Have a go at choosing what might be the correct test to analyse the data from this experiment. Explain your choice.
This is invariably the step that students find the hardest we therefore return to this in interactive exercises in chapters 4 - 8.
The student recorded the number of species in each quadrat and Domin scores for each species in each quadrat.
Using the information in appendix b of the book:
B.1. What type of investigation am I designing?
In this investigation we are starting out with a question so this is an experiment.
B.2. Which type of hypotheses am I testing?
There are three types of hypotheses that you need to choose between. If you are not sure which type of hypotheses you will be testing read the information in B.2.1 - B.2.3 before deciding. For more information about hypotheses and hypothesis testing read Chapter 4.
- Does the data match an expected ratio?
or
- Is there an association between two or more variables?
or
- Do samples come from the same or different populations?
It is not always easy to decide which type of hypothesis you are testing. In this case the student first wanted to compare the number of species in each quadrat in the two fields. She had no expectation and did not want to examine the association between the snails and plants. She was therefore testing the third type of hypotheses. The same is true for the comparison for any one plant species of the Domin scores for that species in the 20 quadrats in each field.
B.2.3. Do samples come from the same or different populations?
To test this type of hypothesis you need to decide if the data are likely to be parametric. To tell if your data are likely to be parametric (Normally distributed) you should refer to Box 3.2 in the book and in the Statistical Software section of the Online Resource Centre. When designing an investigation you can only use criterion a to decide whether your data may be parametric and in this case a decision can be made based on this criterion.
Criterion a. Are the data measured on an interval scale which is therefore quantitative and continuous, such as mm and grams?
For the first measure (numbers of species in each quadrat) the answer is NO, the scale of measurement is numbers of species which is an ordinal scale since you cannot have one and a half species for example.
For the second group of measures for any one species the students recorded Domin scores which is also an ordinal scale.
B2.3.2. Non-parametric tests
Choosing a non-parametric test depends on how many treatment variables you are planning to examine, how many categories in each variable, and how many replicates in each category. In this example there is one treatment variable, (grazing regime). There are 20 quadrats (observations) in each field. From the table you can see that the statistical test that is most likely to be appropriate is the Mann Whitney U test.
Experimental design |
Test |
You have one treatment variable. You are going to compare two samples. The data is unmatched. You have 20 observations or less in each sample. |
Mann Whitney U test (8.1.) |
You have one treatment variable. You are going to compare two samples. The data is unmatched. The data is measured on a continuous scale and you have more than 40 observations in each sample. |
z test for unmatched data (7.1.) |
You have one treatment variable. You are going to compare two samples. The data is unmatched. You have more than 20 observations in each sample. |
Sokal & Rohlf, 1981. |
You have one treatment variable. You are going to compare two samples. The data is matched. You have less than 30 pairs of observations. |
Wilcoxen's rank paired test (8.2.) |
You have one treatment variable. You are going to compare two samples. The data is matched. You have more than 30 pairs of observations. |
z test for matched data (Chapter 7 (7.2)). |
You have one treatment variable. You are going to compare two or more samples. You wish to test general and specific hypotheses. |
One-way ANOVA (Kruskal Wallis test)( 8.3. and 8.4) |
You have more than one treatment variable. You are going to compare two or more samples. You wish to test general and specific hypotheses. You will be using a calculator. |
Two-way non parametric ANOVA (8.5. and 8.6) |
You have more than one treatment variable. You are going to compare two or more samples. You wish to test general hypotheses. You want to use a computer. |
Scheirer - Ray - Hare test (8.7.). |
The criteria for using the Mann Whitney U test (8.1.1.) are that you:
- Wish to test for differences in population medians.
- Have one treatment variable and two samples.
- Have data that is non-parametric and unmatched.
- Have data that can be ranked (3.1. and 3.8.2.).
- Have two samples which both have a similar shaped distribution. For example if one distribution is skewed to the left and the other to the right (3.4.4.) then you should not use this test. (If this does arise you could try transforming the data (3.9.))
- Should not use this test if one sample has only one observation or if both samples have less than 5 observations each.
- Need not have equal sample sizes.
With our current design we can see that most of these criteria are met. We cannot at the moment check criterion 5 and need to do this when the data are collected.
(In reality the student decided to use multivariate analysis using specialist ecological software called TWINSPAN and DECORANA. These two analyzes have additional advantages as they are able to 'extract' more information from the data than the tests we have outlined in our book and are, therefore, recommended for studies of this type if you have access to the software).