Question

Chi-square tests are nonparametric tests that examine nominal categories as opposed to numerical values. Consider a situation in which you may want to transform numerical scores into categories. Provide a specific example of a situation in which categories are more informative than the actual values.

Suppose we had conducted an ANOVA, with individuals grouped by political affiliation (Republican, Democrat, and Other), and we were interested in how satisfied they were with the current administration. Satisfaction was measured on a scale of 1-10, so it was measured on a continuous scale. Explain what changes would be required so that you could analyze the hypothesis using a chi-square test. For instance, rather than looking at test scores as a range from 0 to 100, you could change the variable to low, medium, or high. What advantages and disadvantages do you see in using this approach? Which is the better option for this hypothesis, the parametric approach or nonparametric approach? Why?"

Answer 1

(i)

Explanation of what changes would be required so that you could analyze the hypothesis using a chi-square test.

In ANOVA, we have two or more group means that we have to compare. In Chi Square test, we vave two categorical variables and want to determine whether one variable is related to the other variable. Thus for changing from ANOVA to chi square, rather than looking at test scores as a range from 0 to 100, we could change the variable to low, medium, or high, so that it become categorical, thus amenable for chi square test.

(ii)

(a) Advantages of Chi square test over ANOVA:

Chi square test is robust with respect to the distribution of the data due to its non-parametric characteristic.

(b) Disadvantages of Chi square test over ANOVA:

Chi square test does not give much information about the strength of the relationship.

Chi square test is sensitive to sample size.

Chi square test is sensitive to small expected frequencies in one or more cells in the Table.

(iii)

Non-parametric test is the better option for this hypothesis since data are not given as normally distributed and the non-parametric test which is distribution - free is applicable.