1. Chi-Square
Jacob John Panicker
MBA., SMS@CHMMC

2. The actual agenda of this presentation is to discus…
Phase-1 (Theory)
◦ X2
◦ Characteristics of X2
◦ Use (Application) of X2
Phase-2 (Problems)
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Equation
Level of Significant
Degree of Freedom
Steps for the X2 test

3. Phase 1

4. Chi-Square-X2
 The
statistical test in which the test statistic
follows a X2 –distribution, is called the X2 test.
 X2 test
is one of the simplest and most and most
widely used non-parametric tests in statistical
work.

5. Characteristics of X2 test



It is a non-parametric test
It’s a distribution free test
It is easy to calculate X2 test statistic

6. Uses (Application) of X2 test
Useful for the test of goodness of fit.
 Useful for the test of independence of attributes
 Useful for testing homogeneity
 Useful for testing given population variance


7. Phase 2

8. Equation
‘O’ Observed
value
 ‘E’ Expected value


9. Level of Significance
Confidence with which a null hypothesis is
accepted or rejected depends on what is called
significant level. The probability with which we
may reject a null hypothesis, is called the level
of significance.

10. Degree of freedom
◦ Degree of freedom is defined as the number of
independent observations which is obtained by
subtracting the number of constrains from the total
number of observations.

11. Steps for the X2 test.
H0 and H1 between observed & expected
frequencies.
 Compute the test statistics,
Observed frequencies are available in a given
problem. But expected frequencies are to be
computed.
 Degree of freedom: where than one attribute
D.F=(r-1)(c-1) where ‘r’ is the number of
independent constraints to be satisfied by the
frequencies.


12. Contineued….
Obtain the table value of X2 for the degree of
freedom & for the desired level of significance
 If the calculated value of X2 is less than the
table value we conclude that there is goodness
of fit

Source: Quantitative Methods- L. R. Potti

13. Thanks…