Identifying the type of hypothesis test this question is.

Question

A pharmaceutical company ran a study to compare three different formulations of a drug. One question of interest was whether the rate of side effects differed for the three formulations. Using $\alpha$=0.05, test for evidence that the three formulations differ in the rate of side effect. Be sure to write down the hypotheses and to write your conclusions in the context of the problem.

Formulations; Sample Size; # With Side Effects ;

A; 100 ; 6;

B ; 100 ; 12;

C ; 100 ; 18;

(I do apologise that this is not in a neat format, I am unsure how to do that.)

My issue is trying to identify which test to use for this question. We have recently been learning the Chi-Square tests, and have very briefly touched on F distribution. I believe this to be a Chi-Square test after reading it several more times, but I am very unsure and could use a push in the right direction to get my thoughts in order.

Edit 2: I have a new thought. Couldn't the Chi-Square test for Homogeneity work here?

Thanks

Edit 1: Since more information was requested I have expanded on the question to include its entirety above.

Answer 1

From what you say, this seems to be a one-factor ANOVA with three levels of the factor (corresponding to the three formulations). Assumptions are (1) that the measure of side effects is reasonably close to normal, (2) that the variability is about the same in each of the three groups, and (3) that the groups are independent (that is different subjects were randomized to each of the three formulations).

Tests other than standard ANOVA might be used in case assumptions (1) and (2) are unreasonable. Perhaps not, if assumption (3) is untrue.

The null hypothesis is $H_0: \mu_1 = \mu_2 = \mu_3.$ That is that the population mean level of side effects is the same for each formulation. The alternative is that all three means are not equal. So if $H_0$ is rejected, we would need to investigate the pattern of differences among $\mu_1, \mu_2$ and $\mu_3$ (e.g., $\mu_1 < \mu_2 < \mu_3$ or $\mu_1 = \mu_2 < \mu_3$ or some other pattern of differences).

If you have small amounts of data, and can post them in three separate rows, with observations separated by commas, then I can probably run the analysis and make comments on the results. Please edit this information into your question, so that others can see it, in case they are interested. Also please leave me a comment, so I will know to look at this again.

Addendum: Thanks for the data. I thought you had measures of severity of side reactions on each subject, instead of just a count of the number with side effects in each group. So ANOVA won't work. I like your idea of doing a chi-squared test of homogeneity. Here is output from Minitab, showing that the null hypothesis of homogeneity can be rejected at the 5% level: P-value about 3%.

Chi-Square Test for Association: C1, Formulation 

Rows: C1   Columns: Formulation

             A    B    C  All

SideEff      6   12   18   36
            12   12   12

None        94   88   82  264
            88   88   88

All        100  100  100  300

Cell Contents:      Count
                    Expected count


Pearson Chi-Square = 6.818, DF = 2, P-Value = 0.033
Likelihood Ratio Chi-Square = 7.098, DF = 2, P-Value = 0.029