When the mean fails, use an M-estimator
Abstract
In the field of addictions on many occasions one has to work with quantitative variables, and the arithmetic mean is the most used location index. Nevertheless, the use of this index should be limited to those situations in which the distributions of the variables are symmetrical. The aim of this work is to exemplify the importance of recurring to adequate descriptive statistics in order to summarize quantitative variables, through the study of the quantity of consumption of addictive substances in adolescence.
The sample is made up of 9300 students between 14 and 18 years (47.1% boys and 52.9% girls) who anonymously answered a questionnaire on consumption of substances.
The quantity of weekly consumption of different substances is de- scribed using classical location indexes belonging to Exploratory Data Analysis (EDA). It can be seen how the results vary noticeably according to the statistics selected, with the Huber M-estimator as the index giving more “real” values.
The arithmetic mean is not a good index in order to duly approach the reality of drug consumption when the distributions are asymmetrical, in which cases it becomes necessary to use resistant indexes such as, among others, Huber’s M-estimator.
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