Chi-square is a non-parametric test used to find out whether two nominal variables are independent or dependent on each other. Chi-square test can be used in two ways: first, as a test of goodness of fit; and two, as a test of independence.
The Chi-square Test of Goodness of Fit
It is used to determine how well the assumed theoretical distributions fit with the observed data. The assumed theoretical distributions could be Binomial, Poisson, and Normal distributions. In case the calculated value of Chi-square is less than the table value at a particular level of significance, it is regarded as a good fit. This implies that the difference between the observed and expected frequencies can be attributed to fluctuations in sampling. If the calculated value of Chi-square is greater than its table value the fit is considered to be a bad one.
The Chi-square Test for Independence
It is used to compare the frequency of cases of various categories in one variable across different categories of another variable. For instance, is the proportion of gym goers to non-gym goers the same for men and women? The question can also be expressed as: Are men more likely to be gym goers than women? The Chi-square test can also be used to find out whether two variables are associated or not. For example, we may be interested to know whether there is a relationship between gender and the cause of road accidents over a certain period of time. Chi-square test will help us to make a determination on this particular issue. Our null hypothesis will be stated as: gender and the cause of road accidents are independent (which means that gender does not cause road accidents).
The Chi-square Test for Independence is used to find out the relationship between two categorical variables. These variables may have at least two categories. The two categorical variables result in what is referred to as a 2 by 2 table. When the 2 by 2 table is analyzed through SPSS (Statistical Package for Social Scientists), the Chi-square output includes an additional correction value (Yates’ Correction for Continuity). This is meant to correct what is felt to be an overestimate of the Chi-square value when used with a 2 by 2 table.
Assumptions of Chi-square
• The lowest expected frequency in a cell should be 10 or more. Some authors also suggest that at least 80% of the cells should have expected frequencies of 5 or more. For a 1 by 2 or 2 by 2 tables, it is recommended that the expected frequency be at least 10. If your 2 by 2 table violates this assumption, then you should use Fisher’s Exact Probability Test
• Independent observations: each case should be counted only once, and the data from one subject cannot influence the data from another.
• The total number of items must be reasonable, at least 50
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