Common Errors in Statistics (and How to Avoid Them), 4th Edition

FIRST STEPS

Before we can apply statistical methods properly, we need to establish all of the following:

1. The primary hypothesis and the alternative hypotheses of interest. Will this choice result in a one-tailed or a two-tailed test?

2. The nature and relative magnitude of the losses associated with erroneous decisions.

3. The type of data that is to be analyzed.

4. The statistical test that will be employed.

5. The significance level of each test that is to be performed.

Moreover, all these steps must be completed before the data are examined.

The first step allows us to select a testing procedure that maximizes the probability of detecting such alternatives. For example, if our primary hypothesis in a k-sample comparison is that the means of the k populations from which the samples are taken are the same, and the alternative is that we anticipate an ordered dose response, then the optimal test will be based on the correlation between the doses and the responses, and not the F-ratio of the between-sample and within-sample variances.

If we fail to complete step 2, we also risk selecting a less-powerful statistic. Suppose, once again, we are making a k-sample comparison of means. If our anticipated losses are proportional to the squares of the differences among the population means, then our test should be based on the F-ratio of the between-sample and within-sample variances. But if our anticipated losses are proportional to the absolute values of the differences among ...