ABSTRACT
We begin with contingency tests, tests of association between categorical or qualitative data, using the chi-square distribution. We describe the nature of the null hypothesis and alternative hypothesis then demonstrate the calculation of the test statistic from a contingency table by working out the expected frequency for each cell and difference between it and the actual or observed frequency. We explain the process of standardisation in producing a test statistic and the use of degrees of freedom in determining the critical value and rejection region for the test.
We demonstrate estimation and hypothesis testing with bivariate quantitative data, starting with testing hypotheses about the population correlation coefficient based on a sample correlation coefficient. We proceed to cover testing hypotheses about the values of the population intercept and slope in a simple linear regression model then look at confidence intervals for values of the dependent variable, Y, for given values of the independent variable, X. We distinguish between interval predictions, estimates of the mean value of Y for a given value of X, and prediction intervals, estimates of a single value of Y for a given value of X. We conclude with an outline of non-linear regression and the use of residual plots in exploring it.
