education

3. Hypothesis Test
In hypothesis testing procedure we try to test
claims over different parameters of the
population. Like:
population mean
Population variance
Mean difference among populations
Population correlation/ regression coefficients
etc.

4. To test such hypothesis we use different test procedures like:
 T-test, Independent t- test, F-test etc.
 These tests are based on certain assumptions regarding
the population from which random samples are drawn.
 Hence these tests are called parametric tests and generally
test hypothesis regarding continuous phenomenon.
 The assumptions of the test are verified from the random
samples obtained in study.
 If we are unable to meet the assumptions on the basis of
sample evidence then in place above test we use
distribution free methods generally known as Non
Parametric tests .
 Non Parameter tests generally use the concept of
comparison of distributions in place of parameters and they
are rank based.

8. parametric and their equivalent NP tests
specification
Name of parametric
tool
Name of Non
parametric tool
Single population Mean Test ( No
factor)
Z-test, t-test
sign test &
Wilcoxon
Signed Rank
test
Test of equality of means of two
independent populations (one factor)
Independent samples
t-test
Mann-Whitney
test
Test of equality of means of two or
more than two independent
populations (one factor)
One-way ANOVA
Kruskal-Wallis
test
Test of equality of means of two or
more than two independent
populations (two factors)
Two-way ANOVA
Friedman test
Estimation of Population correlation
coefficient
Product moment
Rank
Correlation
Equality of two population proportions Z-test Chi Square test

10. Chi square test
 If nature of data is discrete then the
hypothesis is mostly based of group
frequencies and proportions.
To test such hypothesis a popular test used
and named as chi square test.
Chi square test is applied in wide rage of
hypothesis tests and some of which are:

11. Different types of Chi square tests
Test of single population variance of normal
population
Test of homogeneity of independent
estimates of population variance
Test of homogeneity of independent
estimates of population correlation
coefficients
Test of Goodness of fit
Test of the independence of attributes

16. The Chi-Square Test
The chi-square test measures the discrepancy
between the observed cell counts and what we
expect if the two variables were unrelated.
If we are having count data on only one variable
under study then it is Goodness of fit test with
H0: Data fits the distribution assumed
If we are having count data on two variable under
study then it is Test of Independence.
H0: The two variables are independent

17. Chi-square test

18. Chi Square test examples

24. Chi square test Good of Fit
Day
SUN
MON
TUE
WED
THU
FRI
SAT
SUM
12/3/2022 6:00 AM 24
GPS, Banaras Hindu University
Deaths
(O)
20
14
13
14
13
15
16
105
Exp Death
by Ho (E)
15
15
15
15
15
15
15
105
(O-E)^2/E
1.67
0.07
0.27
0.07
0.27
0.00
0.07
2.24
Ho: Weekly Deaths are under Uniform law
P value for 6 df & 5%
level of significance
0.90
Chi Square
>0.05

25. CHI SQUARE – test of independence

41. Chi Square Test for Association
OR
Test of independence
12/3/2022 6:00 AM 41
GPS, Banaras Hindu University
To Study relation of smoking habit with
occurrence of Lung disease 120 smokers and
120 non smokers were included in study.
The data so obtained are

42. Chi Square Test for Association
12/3/2022 6:00 AM 42
GPS, Banaras Hindu University
Smoking Habit Lung disease
No Yes
Yes No
No No
No Yes
Yes No
No No
No Yes

43. Chi Square Test for Association
12/3/2022 6:00 AM 43
GPS, Banaras Hindu University
Smoking Total
Yes No
Disease
Yes
No
Total 120 120 240
Smoking Total
Yes No
Disease
Yes 35 35 70
No 85 85 170
Total 120 120 240
H0: No Association Between Lung Disease and Smoking in population OR
H0: Percentage of disease among smoker and non smoker is same.
45
(37.5%)
25
(20.8%)
75
(62.5%)
95
(79.2%)
70
170
Observed
Data
(Sample)
Expected
Data (H0)
Chi square value =8.07
P-value for Chi square value =8.07 with 2 df and 5% LS is 0.005 .
H0 rejected.