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Exercise 3

This exercise is based on research carried out by an undergraduate. The topics covered are those in 4.1 and appendix b.

Example W4.3: The sublethal effects of copper nitrate on the freshwater mollusc Lymnaea stagnalis

A number of characteristics relating to the growth and reproductive success of the freshwater great pond snail (Lymnaea stagnalis) were examined in snails living in water with varying concentrations of copper nitrate. The concentrations of copper nitrate were determined by accepted water quality standards for copper. The treatments were 0.00 mg copper nitrate l-1 water, 0.05 mg copper nitrate l-1 water, 0.02 mg copper nitrate l-1 water and 0.5 mg copper nitrate l-1 water. To examine growth, 10 snails all 11mm in length were placed in a bucket containing one of the treatments. This was repeated for all concentrations of copper. The snails were cared for appropriately for 12 weeks after which time their shell length (mm) was recorded. There were no replicated buckets.

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Q W3.1

Which statistical test(s) should be suitable for analysing these data?

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

One-way parametric ANOVA and Tukey test.

Follow the steps outlined in appendix b to reach this conclusion:

B.1 What type of investigation am I designing?

This is an experiment, you are starting out with a question (hypothesis) (go to B.2).

B.2 Which type of hypotheses am I testing?

There are three types of hypotheses which you need to choose between. If you are not sure which type of hypotheses you will be testing read the information in B2.1 - B.2.3 before deciding. For more information about hypotheses and hypothesis testing read Chapter 4.

In our example the student does not have an expectation. She only had one treatment variable (concentrations of copper) and so did not want to test for an association. Therefore, she wished to test for differences (Hypotheses type 3).

B.2.3 Do samples come from the same or different populations?

These are the type of hypotheses that are most frequently investigated by undergraduates. There are many tests that will test this type of hypotheses. These tests fall into parametric tests (Chapter 7) to be used when you have Normally distributed data and non-parametric tests (Chapter 8) when your data are not Normally distributed. To tell if your data are Normally distributed refer to BOX 3.2.

In this example the observations recorded will be 'length of snails (mm)'. This is an interval scale and therefore at this stage we should consider parametric tests.

B.2.3.1 Parametric tests

These are largely selected on the basis of the experimental design - how many variables, how many categories in each variable, how many replicates in each category. In this example there is one treatment variable (concentration of copper) with four categories or samples (0.00 mg copper nitrate l-1 water, 0.05 mg copper nitrate l-1 water. 0.02 mg copper nitrate l-1 water and 0.5 mg copper nitrate l-1 water). In each treatment there were 10 snails. From the table it would appear that a one-way ANOVA followed by a Tukey's test may be appropriate.

Experimental design

Test

You have one treatment variable. You are going to compare two samples. The data is unmatched.

t or z test for unmatched data (7.1 or 7.2).

You have one treatment variable. You are going to compare two samples. The data is matched.

t or z test for matched data (7.3)

You have one treatment variable. You are going to compare two or more samples. You wish to test general and specific hypotheses.

One-way parametric ANOVA and Tukey's test (7.5 and 7.6)

You have two treatment variables. Each variable has at least two categories or classes and all categories from one variable are combined with all categories from the second variable. You wish to test general and specific hypotheses.

Two-way parametric ANOVA and Tukey's test (7.7 and 7.8)

You have two treatment variables. Each variable has at least two categories. One variable is randomised or nested with respect to the second variable. You wish to test general hypotheses.

Two-way nested ANOVA (7.9)

You have three treatment variables. Each variable has at least two categories and all categories from each variable are combined with all other categories from the other variables. You wish to test general and specific hypotheses.

Three-way parametric ANOVA (7.10)

None of the above

Chapter 8. and Sokal & Rohlf, 1981.



The criteria that need to be met before using a parametric one-way ANOVA are (7.5.1) that you:

  1. Wish to test for differences in population means.
  2. Have one treatment variable.
  3. Have parametric data.
  4. Have an experimental design which means that each item is assigned at random to the samples.
  5. Have samples where the variation is similar (homogeneous).
  6. Have the same number of replicates (observations) in each sample.

Before the experiment is carried out we can see that criteria 1, 2, 4 and 6 are met. The remaining two criteria (3 and 5) need to be confirmed when the data are collected. At present, however, this looks as though it may be an appropriate test to use.

If the ANOVA is significant and a Tukey's test is to be used the criteria are (7.6.1) that you:

  1. Wish to test specific hypotheses following a significant outcome in a parametric one-way ANOVA.
  2. Should have equal numbers of observations in each sample.

Unless some of the snails die it appears that these criteria may be met. However, the ANOVA will need to be carried out first to confirm this.

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