ABSTRACT
In the previous chapters, we mentioned that when numerical or continuous variables represent the outcome (response or dependent), means are used as appropriate measures of effect. Likewise, when the scale of measurement is continuous, the summary statistics involve the mean and standard deviation. For example, in the study on the prevalence and risk factors in postoperative pancreatitis after spine fusion in patients with cerebral palsy, the mean was used to determine the preoperative Cobb angles, preoperative WBC count, and hematocrit, comparing cases with noncases. In these three measures, the investigators were interested in the differences in these preoperative measures between cases and noncases. The statistical inference used was the two-sample t test. Suppose researchers were interested in examining the differences in these three preoperative measures between three groups. The t test will not be an adequate test statistic. To examine these differences, the investigators will need a global test in order to determine whether or not any differences exist in the data before testing the combination of the means for individual group differences. Since there are three groups in this situation, simply comparing these three groups will generate three probability values for statistical inference. The test hypothesis will be H0: μ1 = μ2, H0: μ1 = μ3, and H0: μ2 = μ3. Therefore, each comparison will falsely be termed significant at 5%, implying the occurrence of a type I error three times. The probability or chance, which is the product of alpha (0.05 = −5%), and the number of groups (3) declaring one of the comparisons incorrectly significant will be 15%.1 Consequently, the use of the two-sample t test in comparing the differences in the means between three groups inflates the error and results in an invalid statistical inference.
