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Title: Chi-Square
Description: Learn about chi-square test and different worked examples

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Chi-Square Distribution
Statistics By Lecture Said
Emai: yustofoshizo@gmail
...
Due to
chance? Due to association?
 When can we use the Chi-Square Test?
 Testing Independence – Is one factor associated with another?,

 Testing a population for expected proportions

Assumptions:
 1 or more categories
 Independent observations
 A sample size of at least 10
 Random sampling
 All observations must be used
 For the test to be accurate, the
expected frequency should be at
least 5

1)

Conducting Chi-Square
Make a hypothesis based on your basic biological
Analysis
question

2)

Determine the expected frequencies

3)

Create a table with observed frequencies, expected
frequencies, and chi-square values using the formula:
(O-E)2

E

4)

Find the degrees of freedom: (c-1)(r-1)

5)

Find the chi-square statistic in the Chi-Square
Distribution table

6)

If chi-square statistic > your calculated chi-square
value, you do not reject your null hypothesis and vice
versa
...

HA: Horned lizards eat more amounts of one species of ants than the others
...
25

0
...
45

χ2 = 1
...
g
...
05 or 95%
confidence),
look up Chi-square statistic on a Chi-square distribution table
...
05 = 5
...
25

0
...
45

χ2 = 1
...
991
1
...
There is a significant difference that is
not due to chance
...
991 > 1
...


SAS: Example 1
Included to format
the table

Define your data
Indicate what your
want in your
output

SAS: Example 1

SAS: What does the p-value
mean?
“The exact p-value for a nondirectional test is
the sum of probabilities for the table having a
test statistic greater than or equal to the value of
the observed test statistic
...
Do not reject null
hypothesis
...
Reject null hypothesis
...


We do not reject our null
hypothesis
...

HA: Gender and eye colour are
associated
each other
...

(78
...


Example 2: More SAS
Examples

If there was an
association, can check
which interactions
describe association
by looking at how
much each cell
contributes to the
overall Chi-square
value
...
5 from
the absolute value of each calculated O-E term,
then continue as usual with the new corrected
values

What do these mean?

Likelihood Ratio Chi Square


Continuity-Adjusted Chi-Square Test



Mantel-Haenszel Chi-Square
Test
Q = (n-1)r
MH

2

 r2 is the Pearson correlation coefficient (which
also measures the linear association between
row and column)
◦ http://support
...
com/documentation/cdl/en/procstat/63
104/HTML/default/viewer
...
h
tm

 Tests alternative hypothesis that there is a
linear association between the row and
column variable
 Follows a Chi-square distribution with 1 degree
of freedom

Phi Coefficient


Contigency Coefficient


Cramer’s V


Yates & 2 x 2 Contingency
H : Heart
Disease is not associated with cholesterol levels
...

O
A

High
Cholesterol

Low
Cholesterol

Total

Heart Disease

15

7

22

Expected

12
...
35

22

Chi-Square

0
...
59

1
...
35

7
...
53

0
...
25

TOTAL

23

17

40

Chi-Square Total
Calculate degrees of freedom: (c-1)(r-1) = 1*1 = 1
We need to use the YATES CORRECTION

2
...

Tables
H : Heart Disease is more likely in patients with a high cholesterol diet
...
65

9
...
27

0
...
64

No Heart
Disease

8

Expected

10
...
33

TOTAL

23

Chi-Square Total

10
(|15-12
...
5)2
12
...
65
= 0
...
45
17

18
18
0
...
42

Example 1: Testing for
Proportions

χ2α=0
...
841

Yates & 2 x 2 Contingency
H : Heart
Disease is not associated with cholesterol levels
...

O
A

High
Cholesterol

Low
Cholesterol

Total

Heart Disease

15

7

22

Expected

12
...
35

22

Chi-Square

0
...
37

0
...
35

7
...
33

0
...
78

TOTAL

23

17

40

Chi-Square Total
3
...
42 ∴ We do not reject our null hypothesis
...
42

Fisher’s Exact Test
 Left: Use when the alternative to independence is
negative association between the variables
...
Small p-value = Likely negative
association
...
These observations tend to lie in
upper left and lower right cells or the table
...

 Two-Tail: Use this when there is no prior alternative
...

HA: Heart Disease is more
likely in patients with a high
cholesterol diet
...
enviroliteracy
...
pdf
http://129
...
92
...
pdf
Ozdemir T and Eyduran E
...
Comparison of chi-square and likelihood ratio
chi-square tests: power of test
...
1(2):242244
...
sas
...
html
“FREQ procedure”

YouTube Chi-square SAS Tutorial (user: mbate001):
http://www
...
com/watch?v=ACbQ8FJTq7k


Title: Chi-Square
Description: Learn about chi-square test and different worked examples