This article gives examples of information gained by using ordinal over binary response variables. This is done by showing that for the same sample size and power, smaller effects can be detected

Misinterpretation of P-values and Main Study Results Dichotomania Problems With Change Scores Improper Subgrouping Serial Data and Response Trajectories Cluster Analysis As Doug Altman famously wrote in his Scandal of Poor Medical Research in BMJ in 1994, the quality of how statistical principles and analysis methods are applied in medical research is quite poor. According to Doug and to many others such as Richard Smith, the problems have only gotten worse.

I discussed the many advantages or probability estimation over classification. Here I discuss a particular problem related to classification, namely the harm done by using improper accuracy scoring rules. Accuracy scores are used to drive feature selection, parameter estimation, and for measuring predictive performance on models derived using any optimization algorithm. For this discussion let Y denote a no/yes false/true 0/1 event being predicted, and let Y=0 denote a non-event and Y=1 the event occurred.

Imagine watching a baseball game, seeing the batter get a hit, and hearing the announcer say “The chance that the batter is left handed is now 0.2!”
No one would care. Baseball fans are interested in the chance that a batter will get a hit conditional on his being right handed (handedness being already known to the fan), the handedness of the pitcher, etc. Unless one is an archaeologist or medical examiner, the interest is in forward probabilities conditional on current and past states.

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