Section 8.1: Introduction
From Research Methods in Psychology
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[edit] Introduction
[edit] Why do you need to know this?
When you carry out a research project, you analyse a sample of individuals. However, you are not just interested in that small group of individuals – you are interested in the population from which that sample is taken – you want to be able to generalise from your sample to the population. You take a hypothesis, for example:
Students who work harder at statistics have fuller, happier lives than students who do not work so hard at statistics.
And its corresponding null hypothesis:
Students who work harder at statistics do not have fuller, happier lives than students who do not work so hard at statistics.
You might find that, in your sample, this hypothesis is supported – the students in your sample who worked harder at statistics, did indeed have fuller, happier lives. However, we are not just interested in the students in your sample. If we were only interested in the characteristics of your sample, the findings of your study (and every other study in psychology) would have very limited applicability. What we want to be able to do is to infer something from your sample to the population. If we want to infer something, as we saw in the previous chapter, we are going to have to use inferential statistics. This chapter is about the statistical procedures that are used when we want to generalise from a sample to a population.
[edit] What will we cover here?
In this chapter, we are going to look at inferential statistics - what are normally called statistical tests. We are not going to look at how to do the calculations, because they are not very interesting, and they are not very hard. Yes, that’s correct – they are not very hard. If you have a computer program (and most students nowadays do have access to a computer program) they are easy. If you don’t have a computer program, they are still easy (they are slightly more time-consuming, but they are still easy) - they involve doing arithmetic, which might be tortuous, and dull, but isn't hard. Instead of focussing on the easy stuff, we are going to focus on the parts that students get wrong much more often – knowing what a particular test does, knowing when to use it, and knowing how to write about it.
We are going to at some simple statistical tests. We will look at the standard error, which is used for one variable; then we will look at statistical tests for analysing experimental and quasi-experimental data. Finally, we will look at correlations.
[edit] Two Types of Test
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Concept: Parametric tests are more powerful tests, which make certain assumptions (normal distribution, interval level measurement) of your data. |
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Concept: Non-parametric tests are (usually) less powerful tests, which make fewer assumptions of your data. |
Statistical tests can be broadly divided into two types: parametric tests and non-parametric tests. (Some statisticians argue that non-parametric is a poor name, and prefer to call them ‘distribution-free’ tests.) If you can do a parametric test it is usually better to do so, but the parametric tests cannot be used in all circumstances.
Parametric tests make assumptions about the data that must be satisfied for the tests to work properly. If the assumptions are not satisfied, the results of the test may be misleading.
All parametric tests assume that:
- The data are measured on an interval or ratio scale (see Chapter 5).
- Some aspect of the data is normally distributed (exactly what needs to be normally distributed varies, and we shall discuss this later).
Non-parametric tests are used with ordinal data, and do not make assumptions about the shape of the distribution.
| Tip: The assumptions that have to be made when we use parametric tests are the same as those we have to make when using the mean and standard deviation. If the mean is an appropriate measure of central tendency, you should probably be using a parametric test. If you are using the median, you probably should be using a non-parametric test.
You should note that most of the parametric tests that we will consider are robust against violations of assumptions. To say that a test is robust means that the tests will still give useful answers even when the assumptions behind them are violated, as long as the violations are not too serious.
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