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Chapter 7 - Analysing the Data Part IV - Analysis of Variance Chapter 1 - Behavioural Science and research Chapter 2 - Research Design Chapter 3 - Collecting the Data Chapter 4 - Analysing the Data Part I - Descriptive Statistics Chapter 5 - Analysing the Data Part II - Inferential Statistics Chapter 6 - Analysing the Data Part III - Common Statistical Tests Probability Sampling distributions Steps in hypothesis testing Type I and Type II decision errors Power Bonferroni Confidence Intervals Readings and links


Chapter 5: Analysing the Data
Part II : Inferential Statistics


One or two-tailed tests?

In the examples of hypotheses given above, there are actually two different types of alternative hypotheses. Examples 1 and 3 illustrate non-directional hypotheses (or, "two-tailed" tests) Š these are stated in "not equal to " terms; the direction of deviation of the alternative case is not specified. Examples 2 and 4 illustrate directional hypotheses (also termed "one-tailed" tests) where the direction of deviation from the null value is clearly specified; that is, a specific predicted outcome is stated.

A two-tailed test requires us to consider both sides of the Ho distribution, so we split alpha and place half in each tail. A directional hypothesis only considers one tail (the other tail is ignored as irrelevant to H1), thus all of alpha can be placed in that one tail. A caution should be noted here: one-tailed tests, at present, should only be used in the light of strong previous research, theoretical, or logical considerations. Hence a "claim", "belief", or "hypothesis", or "it was predicted that" is not sufficient to justify the use of a one-tailed test.

A problem with using one-tailed tests is that of placing all of alpha in the wrong tail! This is another type of error - predicting the wrong tail of the distribution, and has consequences, not only of non-significant findings, but acute embarrassment as well! (And donÕt think it doesn't happen!). It is not fair waiting until you see the test results, and then saying, "I wanted a one-tailed test in the direction of the difference indicated by the statistical test" Š such decisions regarding alpha must be made prior to any data collection.

One application in which one-tailed tests are used is in industrial quality control settings. For example, a company making statistical checks on the quality of its medical products is only interested in whether their product has fallen significantly below an acceptable standard. They are not usually interested in whether the product is better than average, this is obviously good, but in terms of legal liabilities and general consumer confidence in their product, they have to watch that their product quality is not worse than it should be. Hence one-tailed tests are often used. Also, in some areas of educational and industrial/organisational research, theory is considered strong enough to allow one-tailed tests. See Howell p. 101 for more on this baffling issue.




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