From samples to populations: estimation and hypothesis testing.
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Controlled clinical trials represent the most scientific methods of evaluating a new form of treatment. In designing such a trial, one must avoid committing two kinds of errors. The Type I error is defined as falsely concluding that a difference between two treatments exists, when they are equal. The Type II error is committed when one concludes that two treatments are the same, when a real difference exists. To reduce the probability of committing these errors, large sample sizes are required. A survey of neurosurgical trials showed that the majority of these trials have an unacceptably high probability of committing a Type II error because of inadequate sample size.
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The properties of likelihood ratio tests and simpler t-tests are investigated by simulation under an assumed beta-binomial model for parameter values typically found in toxicological studies. It is found that likelihood ratio methods are at least as powerful as the simpler approaches and in certain situations can be significantly more powerful.
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