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8.9 Other Useful Hypothesis Tests

The hypothesis tests presented in this chapter are run-of-the-mill techniques that are used in experiments across many disciplines. So far, though, we have only treated techniques for analyzing the mean of one or several samples. Sometimes we are more interested in properties other than the mean, such as variances or proportions. Such analyses require different hypothesis tests. They will not be treated here but to make it easier for the reader to find the appropriate technique for a given situation, a few additional hypothesis tests and the situations in which they are used will be mentioned. Once we have understood the t-test it is quite straightforward to use other techniques, as all tests are based on the same principles:

• Firstly, formulate a question that contains a statistical parameter and a word expressing a difference. It could be “Is the sample mean different from the target value?”, “Are the variances of these two samples different?”, or something similar. In the teatime experiment it would be “Is the proportion of correct classifications higher than what could be expected to occur by chance?”
• Translate the question into a null hypothesis and an alternative hypothesis. These are mathematical relationships between the sample statistic and the population statistic. The null hypothesis assumes that the answer to the question is no – any apparent difference is due to natural, random variation in the data. As it assumes that no difference ...

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