# personal

## personal

• Submitted By: semran
• Date Submitted: 09/01/2015 5:19 AM
• Category: English
• Words: 291
• Page: 2

CHI-SQUARE TEST
Test of Independence

Chi-Square
A test for data presented in
frequencies or data which can
be transformed in frequencies
To test whether the two
variables are independent of
each other.

Formula for X2
(OF- EF)2
X =
2

EF
= (r-1) (c-1)
= observed frequency
expected frequency

df
OF
EF =

Formula for EF
RC
EF=
N
R
is the row totals
C is the
column totals
N is the
total number of observations

Example
Suppose we are interested in
investigating the relationship
between a fisherman’s participation
in a training program on volume of
catch two months after the training.
A random sample of 200 fishermen
was drawn and were classified
according to participation and level
of catch.

Summary of data
Observed frequencies
Volume Participated Did not TOTAL
of catch
participate
Few
10
70
80
Moderate
15
10
25
Many
50
45
95
TOTAL
75
125
200

Computation of expected freq
Volume Participated
Did not
Total
of catch
participate
Few (75x80)/200 (125x80)/200 80
Moderate (75x25)/200 (125x25)/200 25
Many (75x95)/200 (125x95)/200 95
Total
75
125
200

Expected frequencies
Volume Participated Did not TOTAL
of catch
participate
Few
30
50
80
Moderate
9.375
15.625
25
Many
36.625
59.375
200
TOTAL
75
125
200

Computation of X2 statistic
(10-30)2 (70-50)2 (45-59.375)2

X2c =

+
30

= 36.014

+…+
50

59.375

Test of hypothesis
1. Ho : participation and volume of
catch are
independent
H1 :
participation and volume of
catch are related

X2c > X2tab
X2tab at 5% level and 2 df

2. Reject Ho if

Decision
Since X2c = 36.01>
X2tab =5.99,
Reject Ho
Conclusion : At the 5 % level of
significance, sample evidence
indicates that participation to the
training program and volume of
catch are related.