OrientationObservationIn-depth interviewsDocument analysis and semiologyConversation and discourse analysisSecondary Data
SurveysExperimentsEthicsResearch outcomes
Conclusion
A sample is only a sub-group of a much larger set about which we are trying to gather information. We are not interested in the information about the sample for its own sake but what the sample may tell us about the population, of which it is representative.
Because, at best, a sample can only be assumed to be representative of, and not identical to, the population, researchers test the validity of assertions made on the basis of sampling, before applying them to the populations from which the samples are taken. If for some reason the sample is of interest in itself (rather than as an indicator of a population) or if the 'sample' is in fact the entire population, then there is no need for significance testing.
Parametric tests, as the name suggests, use sample parameters for the text rather than comparing the whole sample (which non-parametric tests do).
There are three basic types of parametric tests, z test, t test, F Test. These are named after the sampling distributions.
This Section thus examines the following situations:
1. Test of claimed population mean on the basis of a large sample (one sample z test of means).
2. Test of claimed population mean on the basis of a small sample (one sample t test of means).
3. Test of claimed population proportion (one sample z test of proportions).
4. Test of two independent large sample means (z test of two sample means).
5. Test of two independent small sample means (t test of two sample means).
6. Test of two independent sample proportions (z test of two proportions).
7. Test of more than two sample means of any size sample (Analysis of Variance).
8. Test of means of two related samples (t test of the difference in sample means).
9. Test of two sample variances (F test).
The Section considers the tests of one or two independent samples first in the following order, z, t, and F. Then it addresses the the related sample situation. Finally, the Section considers the multi-sample case of Analysis of Variance, which utilises the F-distribution, and tests both independent and related samples.
Each test will be presented in the following way:
Name of test
When to use test. This depends upon the null hypothesis being tested and the presentation of the sample data.
Hypotheses. The null and alternative hypotheses that are applicable to the test.
What information is required to understake the test. This is information derived from the sample.
Statement of the sampling distribution. What shape the sampling distribution has and where it derives from.
Assumptions. Assumptions made about the sampling distribution and the population when using the test.
Testing statistic. What the relevant formulae for the testing statistic are for all applications of the test.
Critical Values. How to find the critical values and consequent decision rules.
Worked examples for all applications of the test. These are provided to show what is going on when undertaking the test. Most researchers will use computer programs to analyse the data and generate test statistics. However, it is important to know what the statistics mean, which ones are appropriate for any given circumstance, and how their signifcance has been computed, including the assumptions that underlie the statistical analysis.
