Jak uczyć statystyki? - propozycja - Laudański, Ludomir M. (How to Teach Statistics? - A Proposal, 2006)
The presented idea is based on a two-volume book entitled Statistics not only for Undergraduates which is addressed first of all to the students of economics. The first volume develops the course meant for the undergraduate students and is devoted to the so-called general statistics, that is statistics without probability. The second volume closer conforms with the popular courses of mathematical statistics. The first book contains twenty, while the second one - nineteen chapters. They are organized having in mind the assumption restraining the all odd-numbered chapters to the theoretical matters though their successors - even-numbered chapters - are devoted to the problems supporting the theory. Numbering of all the chapters goes in a single succession what underlines the formal union of both volumes. The second feature which probably differentiates this concept from the concepts popular in the literature of the subject becomes the pattern used to group the entire field into four subdivisions called orders. Due to this idea we commence here with the statistics of the first order called traditionally descriptive statistics: they always contain only a small amount of members and we may say - all of them we can see at one glance - what even makes their compression redundant. Nevertheless, on this ground we speak about measures of the position and the measure of the dispersion - defining the basic mean and the variance. The second order statistics have a form of grouping data. Here we find the new statistical entity that is the histogram or more precisely speaking - the frequency histogram. We trace how the raw statistical data - which we may count in hundreds - cannot be seen at glance and via the procedure of grouping they loose their identity on behalf of the members of the intervals represented by the interval medium. These statistics are further analyzed by using percentiles and other similar tools. To find their mean and variance special methods should be developed - stemming from the definitions given for the first order statistics. By the third order statistics we understand distributions - the Gaussian, binomial and Poisson-Bortkiewicz. They describe the infinite number of members - countable - discrete - or continuous, uncountable. By the fourth order statistics we call the sample statistics - Gaussian, Chi-square, t-Student and finally F-Snedecor. To operate with those statistics one has to resort to the theory of probability - as particularly evaluation of the fourth-order statistics needs to use advanced tools of this theory. And in fact - such a statistical theory becomes a branch of the theory of probability - what very often becomes a secret of its users - not expressed in an open way, rather hidden behind as something bashful, unnamed. This concept is a vote against the impoverishment of the subject by teaching how to use fewer concepts and presenting them in depth rather than dealing with a lot of them in a shallow exposition, as suggested by computer software sold by clever and unscrupulous traders.
Prace Naukowe Akademii Ekonomicznej we Wrocławiu; 2006; nr 1117, s. 90-105