The various tests of significance such as t, F and Z are based on the assumption that samples are drawn from normally distributed population. These tests are known a parametric test because they require assumption about the population parameters. There may be situations in which it is not possible to make any rigid assumption about the distribution of the population from which samples are drawn. This has resulted the development of non-parametric tests. These tests are distribution free and do not make any assumptions about the population parameters. Chi-square test of independence and goodness of fit is a prominent example of the non-parametric tests. Here, we are limiting our discussion to Chi-square test.
The Chi square test is one of the simplest and most commonly used non-parametric tests in statistical work. The Greek Letter x2 is used to denote this test. The quantity x2 describes the magnitude of discrepancy theory and observation.
Determine the degrees of freedom in making comparison between calculated value of x2 and table value. Therefore, it is very important to understand what do we mean by degree of freedom. it means the number of classes to which values can be assigned arbitrarily or at will without violating the restriction placed.
The sampling distribution of the Chi-square statistic, X2 can be closely approximated by a continuous curve known as chi-square distribution. This distribution has only one parameter v, the number of degree of freedom. The probability function of Chi-square depends upon degrees of freedom v. As v changes, the probability function of Chi-square also changes. For very small numbers of degree of freedom, the Chi-square distribution is severally skewed to the right. As the number of degree of freedom increases, the curve, rapidly becomes more symmetrical until the number reaches large values, at this point this distribution can be approximated by the normal distribution.
The Chi-square test statistics can be used only it the following conditions are satisfied:
The Chi-square distribution has a number of applications. Most important applications are enumerated below: