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SAN JOSÉ STATE UNIVERSITY
College of Social Work
S. W. 242
Spring 2009
Edward Cohen
Week 6 Preparation for Chi-Square Analysis
The Chi-Square Test for Independence or Chi-Square Test of Association
What is the relationship between the gender of the students and the assignment of a Pass or No
Pass test grade?
The following is called a Crosstabs table, using the (fictional) observed frequencies of
15 males and 15 females (Pass = score 70 or above):
Pass
No Pass
Row Totals
Males
12
3
15
Females
13
2
15
Column Totals
25
5
30
Chi-Square compares
expected frequencies
with
observed frequencies.
Expected frequencies
are those
that would occur most often if the null hypothesis were true. We
estimate
the expected frequencies
from our sample using the Column and Row totals (otherwise known as “marginal totals”). Each of the
four cells (male, pass; male not pass; female pass; and female not pass) will each have an expected
frequency.
SPSS does all the calculating, but for instructional purposes here’s how it’s done:
Calculating the Chi-Square by hand:
Χ
2
=
Σ
[
(O-E)
2
E
]
Σ
= Summation sign, read “the sum of…”
O = Observed frequencies
E = Expected frequencies
Expected frequencies are calculated with the marginal totals….see Weinbach and Grinnell book, p.
195 on how to compute these manually.
O
(observed)
E
(Expected)
O – E
(O – E)
2
(O – E)
2
/ E
Males and Pass
12
12.5
12 – 12.5 = -.5
(-.5)
2
= .25
.25 / 12.5 = .02
Male and No Pass
3
2.5
3 – 2.5 = .5
(.5)
2
= .25
.25 / 2.5 = .10
Females and Pass
13
12.5
13 – 12.5 = .5
(.5)
2
= .25
.25 / 12.5 = .02
Females and No Pass
2
2.5
2 – 2.5 = -.5
(-.5)
2
= .25
.25 / 2.5 = .10
Χ
2
= .24
You now want to know if there is a statistically significant difference in the distribution of passes and
no passes earned between male and female students. Another way of saying this: is there a relationship
between gender and passing the test?

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