topic Re: ANOVA and proportions in Discussions

ANOVA and proportions

EEH — Fri, 09 Jun 2023 00:23:24 GMT

Experts:

I need some assistance with performing an ANOVA given a) unequal sample sizes and b) unequal proportions. Allow me to summarize the problem based on some sample/illustrative data:

Let’s say I have 3 groups (and # of reported incidents in that group):
- Group Alpha reported 150 incidents
- Group Bravo reported 30 incidents
- Group Charlie reported 50 incidents

So, while the Alpha group reported 3 times as many incidents than the Charlie group, the Alpha group is 12 times larger than the Charlie group. So, shouldn't the # of incidents be a function of # of people within the group?

In other words, proportionally speaking, the proportions are: 5%, 7.5%, and 20%, respectively . That is, ...
- Alpha has 3,000 people… so only 5.00% (150/3,000) out of the Alpha group report(ed) incidents
- Bravo has 400 people… so, 7.50% (30/400) out of the Bravo group report(ed) incidents
- Charlie has 250 people… so, 20.00% (50/250) out of the Charlie group report(ed) incidents

Given the proportions (e.g., Charlie group had 50 incidents *less* than the Alpha group), the Charlie group is essentially the “worst offender” given they only have a fraction of people in that group.

All that said, how would you take the proportions into consideration when performing the ANOVA? What are the steps in JMP prior (or after) executing the ANOVA?

Thank you,
EEH

Re: ANOVA and proportions

Mark_Bailey — Thu, 22 Oct 2020 16:55:19 GMT

The contingency table analysis accounts for the difference in the counts. Set up X column with the group and Y column with the incident, no incident values.

Re: ANOVA and proportions

EEH — Thu, 22 Oct 2020 17:58:22 GMT

Mark - thank you for the reply... I truly appreciate it.

Unfortunately, I'm not familiar with using the contingency tables (or concept thereof). How do I use it based on my having 3 numeric columns for Alpha, Bravo, Charlie w/ row values/observations = 150, 30, 50, respectively?

Any additional info would be greatly appreciated. :)

Cheers,
EEH

Re: ANOVA and proportions

P_Bartell — Thu, 22 Oct 2020 18:58:12 GMT

Per @Mark_Bailey 's advice, I suggest taking a look at the JMP online documentation for Contingency Table analysis within the Fit Y by X platform. There are examples for you to follow.

Contingency Tables in Fit Y by X Platform