It is probably best if I give an example because I would like to be well-understood, and I do not know how to deal with the following situation:
I analysed, using the Kruskal-Wallis test (post hoc Dunn's test), three pairs of water quality measurements:
- river VS wells row 1 (closer to the river)
- river VS wells row 2 (further from the river)
- wells row 1 vs wells row 2.
One of the objectives of the analyses was to indicate that, simplifying, the groundwater quality in wells row 1 is 'more similar' to the river water quality than the water in wells row 2 (the closer row 1 to the river, the better).
Thus, when comparing pairs of measurements, I expected that for a selected parameter, e.g. chloride, there would be statistically significant differences between the two wells rows and between the river and row 2. At the same time, there would be no statistically significant differences (in medians) between the river and row 1.
This is because such a result would allow me to conclude that the river significantly (or more significantly than in row B) influences row 1, and the riverbank filtration process functions better there etc. (the water is very similar)
So the lack of evidence to reject H0 is something I would expect. However, writing about it in the discussion, I cannot write that it is a statistically significant result, can I? Because rejection of H0 equates to p > 0.05 (the value I assumed), which is not a statistically significant result.
How should I describe it so as not to come across as a fool (I am doing a PhD in hydrogeology and learning statistics on my own, so please forgive me)?
deleted the new part based on the comment.