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By Chen S.

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Replace the values n ij by their corresponding proportions: Method 2 Method 1 Present Absent Present p 11 p 12 p 1. Absent p 21 p 22 p 2. 2 1 48 Then the estimate of the φcoefficient is defined to be The usual chi-square test is given by The coefficient is precisely the Pearson product-moment coefficient applied to the table of proportions, that is, . The value of can be positive or negative. Hence, if the matching was effective then 0 and there was an advantage to matching. If the correlation is near zero or is negative then the matching was ineffective.

However, more detailed knowledge of the proposed investigation will lead to additional considerations that may affect substantially the sample sizes needed. 5 PAIRING DATA IS NOT ALWAYS GOOD Introduction There is an old rule of thumb in the design of experiments that says that pairing data is always a good thing in that it increases precision. This is not so. Rule of Thumb Pairing should be investigated carefully. 5. Illustration Researchers frequently assume that adjusting for baseline value in a repeated measures experiment increases the precision.

Increasing the observation period T, reduces the sample size proportionately, not as the square root! This is a basis for the observation that the precision of measurements of radioactive sources, which often follow a Poi sson distribution, can be increased by increasing the duration of observation times. Choose T so that the number per sample is 1. To achieve that effect choose T to be of length This again is reasonable since the sum of independent Poisson variables is Poisson, that is, σY i is Poisson (Tθi ) if each Y i is Poisson (θi ).