PRACTICAL STATISTICS FOR ASTRONOMERS .2. CORRELATION, DATA-MODELING AND SAMPLE COMPARISON

Correlation is discussed in various guises in which astronomers may st umble across it, beginning with the pitfalls of searching for correlat ions between two variables and the tests, both parametric and non-para metric, for such correlations. This leads to the subject of regression analysis, a particular form of data modelling. Some general aspects a nd procedures in data modelling and parameter estimation are then desc ribed, including least squares, maximum-likelihood, Bayesian technique s and minimum chi-square. The final topic is sample comparison, an are a of hypothesis testing: here some seven rests in all are described, t hree for the comparison of single samples with prediction and four for inter-sample comparison. Non-parametric methods are emphasized throug hout as being of most use to the astronomer, who frequently faces (i) very small samples and (ii) lack of control over the Universe needed e ither to rerun the experiments or to understand frequency distribution s from which the small samples were drawn.