Chi-Square

Chi square is defined as the square of the standard normal variable. There are certain chi square tests that will be detailed in this document.

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A cross tabulation is a kind of chi square test that is used by the researcher in order to test the statistical significance of the correlation that is observed in the study. The chi square test is used by the researcher for determining the strength of association in the objects under study.

The researcher should note that the greater the difference between the observed value of the cell frequency and the expected value of the cell frequency, the larger the value of the statistic of the chi square in the chi square test. This means that the difference of the observed value and the expected value in the chi square test is directly proportional to the value of the chi square statistic in the chi square test.

For determining the association or the correlation between the two variables that exists in the chi square test, the probability that is computed for obtaining the value of the chi square must be larger or greater, or must have a higher value than the one obtained, which is computed from the chi square test of cross tabulation.

Another popular chi square test is the goodness of fit test. This goodness of fit in the chi square test helps the researcher in understanding if the sample that is collected from some population belongs to some specific distribution. This chi square test is basically applicable in the cases where the discrete type of probability distributions are involved, such as in Poisson distribution, binomial distribution, etc. This chi square test is an alternative for the non parametric type of test, called the Kolmogorov Smirnov goodness of fit test.

The null hypothesis that the researcher assumes in the chi square test is that the drawn data from the population follows the distribution. The definition of the statistic used in the chi square test is the same, which is nothing but the sum of the square of the deviation between the observed and the expected frequency, which is divided by the expected frequency. An important aspect related to the validity of this type of chi square test is that the expected number of the cell frequencies should be less than five.

The researchers generally assume certain assumptions in the chi square test, and on the basis of those assumptions, only the chi square test is carried out.

The first assumption is that in the chi square test, the sampling of the data is collected by the process of random sampling from the population.

A sample size which is sufficiently large is assumed in the chi square test. The chi square test is conducted on the sample of smaller size results and draws an inaccurate inference about the data. If the researcher conducts the chi square test on a small sample size, then it may happen that the researcher might end up committing Type II error.

As in all other significant tests, it is assumed that in the chi square test, the observations are always independent of each other.

The last assumption that is made in the chi square test is that the observations in the sample must acquire the same fundamental distribution.