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I was always thinking that binning of data if data is naturally continuous is bad. However, here is the case. The goal of study was to find if there is an association between a biomarker and disease progression.
I have 40 data points, measured in percents (disease progression). I have one biomarker which is factor (yes or no). I perform Wilcox test between groups with and without biomarker, comparing disease progression, I got p-value 0.07.
Doctors have clinically significant thresholds (symptoms decrease, symptoms remain more or less the same or symptoms highly increase). They divide data into these 3 categories and count number of times this biomarker occur within the subgroup (so it form contingency table $2\times 3$). They perform exact Chi squared test in this binned data (this is actually the case) and get p-value of 0.03. Expected values in contingency tables are not super-low - 40 data points are nicely distributed across 6 cells of the contingency table.
So, 2 questions: 1) in this particular case - does it mean that exact chi squared on binned data is more powerful test than Wilcoxon test? or it is just a coincidence? (I am not surprised that tests gave different p-values - I am surprised by the magnitude of difference in p-values) Or it is likely a violation of parametric assumption of this "exact chi-squared test" (I am unfamiliar with, but I think this test was assumed)? Of course I understand that Wilcox test between groups and proportion test within 3 subgroups are answering different questions - but the initial goal is to find if there is association between biomarker and disease progression and it seems that both statistical tests are answering it.
2) Is binning preferred over continuous data in some situations? In which?