what is a phi coefficient?
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Phi-Coefficient
Conceptual Explanation
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.
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.
Dichotomous means that the
data can take on only two values.
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
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.
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?
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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married
Single
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married
Single
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married
Single
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married
Single
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single
1
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single
1
2
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single
1
2
3
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single
1
2
3
4
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single
1
2
3
4
5
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single
1
2
3
4
5
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single 5
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single 5
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single 5
1
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single 5
1
2
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single 5
1
3
2
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single 5
1
3
4
2
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1
Single 5
1
3
4
2
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5
1
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5
1
2
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5
1
2
Subjects Gender1= Male2= Female
Marital Status1 = Single2 = 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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 2
Similar to a parametric correlation coefficient, the possible values of a Phi coefficient range from -1 to 0 to +1.
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.
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.
GENDER
Male Female
MARITALSTATUS
Married 3 3
Single 3 3
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.
or
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.
orGENDER
Male Female
MARITALSTATUS
Married 5 5
Single 1 1
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.
orGENDER
Male Female
MARITALSTATUS
Married 5 5
Single 1 1
Being male or female does not make you any more likely to be married or single
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.
orGENDER
Male Female
MARITALSTATUS
Married 5 5
Single 1 1
Being male or female does not make you any more likely to be married or single
A positive Phi coefficient would indicate that most of the data are in the diagonal cells.Apositive 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.
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.
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. GENDER
Male Female
MARITALSTATUS
Married
Single
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. GENDER
Male Female
MARITALSTATUS
Married
Single
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. GENDER
Male Female
MARITALSTATUS
Married
Single
For example
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. GENDER
Male Female
MARITALSTATUS
Married 4
Single 5
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. GENDER
Male Female
MARITALSTATUS
Married 4 1
Single 2 5
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. GENDER
Male Female
MARITALSTATUS
Married 4 1
Single 2 5
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
MARITALSTATUS
Married 4 1
Single 2 5+.507
Phi-Coefficient
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. GENDER
Male Female
MARITALSTATUS
Married 4 1
Single 2 5+.507
In terms of how to interpret this value, here is a helpful rule of thumb:
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
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.
In terms of how to interpret this value, here is a helpful rule of thumb:
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
MARITALSTATUS
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.
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.
In terms of how to interpret this value, here is a helpful rule of thumb:
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
MARITALSTATUS
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.
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.
In terms of how to interpret this value, here is a helpful rule of thumb:
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
MARITALSTATUS
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.
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.
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. GENDER
Male Female
MARITALSTATUS
Married
Single
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. GENDER
Male Female
MARITALSTATUS
Married
Single
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. GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 2
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. GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 2-.507
Phi-Coefficient
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.
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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 2-.507
Phi-Coefficient
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.
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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 2-.507
Phi-Coefficient
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.
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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 2-.507
Phi-Coefficient
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.
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.
GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 2-.507
Phi-Coefficient
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. GENDER
Male Female
MARITALSTATUS
Married 1 4
Single 5 2-.507
Phi-Coefficient
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.
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”
• 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”
• 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”
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”
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”
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
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.
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.
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.
Step 2: Determine dependent and independent variables and their formats.
Step 2: Determine dependent and independent variables and their formats.
Step 2: Determine dependent and independent variables and their formats.
• Gender is the independent variable
• Feeling pain is dichotomous, dependent
Step 2: Determine dependent and independent variables and their formats.
• Gender is the independent variable
• Feeling pain is dichotomous, dependentAn independent variable is the variable doing the
causing or influencing
Step 2: Determine dependent and independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable
Step 2: Determine dependent and independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable
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
Step 2: Determine dependent and independent variables and their formats.
• Gender is the independent variable
• Feeling pain is the dependent variable
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
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 = Male2 = Female
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
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 Pain2 = Don’t Feel Pain
Step 3: Choose test statistic
Step 3: Choose test statistic
• Because we are investigating the relationship between two dichotomous variables, the appropriate test statistic is the Phi Coefficient
– 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)
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)
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)
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)
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)
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)
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
Yes4 B E
NoC D F
TotalG H
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
Yes4 6 E
NoC D F
TotalG H
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
Yes4 6 E
No11 D F
TotalG H
Step 4: Run the Test
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
Yes4 6 E
No11 8 F
TotalG H
• 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
Yes4 6 E
No11 8 F
TotalG H
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
Yes4 6 E
No11 8 F
Total15 H
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
Yes4 6 E
No11 8 F
Total14 H
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
Yes4 6 E
No11 8 F
Total14 14
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
Yes1 12 E
No13 2 F
Total14 14
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
Yes1 12 13
No13 2 F
Total14 14
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
Yes1 12 13
No13 2 F
Total12 14
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
Yes1 12 13
No13 2 15
Total12 14
Step 4: Run the Test
Phi Coefficient Test Formula
Phi Coefficient Test Formula
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bc ad
efgh
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
𝟏𝟐∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗𝟏𝟑 −(1∗2)
15∗13∗14∗14= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(𝟏∗2)
15∗13∗14∗14= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗𝟐)
15∗13∗14∗14= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝒆𝑓𝑔ℎ)=
12∗13 −(1∗2)
𝟏𝟓∗13∗14∗14= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝒇𝑔ℎ)=
12∗13 −(1∗2)
15∗𝟏𝟑∗14∗14= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗𝟏𝟒∗14= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 13
Noc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗𝟏𝟒= 154.0
195.5= .788
Phi Coefficient Test Formula
Males Females Total
Yesa = 1 b = 12 e = 15
Noc = 13 d = 2 f = 13
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 𝟏𝟓𝟒.𝟎
𝟏𝟗𝟓.𝟓= .788
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 1 b = 12 e = 13
No - Painc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= -.788
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 1 b = 12 e = 13
No - Painc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= -.788
Result: there is a strong relationship between gender and feeling pain with females feeling more pain than males.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 1 b = 12 e = 13
No - Painc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= -.788
Remember that with the Phi-coefficient the sign (-/+) is irrelevant
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 1 b = 12 e = 13
No - Painc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= -.788
We could have switched the columns and have gotten the same value but with a different sign.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 1 b = 12 e = 13
No - Painc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= -.788
We could have switched the columns and have gotten the same value but with a different sign.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 12 b = 1 e = 13
No - Painc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= -.788
We could have switched the columns and have gotten the same value but with a different sign.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 12 b = 1 e = 13
No - Painc = 13 d = 2 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= -.788
We could have switched the columns and have gotten the same value but with a different sign.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 12 b = 1 e = 13
No - Painc = 2 d = 13 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
12∗13 −(1∗2)
15∗13∗14∗14= 154.0
195.5= -.788
We could have switched the columns and have gotten the same value but with a different sign.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 12 b = 1 e = 13
No - Painc = 2 d = 13 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
𝟏𝟐∗𝟏𝟑 −(𝟏∗𝟐)
15∗13∗14∗14= 154.0
195.5= -.788
We could have switched the columns and have gotten the same value but with a different sign.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 12 b = 1 e = 13
No - Painc = 2 d = 13 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
𝟏∗𝟐 −(𝟏𝟐∗𝟏𝟑)
15∗13∗14∗14= 154.0
195.5= -.788
We could have switched the columns and have gotten the same value but with a different sign.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 12 b = 1 e = 13
No - Painc = 2 d = 13 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
𝟏∗𝟐 −(𝟏𝟐∗𝟏𝟑)
15∗13∗14∗14= 154.0
195.5= +.788
We could have switched the columns and have gotten the same value but with a different sign.
Phi Coefficient Test Formula
Males Females Total
Yes - Paina = 12 b = 1 e = 13
No - Painc = 2 d = 13 f = 15
Totalg = 14 h =14
Φ =(𝑏𝑐 −𝑎𝑑)
(𝑒𝑓𝑔ℎ)=
𝟏∗𝟐 −(𝟏𝟐∗𝟏𝟑)
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.
Step 5: Conclusions
Step 5: Conclusions
There is a strong relationship between gender and pain
• Both males and females have pain (or no pain) at equal frequencies.
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.
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 12No - Pain 13 2
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 12No - Pain 13 2
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 12No - Pain 13 2
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