Confusion about Two Way ANOVA test vs Chi-square test for independence. Which one to use here?

Question

A certain drug is claimed to be effective in curing cold. In an experiment on 500 persons suffering from cold, half of them were given the drug and the other half were given the sugar pills. Patients' reactions to the treatment are recorded in the following table (pls refer attached image). On the basis of the table data, can it be concluded that there is a significant difference in the effect of drug and sugar pills ?

My Doubts -

I have learnt that -

(i)Use 2 way ANOVA when to test difference of mean between two categorical variables

(ii)Use Chi-square test of independence when want to know if there is any relation between two categorical variables.

[Doubt 1 ]Have I leant this correctly ?

[Doubt 2 ] To solve the main question on top which one to use - (i) or (ii) ?

More here on chi sq: https://stats.stackexchange.com/questions/91970/chi-square-test-difference-between-goodness-of-fit-test-and-test-of-independenc — Estimate the estimators, Oct 05 '23 at 16:09
ANOVA is for means. Chi square is for counts. You could consider a Homogeneity test here. — Estimate the estimators, Oct 05 '23 at 16:11

score 3 · Answer 1 · answered Oct 05 '23 at 16:18

ANOVA, in general, is for a dependent variable that is continuous (or a reasonable facsimile. Your DV is categorical (helped/harmed). So, not ANOVA. A two way ANOVA is when there are two INDEPENDENT variables. You have only one (treatment).

So, of the two choices, you should pick chi-square.

However, in the real world, I would do a logistic regression and add covariates. It is rarely ideal to analyze health care data without covariates (even in a randomized trial).

Confusion about Two Way ANOVA test vs Chi-square test for independence. Which one to use here?

1 Answers1