Both of the variables in Assignment Problem 19 are measurements that include some measurement error.

a. How would this measurement error affect the correlation between the two variables?

b. What steps could be taken in the design of the study to minimize the effect of measurement error?

c. For a given variable, what quantity is used to estimate the proportion of the variance among subjects not attributable to measurement error?

Data from problem 19

If you are having trouble solving homework problems, should you sleep on it and try again in the morning? Huber et al. (2004) asked 10 participants to perform a complex spatial learning task on the computer just before going to sleep. EEG recordings were then taken of the electrical activity of brain cells during their sleep. The magnitude of the increase in their “slowwave” sleep after learning the complex task, compared to baseline amounts, is listed in the following table for all 10 participants. Also provided is the increase in performance recorded when the participants were challenged with the same task upon waking.

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Increase in slow-wave sleep (%) 88 1414 1313 1515 1717 1818 3131 3232 4444 Improvement in task performance (%) 88 33 00 00 88 1515 1414 1010 2727