Choosing Your Test Spearman’s? Chi-squared? Mann-Whitney?

Choosing the correct technique Choose your technique BEFORE collecting your data! Your choice will depend on:  What you want to test  What sort of data you can collect Once you’ve chosen your test, it will tell you how much data you must collect

What do you want to test? For Correlation (eg between pollution levels and distance from city centre For AssociationFor Association (eg is there an association between snail shell colour and choice of habitat) Whether Local Data are in accordance with General FiguresWhether Local Data are in accordance with General Figures (eg are there the same proportions of cold, warm and hot days in a local city as in the county as a whole) For a Difference Between Two Populations (eg difference in numbers of a particular invertebrate between short & long grass) Click here Click here for a flow chart on choosing tests

Correlation can be positive, negative or zero  Positive correlation: as one variable increases, so does the other.  Eg nitrate concentration and algal growth  Negative correlation: as one variable increases, the other decreases.  Eg pollution levels and distance from the city centre  No correlation: one variable increasing has no consistent effect on the other Testing for Correlation

Types of correlation Two kinds of correlation:  Straight Line correlation This measures how close your data are to a straight line graph. Data must be continuous  Rank correlation This measures whether things are in the same order, but they don’t have to be in a straight line. Data do not have to be continuous

Choosing A Correlation Coefficient Straight line correlation - Pearson’s Product Moment Correlation Coefficient  Best to use if data actually are near a straight line  If you have lots of data, easier to calculate than Spearman’s (use a spreadsheet)  Lets you work out the equation of a “best-fit” line Rank correlation - Spearman’s Rank Correlation Coefficient  Data do not need to be close to a straight line  Needs absolute minimum of 4 data pairs – but more is better  Not valid if you have too many “ties”

Testing for Association Chi-Squared Association Index This lets you investigate whether there’s any association between two factors – are they linked?  Eg: Are snail shell colour and habitat preference associated?  If they are associated, it means that if we know a snail has a dark shell, it’s more likely to choose a particular habitat To do this test, we need:  Numbers of people/items etc in categories (in the example, it would be numbers of snails of each shell colour living in each habitat)  An average of at least 5 in each category

Testing Whether Local Data fit General Figures Chi-Squared Goodness-of-Fit This lets you compare local data with general – eg county, national or global – figures.  Eg does a city have significantly more warm days than the county it is in? To do this test, we need:  Numbers of people/items etc in categories (in the example, it would be numbers of days of various temperatures)  An average of at least 5 in each category  National/global/county data, to compare your data to

Testing For A Difference Difference between numbers of items in two or more categoriesDifference between numbers of items in two or more categories (eg numbers of invertebrates at 3 locations) Difference between averages (eg average area of lichen at two locations)

Difference between numbers of items in 2+ categories Chi-squared – testing for a difference Tests whether, for example, you get the same number of plants of a given species in different locations We need:  Numbers of people/ things in categories  An average of 5 in each category Use this rather than an “average” test if:  You have more than two categories (eg 3 locations)  You have just two categories, and it’s easier just to work with numbers of people/things

Difference Between Averages To choose the right test for averages, you must ask:  Are the data paired or not? Eg: Matched positions on either side of hedge Corresponding positions on two shores  Are the data likely to be normally distributed?  Only continuous data (eg lengths, widths etc) can be normal  Can check visually whether normal by diagram

Which Test for Averages? Not normal Not paired Mann-Whitney U-test Not normal Paired Wilcoxon Signed Rank Normal Not paired Unpaired t-test Normal Paired Paired t-test You could actually do Mann-Whitney for all of these. But it is easier to get a significant result using the others. All need at least 5 values in each sample.

Choosing A Test Flowchart