CHAP 17
CHI (Kahy) SQURE
1
PARAMETRIC AND NONPARAMETRIC
STATISTICAL TESTS
 PARAMETRIC tests are more
accurate than NONPARAMETRIC
tests because they have 3
assumptions (research).
 1. Random selection
 2. Independent of observation
 3. Sample is taken from a normal
population with a normal distribution
2
3
NONPARAMETRIC
STATISTICAL TESTS
 CHI SQURE is like frequency
distribution (Chap 2)
 It is used for comparative
studies.
 Ex1. Of the two leading brands
of cola, which is preferred by
most Americans?
4
CHI SQURE
Ex2. which
psychotherapy
technique is used by
most psychologists? i.e.
cognitive, behavioral, humanistic,
CBT, psychodynamics, etc.
5
CHI SQURE

=
Σ(fo-fe)² /fe
 fo= observed frequency
 fe= expected frequency
 df = C-1
 C= number of categories
fe = n/c = Ho
n= sample size
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CHI SQURE
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df=C-1
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9
Problems
 Distribution of Eye colors for a sample of
n=40 individuals.
 FYI  From chapter 2 Frequency
Distribution
 (X )eye colors (f ) frequencies
 Blue
12
 Brown
21
 Green
3
 Other
4
see next slide for Chi square
10
Problems
 Distribution of Eye colors for a sample of n=40
individuals.
 Frequency distribution
Fo
Blue
Brown
Green
Others
12
21
3
4
11
The question for the hypothesis test is
whether there are any distribution of the
four possible eye colors. Are any of the
eye color distribution would be expected
simply by chance?
We will set alpha at α =.05
 Step 1)
H0 : fo = fe no preference for any specific
eye color
H1 : fo ≠ fe preference for specific eye
color
12
Problems
 Distribution of Eye colors for a sample of n=40
individuals.
 Frequency distribution
Blue
fo
fe
Brown
Green
Others
12
21
3
4
10
10
10
10
13
Step 2
df=C-1
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Problems
 A psychologist examining art appreciation
selected an abstract painting that had no obvious
top or bottom. Hangers were placed on the
painting so that it could be hung with any one of
the four sides at the top. The painting was shown
to a sample of n=50 participants, and each was
asked to hung the painting in the orientation that
looked correct. The following data indicate how
many people choose each of the four sides to be
placed at the top.
Top up (correct) Bottom up

fo 18
17
Left side up
Right side up
7
8
15
16
17
18
19
Problems
 The question for the hypothesis test
is whether there are any preferences
among the four possible
orientations. Are any of the
orientations selected more (or less)
often than would be expected simply
by chance?
 We will set alpha at α =.05
20
Problems
 Step 1)
H : fo=fe no preference for any specific
0
orientation
H : fo≠fe
1
preference for specific orientation
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Step 2
df=C-1
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Problems
 A researcher is using a chi-square test
for independence to examine the
relationship between TV preferences
and gender for a sample of n = 100
children. Each child is asked to select
his/her favorite from a fixed set of three
TV shows and each child is classified
as male or female. The chi-square
statistic for this study would have df
equal to ?
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 df= c-1
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
Problems
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Check your book for
the critical values.
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