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Chapter 9 Correlation and Tests of Independence 451 percentage bend correlation is easily the most satisfactory, with the estimated probability of a type I error (based on simulations with 10,000 replications) ranging between .046 and .062. If the usual correlation, r , is used instead, the probability of type I error can exceed .2, and when using method GR, it exceeds .15. 9.3.5 R Function pball The R function pball(m,beta=0.2), computes the percentage bend correlation for all pairs of random variables, and it tests the hypothesis that all of the correlations are equal to zero. Here, m is an n-by- p matrix of data. If the data are not stored in a matrix, the function prints an error message and terminates. (Use the R command matrix to store the data in the proper way. See Becker, Chambers, & Wilks, 1988, for details.) Again beta, which is in Table 9.2, defaults to 0.2. The function returns a p-by-p matrix of correlations in pball$pbcorm, another matrix indicating the p-values for the hypotheses that each correlation is zero, plus the test statistic H and its corresponding p-value.