Learn Before
Explain why the student researcher's comprehension of the correlation coefficient is incorrect. Using the properties of Pearson's mentioned in the case, justify which of the two relationships is actually stronger and more predictable.
Case context: A student researcher is examining the relationship between academic procrastination and final exam scores. They calculate a correlation coefficient of Pearson's . A second relationship, between student seating position (front-to-back row) and exam scores, yields Pearson's . The student researcher concludes that seating position has a stronger relationship with exam scores because is a positive number and is closer to than a negative value.
Question: Explain why the student researcher's comprehension of the correlation coefficient is incorrect. Using the properties of Pearson's mentioned in the case, justify which of the two relationships is actually stronger and more predictable.
Sample answer: The student researcher's conclusion is incorrect because the strength of a correlation coefficient is determined by how far the value is from zero, not by its sign. Pearson's is bounded between and . A value of is further from zero than , indicating a much tighter, more predictable relationship between procrastination and exam scores than between seating position and exam scores. The negative sign only denotes the direction of the relationship (as procrastination increases, exam scores decrease), not a weaker relationship.
Key points:
- Identifies that correlation strength is determined by distance from zero, not the sign (+ or -).
- Explains that Pearson's is bounded between and .
- Recognizes that the sign indicates the direction of the linear relationship, not its strength.
- Concludes that the relationship with is stronger and more predictable than the relationship with .
Rubric: Graders should look for an explanation that strength is determined by distance from zero (absolute value) and not the sign, alongside a correct identification that the procrastination relationship () is stronger than the seating position relationship ().
0
1
Tags
KPU
Research Methods in Psychology - 4th American Edition @ KPU
Related
Types of Correlation
A researcher is examining the statistical association between several pairs of variables. Which of the following numerical values represents the strongest association between two variables?
Correlation Matrix
Pearson's r Formula
Restriction of Range
Identifying the Weakest Correlation
Statistical Regression
Test of the Correlation Coefficient
Example of Scatterplots for Pearson's r Values
Cohen's Guidelines for Interpreting Pearson's r
Which of the following best describes the function of a correlation coefficient in psychological research?
A researcher studying stress and academic performance obtains a correlation coefficient of r = −0.82. Because the value is negative, this result indicates a weak relationship between the two variables.
A psychological research team has conducted four different correlational studies. Match each obtained Pearson’s correlation coefficient with the research finding that best represents that specific relationship.
A psychological researcher is evaluating four separate studies to determine which relationship allows for the most accurate predictions between two variables. Arrange the following Pearson’s values in order from the coefficient representing the least predictable linear association to the one representing the most predictable linear association.
A researcher is designing a study to demonstrate a 'strong negative linear association' between two variables to serve as a meaningful effect size. Which of the following sets of research parameters must be synthesized to correctly achieve this specific statistical outcome?
The correlation coefficient, commonly represented as Pearson's , is bounded between the values of and .
A student researcher evaluates a study result where Pearson's and concludes it represents a 'weak' relationship because the value is negative. To critique this evaluation, a supervisor would explain that the _____ of the correlation coefficient, rather than its sign, indicates the strength of the linear association.
A research methods instructor presents four properties or values of Pearson's and asks students to match each one to the correct interpretation. Match each property or value of the correlation coefficient to what it specifically tells a researcher about the relationship between two quantitative variables.
A researcher reports Pearson's between daily stress ratings and quality of sleep. A classmate argues this is a weak relationship because the coefficient is negative. To correct this misanalysis, a student explains that the strength of a linear relationship is determined by the _____ of Pearson's , not by its sign.
A student is critically evaluating whether a researcher correctly applied and interpreted Pearson's as an effect size measure in a published correlational study. Arrange the following steps in the order a critical evaluator should complete them.
State the definition of the correlation coefficient, specify its common representation, and recall its numerical bounds. Briefly outline how its direction and strength are interpreted, and describe its function as an effect size in research.
Explain why the student researcher's comprehension of the correlation coefficient is incorrect. Using the properties of Pearson's mentioned in the case, justify which of the two relationships is actually stronger and more predictable.
A clinical psychologist is investigating the linear relationship between patient treatment attendance (number of sessions) and symptom severity ratings. Explain how the researcher would apply Pearson's to evaluate the connection between these two quantitative variables as an effect size in their population.