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Chi Square
Chi square is employed to test the
difference between an actual sample
and another hypothetical or previously
established distribution such as that
which may be expected due to chance
or probability. Chi square may also be
used to test the differences between two
or more actual samples.
Basic Computation Equation
2
(
observed
frequency

expected
frequency
)
x2 
expected frequency
Basic Computation Equation
With Yates Correction: Used for
Problems With 1 Degree of
Freedom
2
(
observed
frequency

expected
frequency

0
.
5
)
2
x 
expected frequency
One Way Classification
This test is used to when a researcher
is interested in the number of
responses, objects, or people that fall
into two or more categories. This
procedure is sometimes called the
“goodness-of-fit” statistic.
One Way Classification
Suppose a coin toss experiment
involving twenty trials yielded 12 heads
and 8 tails. Is this result significantly
different from the expected frequency of
10 heads and 10 tails?
Observed
Expected
Heads
12
10
Tails
08
10
One Way
Classification
( Fo  Fe  0. 5)
(12  10  0. 5)

. 225
Fe
10
2
2
( Fo  Fe  0. 5)
( 08  10  0. 5)

..225
625
Fe
10
2
x . 225.225
. 625 ..450
850
2
2
One Way Classification
x
2
observed
x
2
critical
..45
85
 3. 84
RESULT : DO NOT REJECT Ho.
Two Way Classification
The two-way chi square is a
convenient technique for determining
the significance of the difference
between the frequencies of
occurrence between two or more
categories with two or more groups.
Calculating Degrees of Freedom
 One
independent variable - df = (r-1), where r
equals the number of levels of the independent
variable
 Two
independent variables - df = (r-1) (s-1),
where r and s are the number of levels of the first
and second independent variables, respectively
 Three
independent variables - df = (r-1) (s-1) (t-1),
where r, s and t are the number of levels of the
first, second and third independent variables,
respectively.
Assumptions
 The
data is in frequency form.
 The observations are independent of each other.
 Distribution basis is decided before data collection.
 The sum of observed and expected frequencies
are equal.
 Sample size is adequate. In a 2x2 table, chi square
should not be used when n is less than 20. In a
larger table, no cell should have an expected value
of less than 1 and not more than 20% of the cells
can have expected values of less than 5.