Conceptual model on application of chi-square test in education and social sciences

Whenever you think you have an idea of how something works, you have a mental model. That is, in effect, a layman's way of talking about having an hypothesis. The hypothesis needs to be tested for how closely it fits reality - and reality is the data collected from an experiment. So the data is collected on the few and compared with a few controls. Is there really a difference between the two groups? It is that sort of question where Chi-square analysis comes in. In short, if the differences between your model and reality are small, that is good; if huge, develop a new model! These differences are denoted as chi-square, which equals the sum of all the squares of the deviations divided by what was expected. A Chi-square test is one of the most frequently used tests with a number of improper applications. Some of the general causes of the improper applications include researchers not understanding the areas and conditions of application of the Chi-square test. To give solutions to the above problems, this paper explored the existing literature on the main areas of application of Chi-square, that include the test of frequencies (goodness of fit, homogeneity, independence) and the test of population variance. The paper identifies the shortfalls in the existing literature, and fills them by the application of appropriate illustrations and examples. To shield the loopholes in data analysis using Chi-square test, a simplified conceptual model which can be adopted by researchers is finally developed.   Key words: Hypothesis, observed frequency and expected frequency.