The document explains the Pearson’s chi-squared test, a statistical method used to determine the significance of differences between proportions, especially in biomedical research. It outlines the steps involved in performing the test, the calculation of expected values, the chi-squared value, and how to interpret the results, using smoking and hypertension as an example. The conclusion emphasizes the association between smoking and higher rates of hypertension, with a significant difference indicated by the chi-squared value.

1. CHI-SQUARED
TEST
Dr Lipilekha Patnaik
Professor, Community Medicine
Institute of Medical Sciences & SUM Hospital
Siksha ‘O’Anusandhan deemed to be University
Bhubaneswar, Odisha, India
Email: drlipilekha@yahoo.co.in

2. Pearson’s chi-squared test
• Chi- Square test is method of testing the significance of difference
between two proportions.
• It has the advantage that at can also be used when more than two
groups are to be compared.
• Commonly applied in biomedical research
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3. • Used to test categorical Data
Especially when the outcomes are in counts or frequency
• Nominal variables
Sex, Blood group
• Ordinal Variables
Birth order
Severity of disease (absent, mild, moderate, severe)
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4. Applications of chi-squared test
• This test is used as
• for finding difference in proportions
• for finding association between variables
4

5. Example
• In a prevalence study of Hypertension, we found that
Hypertension No Hypertension
Non smokers 10 (10%) 90
Smokers 26 (26%) 74
• It is visible from the table that the proportion of HTN was higher
among smokers . The question that arises is whether HTN was really
higher among smokers or the difference was merely due to chance.
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6. Group
Result
Total
Hypertension No HTN
Non smokers 10 (a) 90 (b) 100
(a+b)
Smokers 26 (c) 74 (d) 100
(c+d)
Total 36 (a+c) 164 (b+d) 200 (N)
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7. Steps
• Null hypothesis
• Calculation of expected values
• Calculation of Chi-square value
• Calculation of degrees of freedom
• Conclusion
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8. Null hypothesis
• No significant difference in the proportions
• Alternate- significant difference in the proportions
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9. Calculation of expected values
• Expected value in any cell =
totalGrand
totalRowXtotalColumn
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Expected value of each cell should be more than 5 in
each cell.

10. Expected values in cells
Thus expected value in each cell is
• First cell: 36 X 100 / 200 = 18
• Second cell: 164 X 100 / 200 = 82
• Third cell: 36 X 100 / 200 = 18
• Fourth cell: 164 X 100 / 200 = 82
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11. Chi squared value
∑
−
=
E
EO 2
2 )(
χ
11
df = (c -1) (r-1)
where c and r stand for number of columns and
number of rows respectively.
P < 0.05 – Significant difference between 2 proportions
P > 0.05 – No significant difference between 2
proportions

12. Calculation of Chi-squared value
12
82
)8274(
18
)1826(
82
)8290(
18
)1810( 2222
−
+
−
+
−
+
−
82
)8(
18
)8(
82
)8(
18
)8( 2222
+
−
++
−
=
78.056.378.056.3 +++=
82
64
18
64
82
64
18
64
+++=
68.8=

13. Calculation of degrees of freedom
df = (c -1) (r-1)
where c and r stand for number of columns and number of rows
respectively.
Thus df = (2 -1) X (2 – 1) = (1) X (1) = 1.
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15. Conclusion
• As the Chi-square value is more than the table value for 5%
level of significance at 1 df (3.84), we reject the null hypothesis
and state that there is a statistically significant difference of
proportions of hypertension between smokers and nonsmokers
(P < 0.05).
• Smoking is associated with hypertension.
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