In both examples, as the number of comparisons increases, it becomes more likely that the groups being compared will appear to differ in terms of at least one attribute. As more symptoms are considered, it becomes increasingly likely that the drug will appear to be an improvement over existing drugs in terms of at least one symptom. Suppose we consider the efficacy of a drug in terms of the reduction of any one of a number of disease symptoms.As more attributes are compared, it becomes increasingly likely that the treatment and control groups will appear to differ on at least one attribute due to random sampling error alone. Students in the two groups can be compared in terms of grammar, spelling, organization, content, and so on. Suppose the treatment is a new way of teaching writing to students, and the control is the standard way of teaching writing.Failure to compensate for multiple comparisons can have important real-world consequences, as illustrated by the following examples: Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potential to produce a "discovery." A stated confidence level generally applies only to each test considered individually, but often it is desirable to have a confidence level for the whole family of simultaneous tests. In 1996, the first international conference on multiple comparison procedures took place in Israel. Over the ensuing decades, many procedures were developed to address the problem. The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. 4.1 Assessing whether any alternative hypotheses are true.2.1 Classification of multiple hypothesis tests.
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