Sampling Distribution of Pearson's r (2 of 3)

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It stands to reason that the greater the sample size (N, the number of pairs of scores), the smaller the standard error. Since N is in the denominator of the formula, the larger the sample size, the smaller the standard error. Consider the following problem: If the population correlation (rho) between scores on an aptitude test and grades in school were 0.5, what is the probability that a correlation based on 19 students would be larger than 0.75? The first step is to convert a correlation of 0.5 to z'. This can be done with the r to z' table. The value of z' is 0.55. The standard error is:

= 1/4 = .25.