  Suppose you are told that taking a statin will reduce your risk of a heart
attack or stroke by 3% in the next ten years, or that women have better
emotional intelligence than men. You may wonder how accurate the 3% is, or how
confident we should be about the assertion about women's emotional
intelligence, bearing in mind that these conclusions are only based on samples
of data? My aim here is to present two statistical approaches to questions like
these. Approach 1 is often called null hypothesis testing but I prefer the
phrase "baseline hypothesis": this is the standard approach in many areas of
inquiry but is fraught with problems. Approach 2 can be viewed as a
generalisation of the idea of confidence intervals, or as the application of
Bayes' theorem. Unlike Approach 1, Approach 2 provides a tentative estimate of
the probability of hypotheses of interest. For both approaches, I explain, from
first principles, building only on "common sense" statistical concepts like
averages and randomness, both how to derive answers, and the rationale behind
the answers. This is achieved by using computer simulation methods (resampling
and bootstrapping using a spreadsheet available on the web) which avoid the use
of probability distributions (t, normal, etc). Such a minimalist, but
reasonably rigorous, analysis is particularly useful in a discipline like
statistics which is widely used by people who are not specialists. My intended
audience includes both statisticians, and users of statistical methods who are
not statistical experts.
