strength of a correlation

03 Oct strength of a correlation

PriviteraStats2 15.E.003.

What information does the strength of a correlation coefficient convey?

The strength of a correlation reflects how close data points fall to the regression line. The closer a correlation is to r = 0.0, the stronger the correlation. The strength of a correlation reflects how close data points fall to the regression line. The closer a correlation is to r = ±1.0, the stronger the correlation.     The strength of a correlation, indicated by + or −, reflects the direction or slope of a correlation. A negative correlation is stronger than a positive correlation. The strength of a correlation, indicated by + or −, reflects the direction or slope of a correlation. A positive correlation is stronger than a negative correlation.

2.

PriviteraStats2 15.E.011.

State which correlation coefficient (Pearson, Spearman, point-biserial, or phi) should be used given the following information.

· Part (a)

Both factors are interval or ratio scale.

Pearson Spearman     point-biserial phi

· Part (b)

Both factors are ranked.

Pearson Spearman     point-biserial phi

· Part (c)

One factor is dichotomous and a second factor is continuous.

Pearson Spearman     point-biserial phi

· Part (d)

Both factors are dichotomous.

Pearson Spearman     point-biserial phi

3.

PriviteraStats2 15.E.013.

State whether each of the following is an example of a positive or negative correlation.

· Part (a)

Higher education level is associated with a larger annual income.

positive correlation negative correlation

· Part (b)

The smaller the class size, the more students believe they are receiving a quality education.

positive correlation negative correlation

· Part (c)

Increased testosterone is associated with increased aggression.

positive correlation negative correlation

· Part (d)

Rising prices of apples are associated with the sale of fewer apples.

positive correlation negative correlation

4.

PriviteraStats2 15.E.017.

A medical study found a negative relationship between exercise (in minutes per week) and stress-related heath problems

(r = −0.36).

Which of the following conclusions is appropriate? Explain why the other is not appropriate.

(a) 12.96% of the variance in stress-related health problems can be explained by the amount of weekly exercise. (b) Increasing the amount of exercise per week will cause stress-related health problems to decrease.

Conclusion (b) is appropriate. Conclusion (a) is not appropriate because the amount of variance that can be explained is 36%.

Conclusion (a) is appropriate. Conclusion (b) is not appropriate because correlations do not demonstrate cause.

Conclusion (a) is appropriate. Conclusion (b) is not appropriate because increasing the amount of exercise per week will cause stress-related health problems to also increase.

Conclusion (b) is appropriate. Conclusion (a) is not appropriate because it is impossible to determine the variance in stress-related health problems that can be explained by the amount of weekly exercise.

5.

PriviteraStats2 15.E.019.

A researcher measures the relationship between sleep medication use (times used per week) and time spent working (in hours per week). Answer the following questions based on the results provided.

Sleep Medication Use	Time Spent Working
10	18
4	39
7	17
3	31

· Part (a)

Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)

· Part (b)

Multiply each measurement of drug use times 3 and recalculate the correlation coefficient. (Round your answer to three decimal places.)

· Part (c)

Divide each measurement in half for time spent working and recalculate the correlation coefficient. (Round your answer to three decimal places.)

· Part (d)

True or false: Multiplying or dividing a positive constant to one set of scores (X or Y) does not change the correlation coefficient. Note: Use your answers in (a) to (c) to answer true or false.

True False

6.

PriviteraStats2 15.E.021.

A therapist specializing in family counseling measures the relationship between partners and marital satisfaction. Husbands and wives rated how satisfied they were in their marriage using a 7-point rating scale ranging from 1 (not satisfied at all) to 7 (very satisfied). Using the hypothetical data given in the following table, compute the Pearson correlation coefficient. (Round your answer to three decimal places.)

Husband	Wife
X	Y
1	3
2	3
3	3
4	3
5	3
6	3
7	3

7.

PriviteraStats2 15.E.023.

A researcher measures the relationship between Internet use (hours per week) and social interaction (hours per week) in a sample of 10 students. The following table lists the hypothetical results of this study.

Internet Use	Social Interaction
X	Y
5	3
7	6
5	6
6	5
13	5
4	8
4	3
6	4
2	10
12	2