Calculating the Sample Size When Testing r

Unfortunately, most researchers do not seem to consider the issues of power and effect size prior to the collection of data. It seems as if they simply set up their null hypotheses, collect as much data as time and money permit, and then apply the six-step version of hypothesis testing (or the seven-step version of the hybrid approach to testing null hypotheses). Those who do this run the risk of encountering one of two problems. A correlation coefficient can turn out to be statistically significant even though it (and especially its squared value) is close to zero. Or a correlation coefficient can appear to be far away from Ho's pinpoint number but end up being nonsignificant due to a statistical test of inadequate power. When you come across a study in which the appropriate sample size was determined prior to the collection of any data, give the researcher some bonus points for taking the time to set up the study with sensitivity to both Type I and Type II errors. When you come across a study in which the power associated with the test(s) conducted on the correlation coefficient is computed in a post hoc sense, give the researcher only a few bonus points. And when you come across a study in which there is no mention whatsoever of statistical power, award yourself some bonus points for detecting a study that could have been conducted better than it was.

(From Chapter 10, p. 276)

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