Nirmal Singh presented a seminar on the Chi-Square test. The Chi-Square test is a non-parametric statistical test used to compare observed data with data we expect to obtain according to a specific hypothesis. It can be used with different types of measurements and does not require assumptions about the distribution of the attributes. The value of Chi-Square is calculated by summing the squares of the differences between observed and expected frequencies, divided by the expected frequencies. The degree of freedom, which is needed to compare the calculated Chi-Square value to table values, is determined by the number of rows and columns in the data less one. The Chi-Square test has become widely used for analyzing non-parametric data in statistical

1. Seminar
on
Chi-Square
Presented by :-
Nirmal Singh
M.A,M.ED,M.LIB. SC,M.Phil, UGC NET
Dept. of Library & Information Science
Kurukshetra University, Kurukshetra

2. Chi-Square

3. INRODUCTION
Chi-square is a non-parametric. Non-
parametric theory developed as early as the
middle of the nineteenth century, it was only
after 1945 that non-parametric test came to be
used widely. The following three reasons for
the increasing use of non-parametric test.
• Distribution Free.
• Easy to Handle and Understand.
• It can be used with type of measurements.

4. χ2 DEFINED
The χ2
is one of the simplest and most widely
used non-parametric test in statistical work. The
symbol χ2
is the Greek letter Chi. The χ2
test was first
used by Karl Pearson in the year 1900. The quantity
describes the magnitude of the discrepancy between
theory and observation. It is defined as:-
χ2
= ∑
(O – E)2
E

5. CHARACTERITICS OF χ2
•Chi-square neverbenegative.
•Larger the difference between observed and expected value greater will be the
valueofthe
χ2
.

6. CALCULATION OF χ2
To determine the value of χ2 the steps required are:
• Calculate the expected frequency
E =
• Take the difference between observed and expected
frequencies and obtain the squares of these
differences: i.e.(O - E)2
• Divide the value of (O - E)2
by therespective expected
frequency and obtain the total ∑ [(O - E)2
/ E]. This
gives the value of χ2
.
RT CT
N

7. DEGREE OF FREEDOM
While comparing the calculated value
of chi-square with the table value we have
to determine the degree of freedom .
Degree of Freedom =(c – 1)(r – 1)

8. LIMITTION ON THE USE
OF CHI-SQURE TEST
• Frequencies of non-occurrence should not
be omitted for binominal or multinomial
events.
• The formula presented for Chi-square is in
term of frequencies. Hence an attempt
should not be made to compute on the
basis of proportions or other derived
measures.

9. CONCLUSION
In short we can say that Chi-
square has a significance importance in
analysis of the non parametric data. Now
a days it is widely used in the statistical
research.

10. CONCLUSION
In short we can say that Chi-
square has a significance importance in
analysis of the non parametric data. Now
a days it is widely used in the statistical
research.