Step 3
Calculate
(actual frequency − expected frequency)²
expected frequency
for each square.
The bigger the gap between the actual frequencies and the expected
frequencies, the larger the values in each square become.
If sex and desired way of being asked out have no relationship, the ratio between
phone, e-mail, and face to face should be
for both males and females, according to the sum column in the table in step 2.
Thus, our expected frequency (Formula A) shows the predicted number of males
who wish to be asked out directly when there is no relationship between sex and
desired way of being asked out is 152 × (127 ÷ 300) = (152 × 127) ÷ 300, or
72
72 + 101 + 127
72 : 101 : 127 =
:
101
72 + 101 + 127
:
127
72 + 101 + 127
72
300
=
:
101
300
:
127
300
127
300
152 ×
152 × 127
300
= = 64.3
Sex
Female
Phone E-mail Face to face
Sum
Male
Sum
Desired way of being asked out
148
152
72 101 127 300
148 × 72
300
34 −
²
148 × 72
300
152 × 72
300
38 −
²
152 × 72
300
152 × 101
300
40 −
²
152 × 101
300
152 × 127
300
74 −
²
152 × 127
300
148 × 101
300
61 −
²
148 × 101
300
148 × 127
300
53 −
²
148 × 127
300
Let's Lk at the Relationship betwn Two Variables 131
Step 4
Calculate the sum of the value inside the bold frame in the table of step 3. This value is called Pearson’s
chi-square test statistic. It will be written as χ
0
2
from now on.
As can be understood from step 3, the more the actual measurements
diverge from their expected frequencies, or the greater the correlation
between sex and desired way of being asked out, the larger Pearson’s
chi-square test statistic (χ
0
2
) becomes.
148 × 72
300
34 −
²
148 × 72
300
148 × 101
300
61 −
²
148 × 101
300
148 × 127
300
53 −
²
148 × 127
300
+ +
152 × 72
300
38 −
²
152 × 72
300
152 × 101
300
40 −
²
152 × 101
300
152 × 127
300
74 −
²
152 × 127
300
+ + +
=
χ
0
2
= 8.0091
132 Chapter 6
Step 5
Calculate the Cramer’s coefficient.
min{a,b} means “whichever is smaller, a or b.”
Thus, the cramer's
coeicient is 0.1634.
χ
0
2
the total number of values ×
(min{the number of lines in the cross tabulation, the number of rows in the cross tabulation} − 1)
8.0091
300 × min{2,3} − 1
8.0091
300 × (2 − 1)
8.0091
300
= 0.1634
= =
Help. I'm
fling
diy.
Let's Lk at the Relationship betwn Two Variables 133
I don't think
I can do this
calculation
alone.
You' be a
right! The
calculation is a
bit complicated,
but I am sure
you can do it
if you foow the
steps.
If there is
anything you can't
understand, just
ask me, ok?
!
What's
wrong?
Nothing.
For a moment,
mr. Yamamoto
somehow
smed kind of
gd lking.
STARE...
Why
turn
away?
oh!
Rub
Rub
134 Chapter 6
Here is the cross tabulation of sex and desired way of being asked out (horizontal percentage table) when
the value of the Cramer’s coefficient is 1.
Here is the cross tabulation of sex and desired way of being asked out (horizontal percentage table) when
the value of the Cramer’s coefficient is 0.
As explained earlier, the Cramer’s coefficient is between 0 and 1. The
stronger the correlation between two variables, the closer the coefficient
gets to 1, and the weaker the correlation, the closer the coefficient gets
to 0. See the cross tabulation (horizontal percentage table) below for more
details.
Sum
Sex
Phone E-mail Face to face
Desired way of being asked out
100%
100%
17% 48% 35%
17% 48% 35%
Female
Male
Sum
Sex
Phone E-mail Face to face
Desired way of being asked out
17%
0%
83%
0%
0%
100%
100%
100%
Female
Male
Cramer’s coefficient is 1 the preferences of female and male are completely different
Cramer’s coefficient is 0 the preferences of female and male are the same
Let's Lk at the Relationship betwn Two Variables 135

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