In this paper we will describe and discuss how Chi-square test is applied to the problems of statistics and probability theory. Pearson's Chi-square test is the simplest test of the significance of the relationship between two categorical variables. One variable is considered as dependent variable and another one as independent variable (Ats.ucla.edu). Pearson criterion is based on the null hypothesis that "there is no dependence between the variables". The alternative hypothesis for this test is that “there is a significant relationship between the factors”. This test is based on the assumption that the expected frequencies can be calculated directly. The value of Chi-squared statistic and its significance level depend on the total number of observations and the number of cells in the table. Relatively small differences between observed frequencies and expected frequencies prove the high level of significance, if the number of observations is quite large.
Unlike t-tests and other parametric tests, Pearson’s Chi-square test is a non-parametric test and it does not require the assumption of normality. There is only one significant limitation of using the Chi-square test (aside from the obvious assumption that the observations should be collected at random): expected frequencies should not be very small. This is due to the fact that the Chi-square test inherently checks probabilities in each cell; and if the expected cell frequencies becomes very small (e.g., less than 5), then the probability cannot be estimated with sufficient accuracy using the available frequencies (Deshpande).
Consider a fictitious example problem that may be solved by using Chi-square test. Imagine that 20 men and 20 women interviewed on their smoking status (smoker or nonsmoker). If there is no association between smoking status and gender, it is natural to expect an equal number of smokers and nonsmokers for each gender.
Works Cited
Ats.ucla.edu,. "Choosing The Correct Statistical Test In SAS, Stata And SPSS". N.p., 2016. Web. 25 Jan. 2016.
Deshpande, Bala. "2 Key Assumptions To Be Aware Of Before Applying The Chi-Square Test". Simafore.com. N.p., 2016. Web. 25 Jan. 2016.
