I don't have extensive knowledge in statistics, therefore I have some trouble to understand which metrics I should use for my analysis. I have measure a feature (concentration) of multiple substances in multiple places at two time points (A and B). I was interesting to see whether there is a significant difference when comparing the concentrations I measured in a given place between the two time points. So I thought to visualize the data as simple boxplot, perform a classical unpaired t-test between A and B (or A2 and B2, where 2 is a second place) like
but I learned that when sample size is high, the resulting p-value would not be much informative as it will be extremely low (not visible in the figure here, but it is < 10E-15 for both A/B and A2/B2).
Instead, I saw reporting effect size and its confidence interval rather than p-value, as a more informative metric.
As I am working with R, I found the package
effsize, that can compute effect size and the desired confidence interval. However as you can see from my data, the sample size is definitely not equal between A and B (A has always more data point than B, sometimes just few data point more, sometimes 2-3-4... times more). Also the variance of A and B is not always equal.
I need to compute the effect size and confidence interval more than 1000 times (possible much more if I can get more data from more places) and I cannot check every time for equal sample size and equal variance between A and B. Which effect size should I then used Cohen d? Hedges g? Cliff delta? Vargha-Delaney A? another one from another package?