (NHST) has led to a lot of lazy thinking and sloppy science.

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