The document describes 5 practice problems involving determining the appropriate correlation coefficient to quantify relationships between variables. For problems involving a continuous variable and an ordinal or skewed continuous variable with no ties, Spearman's Rho is appropriate. When the skewed continuous variable has ties, Kendall's Tau is suitable. Point-biserial correlation is used when one variable is dichotomous and the other is continuous. Phi coefficient examines relationships between two dichotomous variables.

1. Practice Problems
Differentiating between relationship problems
that use the following methods:
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

2. Problem #1

3. The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their systolic blood pressure.
Advance the slide to see the options
Patients
Blood Pressure
Readings
(Skewness = .08)
Age
(Skewness = -3.43)
1 75 3
2 85 7
3 85 31
4 95 32
5 95 43
6 97 25
7 97 48
8 97 52
9 102 66
10 102 54
11 102 59
12 102 70
13 110 62
14 115 46
15 115 65
16 120 77
17 120 52
18 125 79

4. Advance the slide to see the answer
The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their systolic blood pressure.
Which is it?
Patients
Blood Pressure
Readings
(Skewness = .08)
Age
(Skewness = -3.43)
1 75 3
2 85 7
3 85 31
4 95 32
5 95 43
6 97 25
7 97 48
8 97 52
9 102 66
10 102 54
11 102 59
12 102 70
13 110 62
14 115 46
15 115 65
16 120 77
17 120 52
18 125 79
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

5. Which is it?
The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their systolic blood pressure.
Advance the slide to see the explanation
Patients
Blood Pressure
Readings
(Skewness = .08)
Age
(Skewness = -3.43)
1 75 3
2 85 7
3 85 31
4 95 32
5 95 43
6 97 25
7 97 48
8 97 52
9 102 66
10 102 54
11 102 59
12 102 70
13 110 62
14 115 46
15 115 65
16 120 77
17 120 52
18 125 79
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

6. The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their systolic blood pressure.
Advance the slide to the next problem
Because the Age variable is
Skewed and there are NO ties in
that variable
Explanation
Patients
Blood Pressure
Readings
(Skewness = .08)
Age
(Skewness = -3.43)
1 75 3
2 85 7
3 85 31
4 95 32
5 95 43
6 97 25
7 97 48
8 97 52
9 102 66
10 102 54
11 102 59
12 102 70
13 110 62
14 115 46
15 115 65
16 120 77
17 120 52
18 125 79
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau
Which is it?

7. Problem #2

8. The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their systolic blood pressure.
Advance the slide to see the options
Patients
Blood Pressure
Readings
(Skewness = .08)
Age
(Skewness = -3.43)
1 75 3
2 85 7
3 85 31
4 95 32
5 95 32
6 97 25
7 97 48
8 97 52
9 102 66
10 102 66
11 102 59
12 102 70
13 110 62
14 115 46
15 115 77
16 120 77
17 120 52
18 125 79

9. Advance the slide to see the answer
The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their systolic blood pressure.
Which is it?
Patients
Blood Pressure
Readings
(Skewness = .08)
Age
(Skewness = -3.43)
1 75 3
2 85 7
3 85 31
4 95 32
5 95 32
6 97 25
7 97 48
8 97 52
9 102 66
10 102 66
11 102 59
12 102 70
13 110 62
14 115 46
15 115 77
16 120 77
17 120 52
18 125 79
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

10. Which is it?
The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their systolic blood pressure.
Advance the slide to see the explanation
Patients
Blood Pressure
Readings
(Skewness = .08)
Age
(Skewness = -3.43)
1 75 3
2 85 7
3 85 31
4 95 32
5 95 32
6 97 25
7 97 48
8 97 52
9 102 66
10 102 66
11 102 59
12 102 70
13 110 62
14 115 46
15 115 77
16 120 77
17 120 52
18 125 79
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

11. The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their systolic blood pressure.
Advance the slide to the next problem
Because the Age variable is
Skewed and there ARE TIES in
that variable
Explanation
Patients
Blood Pressure
Readings
(Skewness = .08)
Age
(Skewness = -3.43)
1 75 3
2 85 7
3 85 31
4 95 32
5 95 32
6 97 25
7 97 48
8 97 52
9 102 66
10 102 66
11 102 59
12 102 70
13 110 62
14 115 46
15 115 77
16 120 77
17 120 52
18 125 79
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

12. Problem #3

13. The director of a health clinic has asked you see if there is a
relationship between systolic blood pressure and gender.
Advance the slide to see the options
Patients Blood Pressure
Reading
(Skewness = .23)
Gender
(1,2)
1 75 1
2 85 1
3 85 2
4 95 1
5 95 1
6 97 1
7 97 2
8 97 2
9 102 2
10 102 1
11 102 2
12 102 1
13 110 2
14 115 1
15 115 2
16 120 1
17 120 2
18 125 1

14. Advance the slide to see the answer
The director of a health clinic has asked you see if there is a
relationship between systolic blood pressure and gender.
Patients Blood Pressure
Reading
(Skewness = .23)
Gender
(1,2)
1 75 1
2 85 1
3 85 2
4 95 1
5 95 1
6 97 1
7 97 2
8 97 2
9 102 2
10 102 1
11 102 2
12 102 1
13 110 2
14 115 1
15 115 2
16 120 1
17 120 2
18 125 1
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

15. The director of a health clinic has asked you see if there is a
relationship between systolic blood pressure and gender.
Advance the slide to see the explanation
Patients Blood Pressure
Reading
(Skewness = .23)
Gender
(1,2)
1 75 1
2 85 1
3 85 2
4 95 1
5 95 1
6 97 1
7 97 2
8 97 2
9 102 2
10 102 1
11 102 2
12 102 1
13 110 2
14 115 1
15 115 2
16 120 1
17 120 2
18 125 1
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

16. The director of a health clinic has asked you see if there is a
relationship between systolic blood pressure and gender.
Because Gender is Dichotomous
and Blood Pressure is scaled
Explanation
Patients Blood Pressure
Reading
(Skewness = .23)
Gender
(1,2)
1 75 1
2 85 1
3 85 2
4 95 1
5 95 1
6 97 1
7 97 2
8 97 2
9 102 2
10 102 1
11 102 2
12 102 1
13 110 2
14 115 1
15 115 2
16 120 1
17 120 2
18 125 1
Advance the slide to the next problem
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

17. Problem #4

18. The director of a health clinic has asked you to determine if there is a
relationship between patients’ religious affiliation status (1 = affiliated, 2 =
unaffiliated) and depression status (1 = depressed, 2 = not depressed).
Advance the slide to see the options
Patient
Religious
Affiliation
Depression
Status
1 1 1
2 2 2
3 1 1
4 1 2
5 1 1
6 2 2
7 1 1
8 1 1
9 1 2
10 2 2
11 2 1
12 1 2
13 2 2
14 1 1
15 2 2
16 2 1
17 1 1
18 1 2

19. Advance the slide to see the answer
The director of a health clinic has asked you to determine if there is a
relationship between patients’ religious affiliation status (1 = affiliated, 2 =
unaffiliated) and depression status (1 = depressed, 2 = not depressed).
Patient
Religious
Affiliation
Depression
Status
1 1 1
2 2 2
3 1 1
4 1 2
5 1 1
6 2 2
7 1 1
8 1 1
9 1 2
10 2 2
11 2 1
12 1 2
13 2 2
14 1 1
15 2 2
16 2 1
17 1 1
18 1 2
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

20. The director of a health clinic has asked you to determine if there is a
relationship between patients’ religious affiliation status (1 = affiliated, 2 =
unaffiliated) and depression status (1 = depressed, 2 = not depressed).
Advance the slide to see the explanation
Patient
Religious
Affiliation
Depression
Status
1 1 1
2 2 2
3 1 1
4 1 2
5 1 1
6 2 2
7 1 1
8 1 1
9 1 2
10 2 2
11 2 1
12 1 2
13 2 2
14 1 1
15 2 2
16 2 1
17 1 1
18 1 2
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

21. Advance the slide to the next problem
Both variables are dichotomous
Explanation
The director of a health clinic has asked you to determine if there is a
relationship between patients’ religious affiliation status (1 = affiliated, 2 =
unaffiliated) and depression status (1 = depressed, 2 = not depressed).
Which is it?
Patient
Religious
Affiliation
Depression
Status
1 1 1
2 2 2
3 1 1
4 1 2
5 1 1
6 2 2
7 1 1
8 1 1
9 1 2
10 2 2
11 2 1
12 1 2
13 2 2
14 1 1
15 2 2
16 2 1
17 1 1
18 1 2
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

22. Problem #5

23. The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their nationally ranked systolic
blood pressure.
Advance the slide to see the options
Patients
Blood Pressure
Readings
(Nationally
Ranked)
Age
(Skewness = -.13)
1 22nd 33
2 34th 47
3 54th 31
4 49th 32
5 50th 43
6 51st 25
7 54th 48
8 55th 52
9 76th 65
10 77th 54
11 78th 59
12 79th 70
13 80th 62
14 81st 46
15 82nd 65
16 95th 77

24. Advance the slide to see the answer
The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their nationally ranked systolic
blood pressure.
Patients
Blood Pressure
Readings
(Nationally
Ranked)
Age
(Skewness = -.13)
1 22nd 33
2 34th 47
3 54th 31
4 49th 32
5 50th 43
6 51st 25
7 54th 48
8 55th 52
9 76th 65
10 77th 54
11 78th 59
12 79th 70
13 80th 62
14 81st 46
15 82nd 65
16 95th 77
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

25. The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their nationally ranked systolic
blood pressure.
Advance the slide to see the explanation
Patients
Blood Pressure
Readings
(Nationally
Ranked)
Age
(Skewness = -.13)
1 22nd 33
2 34th 47
3 54th 31
4 49th 32
5 50th 43
6 51st 25
7 54th 48
8 55th 52
9 76th 65
10 77th 54
11 78th 59
12 79th 70
13 80th 62
14 81st 46
15 82nd 65
16 95th 77
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

26. The director of a health clinic has asked you to determine if there is a
relationship between patients’ age and their nationally ranked systolic
blood pressure.
Advance the slide to the next problem
Because Blood Pressure Readings
are ranked or ordinal and have
NO TIES
Explanation
Patients
Blood Pressure
Readings
(Nationally
Ranked)
Age
(Skewness = -.13)
1 22nd 33
2 34th 47
3 54th 31
4 49th 32
5 50th 43
6 51st 25
7 54th 48
8 55th 52
9 76th 65
10 77th 54
11 78th 59
12 79th 70
13 80th 62
14 81st 46
15 82nd 65
16 95th 77
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

27. Problem #6

28. A political think take wants to determine if there is relationship
between gender and support of Proposition “X”.
Advance the slide to see the options
Patients
Support (1) or Oppose (2)
Proposition “X”
Gender
(1,2)
1 1 1
2 1 1
3 2 2
4 1 1
5 1 1
6 2 1
7 1 2
8 2 2
9 2 2
10 1 1
11 2 2
12 1 1
13 1 2
14 2 1
15 2 2
16 1 1
17 2 2
18 2 1

29. Advance the slide to see the answer
A political think take wants to determine if there is relationship
between gender and support of Proposition “X”.
Patients
Support (1) or Oppose (2)
Proposition “X”
Gender
(1,2)
1 1 1
2 1 1
3 2 2
4 1 1
5 1 1
6 2 1
7 1 2
8 2 2
9 2 2
10 1 1
11 2 2
12 1 1
13 1 2
14 2 1
15 2 2
16 1 1
17 2 2
18 2 1
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

30. A political think take wants to determine if there is relationship
between gender and support of Proposition “X”.
Advance the slide to see the explanation
Patients
Support (1) or Oppose (2)
Proposition “X”
Gender
(1,2)
1 1 1
2 1 1
3 2 2
4 1 1
5 1 1
6 2 1
7 1 2
8 2 2
9 2 2
10 1 1
11 2 2
12 1 1
13 1 2
14 2 1
15 2 2
16 1 1
17 2 2
18 2 1
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau

31. A political think take wants to determine if there is relationship
between gender and support of Proposition “X”.
Because both variables are
dichotomous
Explanation
The End
Patients
Support (1) or Oppose (2)
Proposition “X”
Gender
(1,2)
1 1 1
2 1 1
3 2 2
4 1 1
5 1 1
6 2 1
7 1 2
8 2 2
9 2 2
10 1 1
11 2 2
12 1 1
13 1 2
14 2 1
15 2 2
16 1 1
17 2 2
18 2 1
Which is it?
Phi-Coefficient Point-Biserial
Spearman Rho Kendal Tau