Seminar on

Chi-SquarePresented by :-

Nirmal Singh

M.A,M.ED,M.LIB. SC,M.Phil, UGC NET

Dept. of Library & Information Science

Kurukshetra University, Kurukshetra

Chi-Square

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.

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

CHARACTERITICS OF χ2

• Chi-square never be negative.

• Larger the difference between observed and

expected value greater will be the value of the

χ2 .

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 the respective expected frequency and obtain the total ∑ [(O - E)2 / E]. This

gives the value of χ2 .

RT CTN

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)

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.

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.