Chi-Square Goodness of Fit Test (Essay Sample)

Chi-Square Goodness of Fit Test
Student’s Name
Institutional Affiliation
Chi-Square Goodness of Fit Test
In hypothesis testing, one may come across data that requires the use of the non-parametric methods. In such a case, the chi-square test has proved to be a powerful tool. An example of a x2 test is the chi-square goodness of fit test whose synonym is x2 test for independence or Pearson’s x2 test. The test aids in determining whether there exists a significant difference between the observed frequencies (O) and the expected frequencies (E) of one or more categories of data. Specifically, the test uses a two-way table to determine the strength of association between two variables; hence, the closeness to the assumed model. Formally, one writes the test as x2=‑(O-E)2E. The x2 goodness of fit directs the writer to use numerical values and not ratios or percentages. Statistically, the expected value in each category should be at least five, and if it is not, one should add value in the subsequent category to achieve this. The test assumes that data is categorical, discrete, equally likely outcomes and mutually exclusive events. Apparently, the hypothesis testing shows that if the test statistic is large enough, the researcher should reject the null hypothesis. The hypotheses are:
H0: Data follows a particular distribution.
H1 : The data does not follow the assumed distribution.
The x2 goodness of fit and the independent t-tests are similar because they use categorical data and strive to determine if there exists a significant difference. Contrarily, the independent t-test seeks to assess if the means of two unrelated groups statistically differ while the x2 goodness of fit evaluates if the difference is real or stems from the sampling errors. For example, in determining if students’ population follows a normal distr...