Identifying individuals with a high risk of Alzheimer’ disease usually involves a long series of cognitive tests. However, researchers have developed a 7-Minute Screen, which is a quick and easy way to accomplish the same goal. The question is whether the 7-Minute Screen is as effective as the complete series of tests. To address this question, Juin et al. (2008) administered both tests to a group of patients and compared the results. The following data represent results similar to those obtained in the study.
|Patient||7-Minute Screen||Cognitive Series|
a. Compute the Pearson correlation to measure the degree of relationship between the two test scores.
b. Is the correlation statistically significant? Use a two-tailed test with α = .01.
c. What percentage of variance for the cognitive scores is predicted from the 7-Minute Screen scores? (Compute the value of r2.)
The given data are shown below,
|7-minut screen||Cognitive series|
Formula to calculate the Pearson correlation is,
Where co variability of the variable x and y is , is the variability of the x variable and is the variability of the y variable.
Mean of the variable is,
Thus the mean of the variable is 7.
Mean of the variable is,
Thus the mean of the variable Y is 17.
For calculating and the table is shown below,
To explain: The correlation is statistically significant or insignificant using two tail test at 1% level of significance.
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