A Functional Approach to Teaching Statistics

Music City Center 

Much of statistics can be organized into four types of functions: summary functions, distributions, relational and logical functions. A summary function compresses a set of values into a single item which describes the original set. A distribution function associates a likelihood with a particular input. Relational and logical functions produce truth values defined as 0 and 1 in Iverson notation and the computer language APL.
Operators are higher-order functions which modify or combine existing functions to produce new functions, thus reducing the statistical vocabulary required of students. Confidence Intervals, hypothesis tests, probabilities and simulation can be handled by applying various operators to these four types of functions.
For example, the expression: "normal probability > 1.96" will produce the value 0.025. The operator, "probability" combines the distribution "normal" with the relation ">" to form a new function: the upper-tail cumulative normal distribution applied to the argument "1.96".

Statistical Education

Function

APL 

Section on Statistics and Data Science Education