P/ST/10. Answers on the given questions

The paper provides answers on the following questions:
1. Outline the concepts of simple probability, conditional probability and joint probability, illustrating your answer with examples.
2. What are Type 1 and Type 2 errors? How are they related?
3. Write down the general form of the linear equation used in multiple regression and explain what multiple regression is used for. Why is the term 'least squares' sometimes used to describe the method?
4. The chi-squared test of the independence of two variables is commonly used to analyse contingency tables. Outline the assumptions underlying the test and explain how the test uses the difference between observed and expected values.
5. Height and weight are positively correlated in human populations. Explain the concept of correlation and describe the characteristics of Pearson's r.
6. The descriptive statistics calculated for a data set commonly include measures of central tendency and dispersion. Explain these two types of statistics illustrating your answer with examples.
7. What conditions are required for a sample to be representative of a population? Why is representative sampling important but hard to achieve?
8. The F-statistic, which is used in the analysis of variance (ANOVA), is a ratio of two quantities. Explain what the two quantities are and how they relate to between and within groups variability.
9. Explain the relationship between a region of rejection and a critical value of a test statistic.
10. A hierarchical cluster analysis is based on the "distance" between pairs of items. Explain the concept of distance giving examples of ways in which it can be measured.