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 hypothesisparametric approach or nonparametric approach? Why?" Just need some kind of example because I do not understand this!!

Question

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 hypothesisparametric approach or nonparametric approach? Why?" Just need some kind of example because I do not understand this!!

Answer 1

To conduct a chi-square test instead of an ANOVA, some changes would need to be made in the way the data is organized and analyzed. Here is what is required:

1. Recategorize the satisfaction ratings: In ANOVA, satisfaction scores are measured on a continuous scale from 1-10. However, for a chi-square test, these scores need to be collapsed into categories. For example, you could group the scores into low (1-3), medium (4-7), and high (8-10) levels of satisfaction.

2. Create a frequency table: Once you have recategorized the satisfaction ratings, you need to create a frequency table that shows the number of individuals in each political affiliation group falling into each satisfaction category. For example:

Satisfaction Level | Republican | Democrat | Other
-----------------------------------------------------------------------
Low | 20 | 15 | 10
Medium | 25 | 30 | 20
High | 10 | 20 | 15

3. Perform a chi-square test: With the frequency table prepared, you can now use the chi-square test to assess the hypothesis. The test determines whether the observed distribution of satisfaction levels across political affiliation groups differs significantly from what would be expected if there was no association between the variables.

Advantages and disadvantages of using this approach:

Advantages:
- The chi-square test is more appropriate when working with categorical or nominal data.
- It is a nonparametric test, so it does not rely on any assumptions about the distribution of the data.

Disadvantages:
- By recategorizing the satisfaction ratings, some information may be lost, and the analysis becomes less precise.
- The chi-square test may be less powerful than an ANOVA, especially when there are more than two groups.

Which approach is better for this hypothesis?

In this case, the parametric approach (ANOVA) is generally more appropriate because satisfaction ratings were measured on a continuous scale. By using ANOVA, you can take advantage of the additional information provided by the numerical nature of the data. However, if the satisfaction ratings were initially measured on an ordinal scale (e.g., strongly disagree, disagree, neutral, agree, strongly agree), then the chi-square test might be more suitable. It is always important to choose the statistical test that aligns with the nature of the data and the research question at hand.