8.11 Correlation

In research, as in life, most of the important questions have to do with relationships. An introductory treatment of statistical techniques for experiments would be lopsided without any mention of techniques for investigating relationships among variables. In the previous sections we have compared samples to each other. The reason why we compare them is, of course, that we expect them to differ from each other, probably because they were sampled under different conditions. In other words, we expect that the variables we sample are dependent on other variables. We expect the fuel consumption to vary with the season, the yield of a synthesis to vary with the solvent used, and the hardness of a material to depend on the surface treatment it has undergone. In the t-tests and the ANOVA the independent variables are categorical. This means that they can be labeled but not ordered – the seasons, solvents, or surface treatments have names but not numerical values.

The independent variable is frequently a numerical variable, such as a temperature, a price or a distance. In the remaining parts of this chapter we are going to see how relationships between numerical variables can be investigated. Firstly, we will focus our interest on the strength and direction of the relationship between two variables. Does one variable increase or decrease when the other increases? Such questions are answered using correlation analysis. In the next section, we will see how the relationship ...

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