Other parts of this site explain how to do the common statistical tests. Here is a guide to choosing the right test for your purposes. When you have found it, click on "more information?" to confirm that the test is suitable. If you know it is suitable, click on "go for it!"
Important: Your data might not be in a suitable form (e.g. percentages, proportions) for the test you need. You can overcome this by using a simple transformation.Always check this - click HERE.
Use this test for comparing the means of two samples (but see test 2 below), even if they have different numbers of replicates. For example, you might want to compare the growth (biomass, etc.) of two populations of bacteria or plants, the yield of a crop with or without fertiliser treatment, the optical density of samples taken from each of two types of solution, etc. This test is used for "measurement data" that are continuously variable (with no fixed limits), not for counts of 1, 2, 3 etc. You would need to transform percentages and proportions because these have fixed limits (0-100, or 0-1).
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Use this test like the t-test but in special circumstances - when you can arrange the two sets of replicate data in pairs. For example: (1) in a crop trial, use the "plus" and "minus" nitrogen crops on one farm as a pair, the "plus" and "minus" nitrogen crops on a second farm as a pair, and so on; (2) in a drug trial where a drug treatment is compared with a placebo (no treatment), one pair might be 20-year-old Caucasian males, another pair might be 30-year old Asian females, and so on.
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Use this test if you want to compare several treatments. For example, the growth of one bacterium at different temperatures, the effects of several drugs or antibiotics, the sizes of several types of plant (or animals' teeth, etc.). You can also compare two things simultaneously - for example, the growth of 3 bacteria at different temperatures, and so on. Like the t-test, this test is used for "measurement data" that are continuously variable (with no fixed limits), not for counts of 1, 2, 3 etc. You would need to transform percentages and proportions because these have fixed limits (0-100, or 0-1).
More information? You need this, because there are different forms of this test.
Use this test to compare counts (numbers) of things that fall into different categories. For example, the numbers of blue-eyed and brown-eyed people in a class, or the numbers of progeny (AA, Aa, aa) from a genetic crossing experiment. You can also use the test for combinations of factors (e.g. the incidence of blue/brown eyes in people with light/dark hair, or the numbers of oak and birch trees with or without a particular type of toadstool beneath them on different soil types, etc.).
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Use this test for putting confidence limits on the mean of counts of random events, so that different count means can be compared for statistical difference. For example, numbers of bacteria counted in the different squares of a counting chamber (haemocytometer) should follow a random distribution, unless the bacteria attract one another (in which case the numbers in some squares should be abnormally high, and abnormally low in other squares) or repel one another (in which case the counts should be abnormally similar in all squares). Very few things in nature are randomly distributed, but testing the recorded data against the expectation of the Poisson distribution would show this. By using the Poisson distribution you have a powerful test for analysing whether objects/ events are randomly distributed in space and time (or, conversely, whether the objects/ events are clustered).
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