I have been recently doing two-sample analysis and have a little trouble interpreting the resulting $p$-value. The $p$-value was 0.12, thus at the risk rate of 5% I cannot say the samples are different.
However, does $p=0.12$ still mean I can say there is a detectable difference between samples, just not as obvious?
My current intuition is that until $p<0.5$ the interpretation that the datasets are different is more plausible that they are the same, yet of course at e.g 0.4 the risk of that claim is very high and thus maybe not useful.