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Pearson r scores

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Correlations

Hill (1990) studied the correlations between final exam score in an introductory sociology course and several other variables such as number of absences. The following Pearson r correlation coefficients with final exam score were obtained:

Overall college GPA
.72

Number of absences
−.51

Hours spent studying on weekdays
−.11 (not significant)

Hours spent studying on weekends
.31

Describe each correlation and how graphs might depict the general shape of each relationship. Why might hours spent studying on weekends be correlated with grades but weekday studying not be?

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Solution Preview

Overall college GPA is positively correlated with final exam scores in an introductory sociology course. This is shown through the Pearson r score, which is .72. The closer the Pearson r score is to 1, the stronger the relationship. This means that students who have a higher overall GPA score have a higher final exam score in an introductory sociology course. A graph for this Pearson r score would be a steep line that goes from the bottom left of the graph and go steeply towards the upper right of the graph.

Number of absences is negatively correlated with final exam scores in an introductory sociology ...

Solution Summary

This solution takes a look at a sample of Pearson r scores and what they mean.

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Pearson Correlation Assignment

Please look over what I have done and help me with the rest. My answers are in brackets.

2. What information is provided by the numerical value of the Pearson correlation?

(The sample correlation coefficient, usually denoted r, is a numerical measure of the strength and the direction of the sample linear relationship between two variables. The value of r is always a number from -1to1. If r is positive, then the sample data indicate a positive linear relationship between the two variables; if r is negative, then the sample data indicate a negative linear relationship between the two variables. The closer that r is to the extreme values -1and1, the stronger the linear relationship indicated by the sample data. When r=0, the sample data indicate no linear relationship between the two variables).

6b. For the following scores,

X Y

1 3
3 5
2 1
2 3

b. Compute the Pearson correlation.

14.I identifying individuals with a high risk of Alzheimer's disease usually involve 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, Ijuin et al. (2008). Administered both tests to a group of patient and compared the results. The following data and compared the results. The following data represent results similar to those obtained in the study.

Weight (X) Income (Y)

4 156
3 88
5 49
2 73
1 45
3 92
1 53
5 148

Chapter 16

10. For the following scores,

(X) (Y)

3 6
6 1
3 4
3 3
5 1

Reference

Richard Johnson (2006), probability and Statistics for Engineers, 7th edition, Prentice Hall.

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