Introduction
While medical researchers might be interested in knowing the answers to questions such as ‘Is age related to blood pressure?’ engineers might be interested in knowing the answers to questions such as ‘Is the shear strength of a weld related to its diameter?’ or ‘Is the rate of wear of a petrol engine related to its operating temperature?’ As you already know (from reading the introduction to Section 43.1 concerning the topic of regression), statisticians measure the strength of a relationship between two variables by using a quantity called the correlation coefficient. As you might expect, tests exist which allow us to interpret the meaning of a calculated correlation coefficient.
Prerequisites
- have knowledge of Descriptive Statistics as presented in HELM booklet 36
- have knowledge of Hypothesis Testing based on the $t$ -distribution as presented in HELM booklet 41
- have knowledge of Regression as presented in Section 43.1
Learning Outcomes
- explain what is meant by the term correlation coefficient
- perform a statistical test in order to interpret the possible meaning of a correlation coefficient
Contents
1 Correlation1.1 The calculation of Pearson’s $r$
1.2 The significance of Pearson’s $r$
1.3 Spearman’s coefficient of correlation
1.4 The calculation of Spearman’s $R$
1.5 The significance of spearman’s $R$
1.6 Table 1: Upper 5% points of the $F$ distribution
1.7 Table 2: Critical points of student’s $t$ distribution