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By Stephen S. Senn

Describes statistical equipment for reading the result of cross-over trials during which topics are given sequences of remedies with the article of learning alterations among person remedies. Senn (University university London) addresses either the AB/BA layout and designs with 3 or extra remedies. the second one variation provides a bit on incomplete block designs, and code for acting analyses with GenStat and S-Plus.

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Blocking is not at all necessary to eliminate bias. This is done by conditioning. The estimator, ”t2 , was constructed in such a way as to be conditionally unbiased, whatever the result of the randomization. The value of blocking is that the variance of any estimator which has been constructed so as to be conditionally unbiased will be a minimum when the groups are balanced. 18) is also conditionally unbiased if the trial has been blocked by centre, the issue of conditioning may be avoided altogether.

A more complex phenomenon than a simple period effect would be a period by treatment interaction. It might be the case, for example, that the effect of treatment varied according to the period in which it was given. Suppose we ran a cross-over trial in asthma in which all of the first visits were conducted in June and all of the second visits in October. The patients might be affected by hay fever at the first visit but not at the second. This in itself might lead to a period effect, but if one of the treatments were effective for asthma in general, except when complicated by or provoked by hay fever, this would also lead to a treatment by period interaction.

A little algebra is sufficient to show that p Z=W 1=2 ˆ (X" À )=(” = n), where " 2 =(n À 1) ”2 ˆ Æ(Xi À X) is the usual sample estimate of the population variance. Thus a t statistic may be defined in terms of a population mean, a sample mean and its estimated standard error. Remark This is the simplest example of an application of the t distribution. In this case the estimate of the population variance and the estimate of the population mean are obtained from the same sample. 7). There are occasions when we obtain an estimate of the population variance either partly or entirely using values other than those used to calculate the sample mean: for example when we are studying a number of populations whose variances are equal but whose means may be different.

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