Many authors have sought to simplify the mathematics involved in the teaching of statistics. One manifestation of this is the efforts by many textbook authors to simplify mathematical formulae. Others have gone further and have queried the extent to which mathematics is needed to convey essential statistical ideas. In particular some authors have queried the value of introducing statistical ideas at an elementary level through the medium of formal probability. In this article the focus is on simplifying the statistics rather than the mathematics. First the introduction of statistical significance through statistical control charts is described; formal probability is not required. Next re-expressions of standard formulae to facilitate their statistical interpretation are presented. As an extension of this idea the replacement of standard ANOVA in regression output by analysis of s the residual standard deviation is proposed. The article concludes with discussion of the pros and cons of mathematical and statistical thinking.
