Chi-Square

Jacob John PanickerMBA., SMS@CHMMC

The actual agenda of this presentation is to discus…

Phase-1 (Theory)◦X2

◦Characteristics of X2

◦Use (Application) of X2

Phase-2 (Problems)◦Equation◦Level of Significant◦Degree of Freedom◦Steps for the X2 test

Phase 1

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.

Characteristics of X2 test

It is a non-parametric test It’s a distribution free test It is easy to calculate X2 test

statistic

Uses (Application) of X2

test

Useful for the test of goodness of fit.Useful for the test of independence of

attributesUseful for testing homogeneityUseful for testing given population

variance

Phase 2

Equation

‘O’ Observed value

‘E’ Expected value

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.

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.

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.

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

Thanks…