1. Test of significance-The Chi-Square
Dr. O. E. Adegbilero-Iwari
College of Medicine & Health Sciences,
Afe-Babalola University Ado-Ekiti, Ekiti, Nigeria.
1
2. CONTINGENCY TABLE
The classification, according to two criteria, of a set of
entities, say, people, can be shown by a table in which
the r rows represent the various levels of one criterion
of classification and the c columns represent the
various levels of the second criterion. Such a table is
generally called a contingency table, with dimension
r x c.
3. A 3x 2 CONTINGENCY TABLE
Weight Status
Smoking
Yes No
Underweight 17 97
Overweight 25 142
Appropriate 96 816
4. Chi-Square
It is the most frequently employed statistical
technique in the analysis of count or
frequency data.
It is also the most widely used distribution in
statistical applications
6. EXAMPLE
In 1992, the U.S. Public Health Service and the Centers for
Disease Control and Prevention recommended that all women
of childbearing age consume 400mg of folic acid daily to reduce
the risk of having a pregnancy that is affected by a neural tube
defect such as spina-bifida or anencephaly. In a study by
Stepanuk et al, 636 pregnant women called a teratology
information service about their use of folic acid
supplementation. The researchers wished to determine if
preconception use of folic acid and Race are dependent.
7. Preconceptional use of folic acid
YES NO TOTAL
White 260 299 559
Black 15 41 56
Other 7 14 21
total 282 354 636
8. Steps for testing the Hypothesis
i. Test of Hypotheses
• Null hypothesis (𝐻𝑂)
• Alternative hypothesis (𝐻1)
ii. Significance level
iii. Test statistic
iv. Critical value
v. Decision rule and Decision
vi. Conclusion
9. TEST OF HYPOTHESES
𝐻0 : There is no association between Race and
preconceptional use of folic acid (The
variables are independent)
𝐻1 : There is an association between Race and
Preconceptional use of folic acid (The
variables are dependent)
SIGNIFICANCE LEVEL
𝛼 = 0.05
10. TEST STATISTIC
When 𝐻0 is true,
𝑋2
is distributed ~ 𝜒2
(𝑟−1)(𝑐−1)
CRITICAL VALUE
This Is obtained from the chi-square table
𝜒2
[ 𝑟−1 𝑐−1 , 𝛼] , r = 3, c = 2
= 𝜒2
[2, 0.05] = 𝜒2
[2, 1−0.05 𝑖𝑛 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒]
11.
12. TEST STATISTIC
𝑿𝟐
= 𝒊=𝟏
𝒌
[
(𝑶𝒊−𝑬𝒊)𝟐
𝑬𝒊
] -------------- equation (1)
CALCULATION OF TEST STATISTICS
We need to obtain the expected frequencies and
then substitute them back into equation (1) above
13. In general, to obtain the expected
frequency of a given cell, we multiply the
total of the row in which the cell is
located by the total of the column in
which the cell is located and divide by
the grand total.
19. DECISION RULE
Reject the null hypothesis (𝐻0 ) if calculated
test statistic (𝑋2
) is greater than tabulated
value otherwise do not reject.
DECISION
We reject 𝐻0 since 9.0896 (𝑋2
) is greater
than tabulated 𝜒2
value of 5.991
20. CONCLUSION
We conclude that there exist an association
between the preconception use of folic acid and
race which implies that the two variables are
dependent.
21. Exercise
Some researchers examined the beliefs held by adolescents regarding smoking and
weight. Respondents characterized their weight into three categories: underweight,
overweight or appropriate. Smoking status was categorized according to the answer to
the question, “Do you currently smoke, meaning one or more cigarettes per day?”
The following table shows the results of a telephone study of adolescents in the age
group 12-17. Does the data provide sufficient evidence to suggest that weight
perception and smoking status are related in adolescents? Take 𝛼 = 0.05
Smoking
Weight perception Yes No
Underweight 17 97
Overweight 25 142
Appropriate 96 816
