Questions of Chapter 16

Correlation

Questions of Chapter 16 1
 True/False Questions

01. When there is no linear association between two variables, then 𝒓𝒓 or 𝝆𝝆 will be close to −𝟏𝟏. (F)
02. When there is no linear association between two variables, then 𝒓𝒓 or 𝝆𝝆 will be close to 𝟎𝟎. (T)
03. If 𝑟𝑟 = 𝟎𝟎. 𝟑𝟑, then the coefficient of determination will be 𝟎𝟎. 𝟗𝟗 (F)
04. If 𝑟𝑟 = 𝟎𝟎. 𝟓𝟓, then the coefficient of determination will be 𝟎𝟎. 𝟐𝟐𝟐𝟐 (T)
05. In a negative (−) relationship, low scores on one variable are associated with low scores on the other. (F)
06. In a negative (−) relationship, low scores on one variable are associated with high scores on the other. (T)
07. In a positive (+) relationship, high scores on one variable are associated with low scores on the other. (F)
09. In a positive (+) relationship, high scores on one variable are associated with high scores on the other. (T)
09. When we use Pearson’s (𝒓𝒓), we assume that at least one variable is continuous and normally distributed. (F)
10. When we use Pearson’s (𝒓𝒓), we assume that both variables are continuous and normally distributed. (T)
11. When we use Spearman’s (𝝆𝝆 ), we assume that at least one variable is ordinal. (T)
12. When we use Spearman’s (𝝆𝝆 ), we assume that at least one variable is nominal. (F)
13. If we assume that one variable is ordinal while the other variable is ratio, then we can use Spearman’s (𝝆𝝆 ) . (T)
14. If we assume that one variable is ordinal while the other variable is interval, then we can use Spearman’s (𝝆𝝆 ) . (T)
15. If both variables are nominal, then we can use Spearman’s (𝝆𝝆 ) . (F)
Questions of Chapter 16 2
16. When both variables are measured on nominal scale, we must use ϕ (𝑝𝑝𝑝𝑝𝑝) to express correlation. (T)
17. When both variables are measured on ordinal scale, we must use ϕ (𝑝𝑝𝑝𝑝𝑝) to express correlation. (F)
18. When we use ϕ (𝑝𝑝𝑝𝑝𝑝), we assume that at least one variable is nominal. (F) (It should be both are nominal)
19. As the value of 𝒓𝒓 increases, the proportion of variability (𝒓𝒓𝟐𝟐 ) decreases. (F) (Both 𝒓𝒓 and 𝒓𝒓𝟐𝟐 increase or both decrease)
20. As the value of 𝒓𝒓 decreases, the proportion of variability (𝒓𝒓𝟐𝟐 ) decreases. (T)
21. The calculated values of correlation coefficients range from −𝟏𝟏 and 𝟎𝟎. (F)
22. The calculated values of correlation coefficients range from 𝟎𝟎 𝑡𝑡𝑡𝑡 𝟏𝟏. (F)
23. The calculated values of correlation coefficients range from −𝟏𝟏 𝑡𝑡𝑡𝑡 𝟏𝟏. (T)
24. A correlation coefficient of 𝟎𝟎. 𝟒𝟒𝟒𝟒 represents a positive moderate linear correlation. (T)
25. A correlation coefficient of 𝟎𝟎. 𝟏𝟏𝟏𝟏 represents a positive weak linear correlation. (T)
26. A correlation coefficient of −𝟎𝟎. 𝟐𝟐𝟐𝟐 represents a negative strong linear correlation. (F)
27. A correlation coefficient of −𝟎𝟎. 𝟕𝟕𝟕𝟕 represents a negative strong linear correlation. (T)
28. A correlation coefficient of 𝟎𝟎. 𝟖𝟖𝟖𝟖 represents a positive moderate linear correlation. (F)
29. A correlation coefficient of −𝟎𝟎. 𝟓𝟓𝟓𝟓 represents a negative moderate linear correlation. (T)
30. A correlation coefficient of 𝟎𝟎. 𝟒𝟒𝟒𝟒 represents a positive weak linear correlation. (F)
Questions of Chapter 16 3
31. If 𝒓𝒓 = 𝟎𝟎. 𝟗𝟗 between two variables 𝒙𝒙 and 𝒚𝒚, then 𝟗𝟗𝟗𝟗𝟗 of the scores of 𝒚𝒚 can be explained in terms of 𝒙𝒙. (F) (Should be 81%)

32. If 𝒓𝒓 = 𝟎𝟎. 𝟗𝟗 between two variables 𝒙𝒙 and 𝒚𝒚, then 𝟖𝟖𝟖𝟖𝟖 of the scores of 𝒚𝒚 can be explained in terms of 𝒙𝒙. (T)

33. If 𝒓𝒓 = 𝟎𝟎. 𝟐𝟐 between two variables 𝒙𝒙 and 𝒚𝒚, then 𝟒𝟒𝟒𝟒𝟒 of the scores of 𝒚𝒚 can be explained in terms of 𝒙𝒙. (F) (Should be 4%)

34. If 𝒓𝒓 = 𝟎𝟎. 𝟐𝟐 between two variables 𝒙𝒙 and 𝒚𝒚, then 𝟒𝟒𝟒 of the scores of 𝒚𝒚 can be explained in terms of 𝒙𝒙. (T)

35. If 𝒓𝒓 = +1 between two variables 𝒙𝒙 and 𝒚𝒚, then 𝟏𝟏𝟎𝟎𝟎𝟎 % of the scores of 𝒚𝒚 can be explained in terms of 𝒙𝒙. (T)

36. If 𝒓𝒓 = -1 between two variables 𝒙𝒙 and 𝒚𝒚, then −𝟏𝟏𝟏𝟏𝟏𝟏 % of the scores of 𝒚𝒚 can be explained in terms of 𝒙𝒙. (F) (Should be 100%)
37. If a correlation coefficient is close to 1, then the test is unreliable. (F) (Should be reliable, because it is strong)

38. If a correlation coefficient is close to 0, then the test is reliable. (F) (Should be unreliable, because it is weak)

39. If a correlation coefficient 𝒓𝒓 = 𝟎𝟎. 𝟐𝟐, then the test has low (weak) predictive validity. (T)

40. If a correlation coefficient 𝒓𝒓 = 𝟎𝟎. 𝟔𝟔𝟔𝟔, then the test has moderate (acceptable) predictive validity. (T)

41. Correlation coefficient, is defined as the relative difference between two variables. (F)

Questions of Chapter 16 4
42. Correlation coefficient, is defined as a statistic which expresses quantitatively the magnitude and direction of the correlation. (T)

43. The association between two variables can be plotted on a scattergram. (T)

44. If the distribution of paired scores is best represented by a curve, then the relationship is non-linear. (T)

45. If the distribution of paired scores is best represented by a curve, then the relationship is linear. (F)

46. The selection of the correlation coefficient, is determined by the level of scaling of the two variables. (T)

47. When we use Pearson’s (𝒓𝒓), we assume that both variables are continuous and have a skewed distribution. (F) (Normal)

48. A correlation coefficient of 𝑟𝑟 = −1 represents a very low linear correlation. (F) (Very strong)

49. Where there is a correlation 𝑟𝑟 = +1 between two variables 𝑥𝑥 and 𝑦𝑦, then 𝒁𝒁𝒙𝒙 = 𝒁𝒁𝒚𝒚 (T)

50. Where there is a correlation 𝑟𝑟 = −1 between two variables 𝑥𝑥 and 𝑦𝑦, then 𝒁𝒁𝒙𝒙 = 𝒁𝒁𝒚𝒚 (F) (Should be 𝒁𝒁𝒙𝒙 = −𝒁𝒁𝒚𝒚 )

Questions of Chapter 16 5
51. Where there is a correlation 𝑟𝑟 = +1 between two variables 𝑥𝑥 and 𝑦𝑦, then 𝑍𝑍𝑥𝑥 ≠ 𝑍𝑍𝑦𝑦 (F)

52. The proportion of variance (coefficient of variation), is the square of the correlation coefficient. (T)

53. As the correlation coefficient approaches zero, the possible error in linear prediction increases. (T)

54. As the correlation coefficient approaches zero, the possible error in linear prediction decreases. (F)

55. As the correlation coefficient approaches +𝟏𝟏, the possible error in linear prediction increases. (F)

56. As the correlation coefficient approaches −𝟏𝟏, the possible error in linear prediction decreases. (T)

57. A scattergram is used to decide if the relationship between two variables is linear or curvilinear. (T)

58. The closer the correlation coefficient to zero, the greater the predictive validity. (F) (Should be smaller)

59. The closer the correlation coefficient to ±𝟏𝟏, the greater the predictive validity. (T)

60. If the relationship between two variables is non-linear, the value of the correlation coefficient must be zero. (F)

The end of True / False Questions

Questions of Chapter 16 6
MCQ Questions

1. Assume we are interested to see whether student test scores out of 10 for Biology examinations are correlated with
test scores for Chemistry. Assume there were only 5 students who sat for the examinations (see the table below)

Refer to this table, calculate the correlation coefficient Pearson (𝑟𝑟) and mention its direction and strength.
A r=0.788 and positively strong.
B r=-0.394 and negatively moderate.
C r=0.394 and positively moderate.
∑ 𝑧𝑧𝑥𝑥 𝑧𝑧𝑦𝑦
D r=- 0.788 and negatively strong. Remember: 𝑟𝑟 =
𝑛𝑛

Questions of Chapter 16 7
2. If the correlation coefficient between the variables ‘amount of exercise’ and ‘incidence of heart disease’ is −𝟎𝟎. 𝟗𝟗,
which of the following statements is true?

A. 81% of ‘incidence of heart disease’ scores are explained in terms of ‘amount of exercise’ scores.
B. 81% of ‘amount of exercise’ scores are explained in terms of ‘incidence of heart disease’ scores.
C. 90% of ‘amount of exercise’ scores are explained in terms of ‘incidence of heart disease’ scores.
D. 90% of ‘incidence of heart disease’ scores are explained in terms of ‘amount of exercise’ scores.

3. The lowest strength of association is reflected by which of the following correlation coefficients?

A. 0.8 B. −0.79 C. −0.34 D. 0.19

4. The highest strength of association is reflected by which of the following correlation coefficients?

A. 0.85 B. −0.79 C. 0.66 D.−0.95

Questions of Chapter 16 8
5. Which of the following statements is false?

A. Spearman’s ( 𝜌𝜌 ) is used when one or both variables are at least nominal.

B. The range of the correlation coefficient is from −𝟏𝟏 to 𝟏𝟏.

C. A correlation of 𝒓𝒓 = −𝟎𝟎. 𝟕𝟕𝟕𝟕 implies a stronger association than 𝒓𝒓 = 𝟎𝟎. 𝟔𝟔𝟔𝟔.

D. In a perfect positive correlation, each individual obtains the same 𝒛𝒛 score on each variable.

6. You are told that there is a strong positive correlation between measures of ‘fitness’ and ‘hours of exercise’.
The correlation coefficient consistent with the above statement is:

A. 0.68 B. 0.85 C. −0.92 D. 1.0

7. The correlation coefficient appropriate for establishing the degree of association between the two variables
‘Gender’ and the ‘Blood Group’ is

A. 𝑟𝑟 B. 𝜙𝜙 (𝑝𝑝𝑝𝑝𝑝) C. 𝜌𝜌 (𝑟𝑟𝑟𝑟𝑟) D. 𝜂𝜂 (𝐸𝐸𝐸𝐸𝐸𝐸)

Questions of Chapter 16 9
8. It was demonstrated a correlation of − 𝟎𝟎. 𝟖𝟖𝟖𝟖 between ‘ 𝒃𝒃𝒃𝒃𝒃𝒃𝒃𝒃 𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘 ’ and ‘ 𝑰𝑰𝑰𝑰 ’. This means that:

A. People with low IQs are likely to be overweight.

B. Heavy people have higher IQs than light people.
C. Light people have lower IQs than heavy people.
D. Obesity decreases intelligence.

9. If the correlation coefficient between the variables ‘hours of exercise’ and ‘fitness’ is 𝟎𝟎. 𝟖𝟖 ,
which of the following statements is true?

A. 64% of ‘fitness’ scores are explained in terms of ‘hours of exercise’ scores.

B. 80% of ‘fitness’ scores are explained in terms of ‘hours of exercise’ scores.

C. 64% of ‘hours of exercise’ scores are explained in terms of ‘fitness’ scores.

D. 80% of ‘hours of exercise’ scores are explained in terms of ‘fitness’ scores.

Questions of Chapter 16 10
10. If an investigator is interested in the correlation between the ‘socio-economic status’ and
‘severity of respiratory illness’, and assuming that both variables were measured on an ordinal scale,
the investigator ranks for the raw scores x and y are given in the table below:
Patient ‘socio-economic status’ ‘severity of respiratory illness’ 𝑑𝑑 𝑑𝑑2
(rank) (rank)
1 6 7 -1 1
2 7 5 2 4
3 3 3 0 0
4 2 4 -2 4
5 8 5 3 9
6 1 4 -3 9
7 5 3 2 4
8 4 3 1 1
� 𝑑𝑑2 = 32

Calculate the correlation coefficient ρ and mention its direction and strength.

A. ρ= 0.619 and positively moderate. 6 ∑ 𝑑𝑑 2

ρ = - 0.619 and negatively moderate. 𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹: 𝜌𝜌 = 1 − 3
B. 𝑛𝑛 − 𝑛𝑛
C. ρ = - 0.937 and negatively strong. where d = difference in a pair of ranks and n = number of pairs.
D. ρ = 0.937 and positively strong.

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11. Which of the following statements about correlation is false?

A. Spearman’s 𝝆𝝆 (rho) is appropriate to use when the relationship between two variables is non-linear.

B. A correlation coefficient of −𝟎𝟎. 𝟗𝟗𝟗𝟗 is higher than a correlation coefficient of +𝟎𝟎. 𝟕𝟕𝟕𝟕

C. The scattergram is useful to determine whether a relationship between two variables is linear or non-linear.
D. Negative (−) correlation implies that low scores in one variable are related to high scores on another variable.

12. A scattergram:

A. It is a graph of 𝑥𝑥 𝑎𝑎𝑎𝑎𝑎𝑎 𝑦𝑦 scores.

B. Must be linear

C. A statistical test

D. Must be linear
Questions of Chapter 16 12
13. We find that the correlation coefficient representing the outcome for the predictive validity of a test is 𝒓𝒓 = 𝟎𝟎. 𝟓𝟓𝟓𝟓.

Such finding would indicate that the test had:

A. Acceptable predictive validity

B. Low predictive validity

C. High predictive validity

D. 57% predictive validity

14. The proportion of variance accounted for by the level of correlation between two variables 𝒙𝒙 and 𝒚𝒚 is calculated by:

A. 𝑟𝑟 2 B. 𝑋𝑋� C. ∑ 𝑥𝑥 D. ∑ 𝑦𝑦

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The end of MCQ Questions
Questions of Chapter 16 13
 Numeric Questions:

1. If 𝑟𝑟 = ± 𝟎𝟎. 𝟓𝟓, then the coefficient of determination (proportion of variance) = 𝟎𝟎. 𝟐𝟐𝟐𝟐

2. If 𝑟𝑟 = ± 𝟎𝟎. 𝟒𝟒, then the coefficient of determination (proportion of variance) = 𝟎𝟎. 𝟏𝟏𝟏𝟏

3. If 𝑟𝑟 = ± 𝟎𝟎. 𝟏𝟏, then the coefficient of determination (proportion of variance) = 𝟎𝟎. 𝟎𝟎𝟎𝟎

4. If 𝑟𝑟 = ± 𝟎𝟎. 𝟖𝟖, then the coefficient of determination (proportion of variance) = 𝟎𝟎. 𝟔𝟔𝟔𝟔

5. If 𝑟𝑟 = ± 𝟎𝟎. 𝟕𝟕, then the coefficient of determination (proportion of variance) = 𝟎𝟎. 𝟒𝟒𝟒𝟒

6. If 𝒓𝒓 is a perfect positive (negative) correlation, then the coefficient of determination (proportion of variance) = 𝟏𝟏

Questions of Chapter 16 14
07. If 𝒓𝒓 = 𝟎𝟎. 𝟏𝟏𝟏𝟏 between two variables 𝒙𝒙 and 𝒚𝒚, then the variability of 𝒚𝒚 can be explained in terms of 𝒙𝒙 = 2.25%

08. If 𝒓𝒓 = −𝟎𝟎. 𝟒𝟒𝟒𝟒 between two variables 𝒙𝒙 and 𝒚𝒚, then the variability of 𝒚𝒚 can be explained in terms of 𝒙𝒙 = 20.25%

09. If 𝒓𝒓 = 𝟎𝟎. 𝟕𝟕𝟕𝟕 between two variables 𝒙𝒙 and 𝒚𝒚, then the variability of 𝒚𝒚 can be explained in terms of 𝒙𝒙 = 60.84%

10. If 𝒓𝒓 = −𝟎𝟎. 𝟖𝟖𝟖𝟖 between two variables 𝒙𝒙 and 𝒚𝒚, then the variability of 𝒚𝒚 can be explained in terms of 𝒙𝒙 = 72.25%

11. If 𝒓𝒓 = −𝟎𝟎. 𝟐𝟐𝟐𝟐 between two variables 𝒙𝒙 and 𝒚𝒚, then the variability of 𝒚𝒚 can be explained in terms of 𝒙𝒙 = 5.76%

12. If 𝒓𝒓 = 𝟎𝟎. 𝟔𝟔𝟔𝟔 between two variables 𝒙𝒙 and 𝒚𝒚, then the variability of 𝒚𝒚 can be explained in terms of 𝒙𝒙 = 42.25%

13. If 𝒓𝒓 = 𝟎𝟎. 𝟏𝟏𝟏𝟏 between two variables 𝒙𝒙 and 𝒚𝒚, then the variability of 𝒚𝒚 can be explained in terms of 𝒙𝒙 = 3.24%

14. If 𝒓𝒓 = 𝟎𝟎. 𝟗𝟗𝟗𝟗 between two variables 𝒙𝒙 and 𝒚𝒚, then the variability of 𝒚𝒚 can be explained in terms of 𝒙𝒙 = 90.25%

Questions of Chapter 16 15
Matching Questions:

Question 1

Variables The appropriate correlation

coefficient
1 ‘Gender’ and ‘Blood Group’ (A) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆: 𝜌𝜌
1 C
2 ‘Body Weight’ and ‘Hours of Exercise’ (B) 𝜂𝜂 (𝐸𝐸𝐸𝐸𝐸𝐸)
2 D
3 ‘Educational Level’ and ‘Body Weight’ 𝐶𝐶 ϕ (𝑝𝑝𝑝𝑝𝑝) 3 A
4 Non-linear relationship between any two variables (D) 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃: 𝑟𝑟 4 B

Questions of Chapter 16 16
Question 2

Correlation Coefficient Value Direction and Strength

1 ϕ = 0.41 (A) Negative Perfect Correlation
2 𝑟𝑟 = −0.73 (B) Not Possible 1 E
3 𝜌𝜌 = 0.19 (C) Positive Weak Correlation 2 G
4 𝜂𝜂 = 0 (D) Positive Perfect Correlation 3 C
5 𝑟𝑟 = −1 (E) Positive Moderate Correlation 4 F
5 A
6 𝜌𝜌 = +1 (F) No Correlation
6 D
7 𝑟𝑟 = 1.3 (G) Negative Strong Correlation
7 B

The end of questions

Questions of Chapter 16 17