This test (as a non-parametric test) is based on frequencies and not on the parameters like mean and standard deviation. The test is used for testing the hypothesis and is not useful for estimation. This test possesses the additive property as has already been explained.

1. CHI SQUARE TEST AND ITS TYPES

2. INTRODUCTION
• Chi square test, also called Pearson’s chi
square test.
• First investigated by KARL PEARSON in
1990

3. APPLICATION OF CHI SQUARE TEST
• Goodness of fit- whether an observed frequency
distribution differs from a theoretical distribution.
• Homogeneity- compares the distribution of
counts for two or more groups using the same
categorical variable
• Independence (most commonly used)- assesses
whether unpaired observation on two variables are
independent of each other

4. IMPORTANT CHARACTERISTIC OF A
CHI SQUARE TEST
• This test (as a non-parametric test) is based on frequencies and not on the parameters like
mean and standard deviation.
• The test is used for testing the hypothesis and is not useful for estimation.
• This test possesses the additive property as has already been explained.
• This test can also be applied to a complex contingency table with several classes and as
such is a very useful test in research work.
• This test is an important non-parametric test as no rigid assumptions are necessary in
regard to the type of population, no need of parameter values and relatively less
mathematical details are involved

5. APPLICATIONS OF CHI SQUARE
TESTING
This test can be used in
• Goodness of Fit of distribution
• Test of independence of attributes
• Test of homogeneity

6. GOODNESS OF FIT OF DISTRIBUTION
This test enables us to see how well does the assumed theorotical distribution (such as
binomial distribution Poisson distribution or normal distribution)fit to the observed data
The formula for the chi-square statistic used in the chi square test is:
Where
O=observed frequency
E=expected frequency

7. GOODNESS OF FIT OF DISTRIBUTION
If x2 (calculated)>(tabulated),with (n-1) 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.

8. TEST OF INDEPENDENCE OF ATTRIBUTES
 Test enables us to explain whether or not two attributes are
associated
 for instance we may be interested in knowing whether a new
medicine is effective controlling fever or not, x2 is useful.
 in such a situation we proceed with the null hypothesis that the two
attributes (medicine and control of fever) are independent which
means medicine is not effective.

9. TEST OF INDEPENDENCE OF ATTRIBUTES
X2 (calculated)> x2 (tabulated) at a certain level of significance for given
degrees of freedom, the null hypothesis is rejected, two variables are
dependent (the new medicine is effective in controlling the fever)And if , x2
(calculated)<x2 (tabulated) the null hypothesis is accepted 2 variables are
independent (so the new medicine is not effective in controlling the fever)

10. TEST OF HOMOGENITY
This test can also be used to test whether the occurrence of events follow
uniformity or not e.g. the admission of patients in government hospital in all
days of week is uniform or not can be tested with the help of chi square test.

11. WE COLLECT DATA BY FLIPPING THE COIN 200
TIMES.
THE COIN LANDED HEADS-UP 108 TIMES AND
TAILS-UP 92 TIMES. AT FIRST GLANCE, WE
MIGHT SUSPECT THAT THE COIN IS BIASED
BECAUSE HEADS RESULTED MORE OFTEN
THAN THAN TAILS.

13. Heads Tails Total
Observed 108 92 200
Expected 100 100 200
Total 208 192 400

14. df/pro
b.
0.99 0.95 0.90 0.80 0.70 0.50 0.30 0.20 0.10 0.05
1
0.0001
3
0.0039 0.016 0.64 0.15 0.46 1.07 1.64 2.71 3.84
2 0.02 0.10 0.21 0.45 0.71 1.39 2.41 3.22 4.60 5.99
3 0.12 0.35 0.58 1.00 1.42 2.37 3.66 4.64 6.25 7.82
4 0.3 0.71 1.06 1.65 2.20 3.36 4.88 5.99 7.78 9.49
5 0.55 1.14 1.61 2.34 3.00 4.35 6.06 7.29 9.24 11.07