1. X2-Test
PA P E R 5 : B I O S TAT I S T I C S & C O M P U T E R
A P P L I C AT I O N I N B I O T E C H N O L O G Y
SUBMITTED BY:
Katha Sanyal
G U I D E D B Y:
Ms. Sulagna
Ghosh
M S c . B I O T E C H N O L O G Y
S E M E S T E R I I
S E S S I O N 2 1 - 2 2

2. S Y N O P S I S
IMPORTANT TERMS
INTRODUCTION
CHARACTERISTICS OF CHI-SQUARE TEST
CHI-SQUARE DISTRIBUTION
CALCULATIONS OF X 2
APPLICATIONS
CONDITIONS
REFERENCES

3. PARAMETRIC TEST NON PARAMETRIC TEST
HYPOTHESIS
I M P O R TA N T T E R M S
Test in which
population follows a
fixed set of
parameters.
Test in which
population does not
follow a constant
parameter.
A definite statement
about population
parameters.

4. I M P O R TA N T T E R M S
• No statistical relationship and significance
exists in a set of given single observed variable.
• All the observed variables are equal.
NULL
HYPOTHESIS
(H0)
• In contrast to Null Hypothesis, Alternative
Hypothesis considers 1 variable to be
dominating over the other.
ALTERNATIVE
HYPOTHESIS
(H1)

5. DEGREE
OF
FREEDOM
(n-1)
or
(r-1)(c-1)
Degrees of freedom
refers to:
The maximum
number of logically
independent values
r = rows
c = columns

6. DEGREE
OF
FREEDOM
(n-1)
or
(r-1)(c-1)
Source: https://www.mun.ca/biology/scarr/4250_Chi-
square_critical_values.html
r = rows
c = columns

7. CONTINGENCY
TABLE
A contingency table
is
A tabular
representation of
categorical data.

8. INTRODUCTION
• Developed by
Karl Pearson (1900)
• Non-parametric test
• Follows Chi-square
distribution
• Measures difference
between observed
and expected values

9. X2 = (𝒇𝒐 − 𝒇𝒆)2/ 𝒇𝒆

10. CHARACTERISTICS OF
CHI-SQUARE TEST
• Based on frequencies only
• Non-parametric
TEST
• Testing difference between entire set of
the expected and observed frequencies
SIGNIFICANCE
• Testing hypothesis and not for
estimation
APPLIED FOR

11. CHI-SQUARE DISTRIBUTION
k=d.f.= 1,2,3,4,6,9
If null hypothesis is true, X2 can be
closely approximated by a continuous
curve known as chi-square
distribution.
For small no. of d.f., X2 skewed to right.
As no. of d.f. increases, curve becomes
more symmetrical.
RELATIVE
FREQUENCY
CHI-SQUARE VALUE
Source:
https://www.statisticshowto.com/probability-and-
statistics/chi-square/

12. C A L C U L AT I O N S O F X 2
STEP
I
Expected
Frequencies
fe
STEP
II
Put in formula
χ2 = ∑(fo – fe)2/fe
STEP
III
Compare the
values with
the table
value for given
degree of
freedom at
either 5% or
1%.

13. E X A M P L E
Examples to demonstrate application of χ2 test
1. Apply χ2 test to find the efficacy of drug from the data given in
Table 11.1 reproduced in Table 11.4. The table is reproduced
with expected (E) values noted below the observed (O).

14. E X A M P L E
STEP
I
Expected
Frequencies
fe
STEP
II
STEP
III
Put in formula
χ2 = ∑(fo – fe)2/fe
Check degree of
freedom at either
5% or 1%.
Source: Khanal A. B. (2016). MAHAJAN’S METHODS IN BIOSTATISTICS FOR MEDICAL STUDENTS
AND RESEARCH WORKERS (Eight Edition ed.). The Health Sciences Publisher. (222-224)

15. DEGREE
OF
FREEDOM
(n-1)
or
(r-1)(c-1)
r = rows
c = columns Source: https://www.mun.ca/biology/scarr/4250_Chi-
square_critical_values.html
DRUG
IS
EFFICACIOUS

16. APPLICATIONS

17. TEST OF GOODNESS OF FIT OF
DISTRIBUTION
To determine whether there is a significant difference between
observed frequency and theoretical frequency distribution such as
binomial, poisson and normal.
If X2 (calculated) > X2 (tabulated), with (n-1) d.f, then null hypothesis is
rejected otherwise accepted.
And if null hypothesis is accepted, then it can be concluded that the
given distribution follows theoretical distribution.

18. TEST OF INDEPENDENCE OF
ATTRIBUTES
To determine whether or not 2 attributes are associated.
Ex: To check whether a new medicine is effective in controlling fever or
not, X2 test is useful.

19. T E S T O F H O M O G E N I T Y
To test whether two or more independent random samples are drawn
from the same population or from different populations.
X2(calculated)< X2 (tabulated), then null hypothesis is accepted and it
can be concluded that there is a uniformity in the occurrence of the
events.

20. Data must be in the form of frequencies
Precise numerical value should be given
Random observations should be recorded
Items must be independent.
No group should contain very few items.
Overall number of items must be reasonably large
C O N D I T I O N S

21. R E F E R E N C E S
Khanum, Khan (2008). FUNDAMENTALS of BIOSTATISTICS (3rd Revised
Edition ed.). Hyderabad: UkaaZ Publications. (218-235)
Khanal A. B. (2016). MAHAJAN’S METHODS IN BIOSTATISTICS FOR
MEDICAL STUDENTS AND RESEARCH WORKERS (8th Edition ed.). The
Health Sciences Publisher. (218-234)

22. THANK YOU