A Phi coefficient is a non-parametric test used to measure the strength of association between two dichotomous (binary) variables. It analyzes the variables in a 2x2 contingency table to determine if there is a non-random pattern across the four cells. The Phi coefficient ranges in value from -1 to 1, similar to a correlation coefficient, with values closer to 1 or -1 indicating a stronger association.

1. Phi-Coefficient
Conceptual Explanation

2. A Phi coefficient is a non-parametric test of
relationships that operates on two dichotomous
(or dichotomized) variables. It intersects
variables across a 2x2 matrix to estimate
whether there is a non-random pattern across
the four cells in the 2x2 matrix. Similar to a
parametric correlation coefficient, the possible
values of a Phi coefficient range from -1 to 0 to
+1.

3. A Phi coefficient is a non-parametric test of
relationships that operates on two dichotomous
(or dichotomized) variables. It intersects
variables across a 2x2 matrix to estimate
whether there is a non-random Dichotomous
pattern across
means that the
the four cells in the 2x2 matrix. data can take Similar on
to a
only two values.
parametric correlation coefficient, the possible
values of a Phi coefficient range from -1 to 0 to
+1.

4. A Phi coefficient is a non-parametric test of
relationships that operates on two dichotomous
(or dichotomized) variables. It intersects
variables across a 2x2 matrix to estimate
whether there is a non-random pattern across
the four cells in the 2x2 matrix. Similar to a
parametric correlation coefficient, the possible
values of a Phi coefficient range from -1 to 0 to
+1.
Like –
• Male/Female
• Yes/No
• Opinion/Fact
• Control/Treatment

5. It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.

6. It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
What does
this mean?

7. It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Here is an
example
Data Set

8. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.

9. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Two Dichotomous
Variables

10. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A
B
C
D
E
F
G
H
I
J
K
L
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.

11. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1
B 1
C 1
D 2
E 2
F 1
G 2
H 2
I 2
J 1
K 1
L 2
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.

12. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.

13. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Male

14. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Male

15. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Female

16. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Female

17. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Single

18. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Single

19. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Married

20. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.
Married

21. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.

22. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
coefficient, the possible
values of a Phi coefficient
range from -1 to 0 to +1.

23. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married
Single

24. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married
Single

25. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married
Single

26. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married
Single

27. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single

28. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single

29. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single
1

30. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single
1
2

31. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single
1
2
3

32. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single
1
2
3
4

33. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single
1
2
3
4
5

34. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single
1
2
3
4
5

35. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single 5

36. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single 5

37. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single 5
1

38. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single 5
1
2

39. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single 5
1
2
3

40. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single 5
1
2
3
4

41. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1
Single 5
1
2
3
4

42. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1 4
Single 5

43. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1 4
Single 5

44. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1 4
Single 5

45. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1 4
Single 5
1

46. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1 4
Single 5
1
2

47. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1 4
Single 5
1
2

48. Subjects Gender
1= Male
2= Female
Marital Status
1 = Single
2 = Married
A 1 2
B 1 1
C 1 1
D 2 2
E 2 2
F 1 1
G 2 2
H 2 1
I 2 2
J 1 1
K 1 1
L 2 1
It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1 4
Single 5 2

49. It intersects variables
across a 2x2 matrix to
estimate whether there is
a non-random pattern
across the four cells in the
2x2 matrix. Similar to a
parametric correlation
GENDER
coefficient, the possible
Male Female
values of a Phi coefficient
range from -1 to 0 to +1.
MARITAL
STATUS
Married 1 4
Single 5 2

50. Similar to a parametric correlation coefficient,
the possible values of a Phi coefficient range
from -1 to 0 to +1.

51. A Phi coefficient of 0 would indicate that there is
no systematic pattern across the 2x2 matrix. A
negative Phi coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“lower’ coded values on the other variable. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.

52. A Phi coefficient of 0 would indicate that there is
no systematic pattern across the 2x2 matrix. A
negative Phi coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable GENDER
are associated with
“lower’ coded values Male on the Female
other variable. A
Married 3 3
positive MARITAL
STATUS
phi-Single coefficient 3 would 3
indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.

53. A Phi coefficient of 0 would indicate that there is
no systematic pattern across the 2x2 matrix. A
negative Phi coefficient would indicate a
systematic pattern in which or
“higher” coded
values on one variable are associated with
“lower’ coded values on the other variable. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.

54. A Phi coefficient of 0 would indicate that there is
no systematic pattern across the 2x2 matrix. A
negative Phi coefficient would indicate a
systematic pattern in which or
“higher” coded
values on one variable are associated with
“lower’ coded values on the GENDER
other variable. A
positive phi-coefficient Male would Female
indicate a
systematic MARITAL
pattern Married in which 5 “higher” 5
coded
STATUS
Single 1 1
values on one variable are associated with
“higher” coded values on the other variable.

55. A Phi coefficient of 0 would indicate that there is
no systematic pattern across the 2x2 matrix. A
negative Phi coefficient would indicate a
systematic pattern in which or
“higher” coded
values on one variable are associated with
“lower’ coded values on the GENDER
other variable. A
positive phi-coefficient Male would Female
indicate a
systematic MARITAL
pattern Married in which 5 “higher” 5
coded
STATUS
Single 1 1
values on one variable are associated with
“higher” coded values on the other variable.
Being male or female does not make you any
more likely to be married or single

56. A Phi coefficient of 0 would indicate that there is
no systematic pattern across the 2x2 matrix. A
negative Phi coefficient would indicate a
systematic pattern in which or
“higher” coded
values on one variable are associated with
“lower’ coded values on the GENDER
other variable. A
positive phi-coefficient Male would Female
indicate a
systematic MARITAL
pattern Married in which 5 “higher” 5
coded
STATUS
Single 1 1
values on one variable are associated with
“higher” coded values on the other variable.
Being male or female does not make you any
more likely to be married or single

57. A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.

58. A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.

59. A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married
Single

60. A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married
Single

61. A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married
Single
For example

62. A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married 4
Single 5

63. A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married 4 1
Single 2 5

64. A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married 4 1
Single 2 5

65. positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.
GENDER
Male Female
MARITAL
STATUS
Married 4 1
Single 2 5
Phi-
Coefficient
+.507

66. In terms of how to interpret this value, here is a helpful rule of
thumb:
A positive Phi coefficient would indicate that
most of the data are in the diagonal cells.
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married 4 1
Single 2 5
+.507
Value of r Strength of relationship
-1.0 to -0.5 or 1.0 to 0.5 Strong
-0.5 to -0.3 or 0.3 to 0.5 Moderate
-0.3 to -0.1 or 0.1 to 0.3 Weak
-0.1 to 0.1 None or very weak

67. In terms of how to interpret this value, here is a helpful rule of
thumb:
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.
Value of r Strength of relationship
-1.0 to -0.5 or 1.0 to 0.5 Strong
-0.5 to -0.3 or 0.3 to 0.5 Moderate
-0.3 to -0.1 or 0.1 to 0.3 Weak
-0.1 to 0.1 None or very weak
GENDER
Male Female
MARITAL
STATUS
Married 4 1
Single 2 5
+.507
So, the interpretation would be, that there is a strong relationship
between marital status and gender with being male making it
more likely you are married and being female making it more likely
to be single.

68. In terms of how to interpret this value, here is a helpful rule of
thumb:
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.
Value of r Strength of relationship
-1.0 to -0.5 or 1.0 to 0.5 Strong
-0.5 to -0.3 or 0.3 to 0.5 Moderate
-0.3 to -0.1 or 0.1 to 0.3 Weak
-0.1 to 0.1 None or very weak
GENDER
Male Female
MARITAL
STATUS
Married 4 1
Single 2 5
+.507
So, the interpretation would be, that there is a strong relationship
between marital status and gender with being male making it
more likely you are married and being female making it more likely
to be single.

69. In terms of how to interpret this value, here is a helpful rule of
thumb:
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.
Value of r Strength of relationship
-1.0 to -0.5 or 1.0 to 0.5 Strong
-0.5 to -0.3 or 0.3 to 0.5 Moderate
-0.3 to -0.1 or 0.1 to 0.3 Weak
-0.1 to 0.1 None or very weak
GENDER
Male Female
MARITAL
STATUS
Married 4 1
Single 2 5
+.507
So, the interpretation would be, that there is a strong relationship
between marital status and gender with being male making it
more likely you are married and being female making it more likely
you are single.

70. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on the other variable.

71. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married
Single

72. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married
Single

73. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married 1 4
Single 5 2

74. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Male Female
MARITAL
STATUS
Married 1 4
Single 5 2
Phi-
Coefficient
-.507

75. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are GENDER
associated with
“higher” coded values on Male the other Female
variable.
MARITAL
STATUS
Married 1 4
Single 5 2
Phi-
Coefficient
-.507
So, the interpretation would be, that there is a strong relationship
between marital status and gender with being male making it
more likely that you are single and being female making it more
likely you are married.

76. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are GENDER
associated with
“higher” coded values on Male the other Female
variable.
MARITAL
STATUS
Married 1 4
Single 5 2
Phi-
Coefficient
-.507
So, the interpretation would be, that there is a strong relationship
between marital status and gender with being male making it
more likely that you are single and being female making it more
likely you are married.

77. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are GENDER
associated with
“higher” coded values on Male the other Female
variable.
MARITAL
STATUS
Married 1 4
Single 5 2
Phi-
Coefficient
-.507
So, the interpretation would be, that there is a strong relationship
between marital status and gender with being male making it
more likely that you are single and being female making it more
likely you are married.

78. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are GENDER
associated with
“higher” coded values on Male the other Female
variable.
MARITAL
STATUS
Married 1 4
Single 5 2
Phi-
Coefficient
-.507
So, the interpretation would be, that there is a strong relationship
between marital status and gender with being male making it
more likely that you are single and being female making it more
likely you are married.

79. A negative Phi coefficient would indicate that
most of the data are in the off-diagonal cells. A
positive phi-coefficient would indicate a
systematic pattern in which “higher” coded
values on one variable are associated with
“higher” coded values on tGhENeD oERther variable.
Note: the sign (+ or -) is irrelevant. The main thing to consider is
the strength of the relationship between the two variables and
then look at the 2x2 matrix to determine what it means.
Male Female
MARITAL
STATUS
Married 1 4
Single 5 2
Phi-
Coefficient
-.507

80. Phi Coefficient Example
• A researcher wishes to determine if a significant
relationship exists between the gender of the
worker and if they experience pain while
performing an electronics assembly task.
• One question asks “Do you experience pain
while performing the assembly task? Yes No”
• The second question asks “What is your
gender? ___ Male ___ Female”

81. • A researcher wishes to determine if a significant
relationship exists between the gender of the
worker and if they experience pain while
performing an electronics assembly task.
e question asks “Do you experience pain while
performing the assembly task? Yes No”
• The second question asks “What is your
gender? ___ Male ___ Female”

82. • A researcher wishes to determine if a significant
relationship exists between the gender of the
worker and if they experience pain while
performing an electronics assembly task.
e question asks “Do you experience pain while
performing the assembly task? Yes No”
• The second question asks “What is your
gender? ___ Male ___ Female”

83. Two survey questions are asked of the
workers:
• One question asks “Do you experience
pain while performing the assembly
task? Yes No”
• The second question asks “What is your
gender? ___ Male ___ Female”

84. Two survey questions are asked of the
workers:
• “Do you experience pain while
performing the assembly task? Yes No”
• The second question asks “What is your
gender? ___ Male ___ Female”

85. Two survey questions are asked of the
workers:
• “Do you experience pain while
performing the assembly task? Yes No”
• “What is your gender?
___ Female ___ Male”
adsfj;lakjdfs;lakjsdf;lakdsjfa

86. Step 1: Null and Alternative Hypotheses
• Ho: There is no relationship
between the gender of the worker
and if they feel pain while
performing the task.
• H1: There is a significant
relationship between the gender of
the worker and if they feel pain
while performing the task.

87. Step 1: Null and Alternative Hypotheses
• Ho: There is no relationship
between the gender of the worker
and if they feel pain while
performing the task.
• H1: There is a significant
relationship between the gender of
the worker and if they feel pain
while performing the task.

88. Step 1: Null and Alternative Hypotheses
• Ho: There is no relationship
between the gender of the worker
and if they feel pain while
performing the task.
• H1: There is a significant
relationship between the gender of
the worker and if they feel pain
while performing the task.

89. Step 2: Determine dependent and
independent variables and their formats.

90. Step 2: Determine dependent and
independent variables and their formats.

91. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is dichotomous, dependent

92. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is dichotomous, dependent
An independent variable
is the variable doing the
causing or influencing

93. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable

94. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable

95. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable
A dependent variable is
the thing being caused
or influenced by the
independent variable

96. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable

97. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable
• Gender is a dichotomous variable

98. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable
• Gender is a dichotomous variable
In this study it can only
take on two variables:
1 = Male
2 = Female

99. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable
• Gender is a dichotomous variable
• Feeling pain is a dichotomous variable

100. Step 2: Determine dependent and
independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable
• Gender is a dichotomous variable
• Feeling pain is a dichotomous variable
In this study it can only
take on two variables:
1 = Feel Pain
2 = Don’t Feel Pain

101. Step 3: Choose test statistic

102. Step 3: Choose test statistic
• Because we are investigating the relationship between
two dichotomous variables, the appropriate test statistic
is the Phi Coefficient

103. Step 4: Run the Test
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes
to the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No
to the pain item (8)

104. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes
to the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No
to the pain item (8)

105. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes
to the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No
to the pain item (8)

106. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes
to the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No
to the pain item (8)

107. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No
to the pain item (8)

108. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No
to the pain item (8)

109. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 4 B E
No C D F
Total G H

110. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 4 6 E
No C D F
Total G H

111. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 4 6 E
No 11 D F
Total G H

112. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 4 6 E
No 11 8 F
Total G H

113. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 4 6 E
No 11 8 F
Total G H

114. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 4 6 E
No 11 8 F
Total 15 H

115. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 4 6 E
No 11 8 F
Total 14 H

116. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 4 6 E
No 11 8 F
Total 14 14

117. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 1 12 E
No 13 2 F
Total 14 14

118. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 1 12 13
No 13 2 F
Total 14 14

119. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 1 12 13
No 13 2 F
Total 12 14

120. Step 4: Run the Test
• The Phi Coefficient should be set up as follows:
– Box A contains the number of Males that said Yes to
the pain item (4)
– Box B contains the number of Females that said Yes to
the pain item (6)
– Box C contains the number of Males that said No to
the pain item (11)
– Box D contains the number of Females that said No to
the pain item (8)
Males Females Total
Yes 1 12 13
No 13 2 15
Total 12 14

121. Phi Coefficient Test Formula

122. Phi Coefficient Test Formula
bc ad
( 
)
efgh
( )
 

123. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= .788

124. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
ퟏퟐ∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= .788

125. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗ퟏퟑ −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= .788

126. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(ퟏ∗2)
15∗13∗14∗14
=
154.0
195.5
= .788

127. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗ퟐ)
15∗13∗14∗14
=
154.0
195.5
= .788

128. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(풆푓푔ℎ)
=
12∗13 −(1∗2)
ퟏퟓ∗13∗14∗14
=
154.0
195.5
= .788

129. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒풇푔ℎ)
=
12∗13 −(1∗2)
15∗ퟏퟑ∗14∗14
=
154.0
195.5
= .788

130. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗ퟏퟒ∗14
=
154.0
195.5
= .788

131. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 13
No c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗ퟏퟒ
=
154.0
195.5
= .788

132. Phi Coefficient Test Formula
Males Females Total
Yes a = 1 b = 12 e = 15
No c = 13 d = 2 f = 13
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
ퟏퟓퟒ.ퟎ
ퟏퟗퟓ.ퟓ
= .788

133. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 1 b = 12 e = 13
No - Pain c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= -.788

134. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 1 b = 12 e = 13
No - Pain c = 13 d = 2 f = 15
Total g = 14 h =14
Result: there is a strong relationship between gender and feeling pain with
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= -.788
females feeling more pain than males.

135. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 1 b = 12 e = 13
No - Pain c = 13 d = 2 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= -.788
Remember that with the Phi-coefficient the sign (-/+) is irrelevant

136. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 1 b = 12 e = 13
No - Pain c = 13 d = 2 f = 15
Total g = 14 h =14
We could have switched the columns and have gotten the same value but
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= -.788
with a different sign.

137. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 1 b = 12 e = 13
No - Pain c = 13 d = 2 f = 15
Total g = 14 h =14
We could have switched the columns and have gotten the same value but
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= -.788
with a different sign.

138. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 12 b = 1 e = 13
No - Pain c = 13 d = 2 f = 15
Total g = 14 h =14
We could have switched the columns and have gotten the same value but
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= -.788
with a different sign.

139. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 12 b = 1 e = 13
No - Pain c = 13 d = 2 f = 15
Total g = 14 h =14
We could have switched the columns and have gotten the same value but
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= -.788
with a different sign.

140. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 12 b = 1 e = 13
No - Pain c = 2 d = 13 f = 15
Total g = 14 h =14
We could have switched the columns and have gotten the same value but
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
12∗13 −(1∗2)
15∗13∗14∗14
=
154.0
195.5
= -.788
with a different sign.

141. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 12 b = 1 e = 13
No - Pain c = 2 d = 13 f = 15
Total g = 14 h =14
We could have switched the columns and have gotten the same value but
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
ퟏퟐ∗ퟏퟑ −(ퟏ∗ퟐ)
15∗13∗14∗14
=
154.0
195.5
= -.788
with a different sign.

142. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 12 b = 1 e = 13
No - Pain c = 2 d = 13 f = 15
Total g = 14 h =14
We could have switched the columns and have gotten the same value but
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
ퟏ∗ퟐ −(ퟏퟐ∗ퟏퟑ)
15∗13∗14∗14
=
154.0
195.5
= -.788
with a different sign.

143. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 12 b = 1 e = 13
No - Pain c = 2 d = 13 f = 15
Total g = 14 h =14
We could have switched the columns and have gotten the same value but
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
ퟏ∗ퟐ −(ퟏퟐ∗ퟏퟑ)
15∗13∗14∗14
=
154.0
195.5
= +.788
with a different sign.

144. Phi Coefficient Test Formula
Males Females Total
Yes - Pain a = 12 b = 1 e = 13
No - Pain c = 2 d = 13 f = 15
Total g = 14 h =14
Φ =
(푏푐 −푎푑)
(푒푓푔ℎ)
=
ퟏ∗ퟐ −(ퟏퟐ∗ퟏퟑ)
15∗13∗14∗14
=
154.0
195.5
= +.788
The Result is the Same: there is a strong relationship between gender and
feeling pain with females feeling more pain than males.

145. Step 5: Conclusions

146. Step 5: Conclusions
There is a strong relationship between gender and pain
• Both males and females have pain (or no pain) at equal
frequencies.

147. Step 5: Conclusions
There is a strong relationship between gender and pain
with more females reporting pain than males.
• Both males and females have pain (or no pain) at equal
frequencies.

148. Step 5: Conclusions
There is a strong relationship between gender and pain
with more females reporting pain than males.
• Both males and females have pain (or no pain) at equal
frequencies.
Males Females
Yes - Pain 1 12
No - Pain 13 2

149. Step 5: Conclusions
There is a strong relationship between gender and pain
with more females reporting pain than males.
• Both males and females have pain (or no pain) at equal
frequencies.
Males Females
Yes - Pain 1 12
No - Pain 13 2

150. Step 5: Conclusions
There is a strong relationship between gender and pain
with more females reporting pain than males.
• Both males and females have pain (or no pain) at equal
frequencies.
Males Females
Yes - Pain 1 12
No - Pain 13 2