Post from Beijing

In response to my post on "The appliedness of Statistical Research"

Nick Payne said...
This is somewhat only tangential to your comment. After years of being a client of statisticians and then becoming one, I am struck by something. Most scientistis and researchers who generate data understand that their data is only some approximation of the variable they are truly studying, while most consulting statisticans acti=as if the data WERE the variable of interest.How can I get applied statisticians to look past the data towards the actual variable? Issues in this are often that the measuring instrument introduces (or subtracts) attributes that are not releveant to thr true underlying variable.

I have thought about this before. I feel the term "variable" is a vaguely defined scientific term, which may have different meanings in different physical & social sciences, AND is of unambiguous meaning in mathematics. In statistics, when we study the properties of methods, we treat variables at the utmost mathematical level since we would use tools in mathematics domains. However, when interpreting the values of statistics, or outputs from a statistical procedure, one needs to distinguish between the variables as in data and the variables as in reality (or the true quantities we are trying to do inference on). The true quantitites that scientists are trying to study sometime can be called parameters in statistcs, but not always. I believe the whole philosophy behind formal statistical inference is trying to quantify and understand the "gap" between what we observe in the data collected and the truth.