Chi-Square
Chi square is defined as the square of the standard normal variable. There are certain chi square tests and they are discussed below in a detailed manner.
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A cross tabulation is also 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 to determine the strength of the 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. 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.
To determine the association or the correlation between the two variables that exist 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 to understand whether or not the sample that is collected from some population belongs to some specific distribution. This chi square test is basically applicable in cases where the discrete type of probability distributions is involved, like Poisson distribution, binomial distribution, etc. This chi square test is an alternative to the non parametric type of test, called the Kolmogorov Smirnov goodness of fit test.
The null hypothesis that the researcher assumes in this 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 the sum of the square of the deviation between the observed and the expected frequency that is divided by the expected frequency. An important point related to the validity of this type of chi square test is that the expected number of cell frequencies should be less than five.
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 in the chi square test is that the sampling of the data is collected by the process of random sampling from the population.
A sample size that is sufficiently large is assumed in the chi square test. The chi square test that is conducted on the sample of a smaller size results in the drawing of 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 a 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.