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Personality traits and job performance. When attemptingto
Chapter 12, Problem 54E(choose chapter or problem)
Personality traits and job performance. When attempting to predict job performance using personality traits, researchers typically assume that the relationship is linear. A study published in the Journal of Applied Psychology (Jan.2011) investigated a curvilinear relationship between job task performance and a specific personality trait—conscientiousness. Using data collected for 602 employees of a large public organization, task performance was measured on a 30-point scale (where higher scores indicate better performance) and conscientiousness was measured on a scale of -3 to +3 (where higher scores indicate a higher level of conscientiousness).
a. The coefficient of correlation relating task performance score to conscientiousness score was reported as r = .18. Explain why the researchers should not use this statistic to investigate the curvilinear relationship between task performance and conscientiousness.
b. Give the equation of a curvilinear (quadratic) model relating task performance score (y) to conscientiousness score (x).
c. The researchers theorized that task performance increases as level of conscientiousness increases, but at a decreasing rate. Draw a sketch of this relationship.
d. If the theory in part c is supported, what is the expected sign of \(\beta_{2}\) in the model, part b?
e. The researchers reported \(\hat{\beta}_{2}=-.32\) with an associated p-value of less than .05. Use this information to test the researchers' theory at \(\alpha\) = .05.
Questions & Answers
QUESTION:
Personality traits and job performance. When attempting to predict job performance using personality traits, researchers typically assume that the relationship is linear. A study published in the Journal of Applied Psychology (Jan.2011) investigated a curvilinear relationship between job task performance and a specific personality trait—conscientiousness. Using data collected for 602 employees of a large public organization, task performance was measured on a 30-point scale (where higher scores indicate better performance) and conscientiousness was measured on a scale of -3 to +3 (where higher scores indicate a higher level of conscientiousness).
a. The coefficient of correlation relating task performance score to conscientiousness score was reported as r = .18. Explain why the researchers should not use this statistic to investigate the curvilinear relationship between task performance and conscientiousness.
b. Give the equation of a curvilinear (quadratic) model relating task performance score (y) to conscientiousness score (x).
c. The researchers theorized that task performance increases as level of conscientiousness increases, but at a decreasing rate. Draw a sketch of this relationship.
d. If the theory in part c is supported, what is the expected sign of \(\beta_{2}\) in the model, part b?
e. The researchers reported \(\hat{\beta}_{2}=-.32\) with an associated p-value of less than .05. Use this information to test the researchers' theory at \(\alpha\) = .05.
ANSWER:Step 1 of 6
(a)
The correlation coefficient (r) is used to measure the linear relationship between the two variables. Suppose, if there is a curvilinear relationship between the two variables, the correlation coefficient should not be used to measure the relationship. Thus, the researchers should not use this statistic to investigate the curvilinear relationship between the task performance and conscientiousness.