Consider the situation in which one should investigate, which treatment or treatments (of A, B, C, D, E, F, G, H) is/are the most effective (highest decrease) and which is/are the worst (lowest decrease, see figure below).
One made an ANOVA/Kruskal-Wallis-like test, which showed a statistically significant difference. Then continued with posthoc pairwise comparisons and summarized the results in the plot below. Non-capital letters a, b, c (the compact letter display, cld) above the box-plots and jittered points of data indicate statistical (in)significance in a concise way: if treatment groups share the same non-capital letter, then the differences between the groups are not statistically significant. E.g., comparing treatments G and H result is insignificant ($p \ge 0,05$) as G and H shares the same letter "e".
- It's not clear for me: basing on the results, how should I answer the question, which treatment (or group of treatments) is the most effective and which is the least effective?
- Is it correct to state that treatments, which share letter "a", are the least effective and the ones, which share "e", are the most effective? Won't it be a misinterpretation of the results as there is no strict boundary between groups of treatments, e.g., treatment G has letter "e" but E has letters "d" and "e", treatment D has "c" and "d" and so on?
For the analysis, I used
R and dataset called
My question is related to this one but touches different aspects of result interpretation.