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Exercise 2

The aim of this exercise is to allow you to test your understanding of the information given in the introduction to Chapter 6. In section 6.5 we used Example 6.2 to illustrate the uses of a simple linear regression. If you had decided, however, that you did not wish to model the association but only wanted to test the significance of a possible association you could choose to use a correlation.

Example 6.2: Heavy metal contamination of soil under electricity pylons

An undergraduate investigated heavy metal tolerance in plants growing under electricity pylons. As part of her study she recorded the concentration of zinc in soil samples taken at regular intervals moving away from the pylons (Table 6.4). The aim of her investigation was to see if there was an association between the distance from the pylon and the concentration of zinc in the soil.

Table 6.4: Zinc concentrations (µg Zn g-1 soil) in soil at specific distances from an electricity pylon

Distance from pylon (m)

Zinc concentration (µg Zn g-1 soil)

1.0

648

1.5

610

2.0

534

2.5

500

3.0

472


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Q W2.1

Read the introduction to chapter 6 and appendix b 'Which statistical test should I choose?' Which correlation would be the most appropriate to use for these data and why?

[If you would like to save a record of your answer, please type it into this Word document instead of the text box below]

Spearman rank test.

However, the choice in this example is not an easy one to make. Usually if you have parametric data you should use the Pearson's product moment correlation as parametric tests are more powerful. However, there is so little data in this example that it is difficult to confirm that the data are parametric.

The only criterion (BOX 3.2) which you can use in this example as an indication of parametric data is a: 'Are the data measured on an interval scale and therefore quantitative and continuous, such as mm and grams?'.

The answer for both variables is YES. However using this one criterion is not a very convincing argument that the data are parametric.

Therefore, we have elected to use the Spearman rank test even though it is less powerful. Check your answer