# [R] Sample size Determination to Compare Three Independent Proportions

AbouEl-Makarim Aboueissa @boue|m@k@r|m1962 @end|ng |rom gm@||@com
Tue Aug 10 12:34:06 CEST 2021

Hi Marc:

First, thank you very much for your help in this matter.

Will perform an initial omnibus test of all three groups (e.g. 3 x 2
chi-square), possibly followed by
all possible 2 x 2 pairwise comparisons (e.g. 1 versus 2, 1 versus 3,
2 versus 3),

We can assume *either* the desired sample size in each group is the same
*or* proportional to the population size.

We can set p=0.25 and set p1=p2=p3=p so that the H0 is true.

We can assume that the expected proportion of "Yes" values in each group is
0.25

For the alternative hypotheses, for example,  we can set  p1 = .25, p2=.25,
p3=.35

Again thank you very much in advance.

abou

______________________

*AbouEl-Makarim Aboueissa, PhD*

*Professor, Statistics and Data Science*

*Department of Mathematics and Statistics*
*University of Southern Maine*

On Mon, Aug 9, 2021 at 10:53 AM Marc Schwartz <marc_schwartz using me.com> wrote:

> Hi,
>
> You are going to need to provide more information than what you have
> below and I may be mis-interpreting what you have provided.
>
> Presuming you are designing a prospective, three-group, randomized
> allocation study, there is typically an a priori specification of the
> ratios of the sample sizes for each group such as 1:1:1, indicating that
> the desired sample size in each group is the same.
>
> You would also need to specify the expected proportions of "Yes" values
> in each group.
>
> Further, you need to specify how you are going to compare the
> proportions in each group. Are you going to perform an initial omnibus
> test of all three groups (e.g. 3 x 2 chi-square), possibly followed by
> all possible 2 x 2 pairwise comparisons (e.g. 1 versus 2, 1 versus 3, 2
> versus 3), or are you just going to compare 2 versus 1, and 3 versus 1,
> where 1 is a control group?
>
> Depending upon your testing plan, you may also need to account for p
> value adjustments for multiple comparisons, in which case, you also need
> to specify what adjustment method you plan to use, to know what the
> target alpha level will be.
>
> On the other hand, if you already have the data collected, thus have
> fixed sample sizes available per your wording below, simply go ahead and
> perform your planned analyses, as the notion of "power" is largely an a
> priori consideration, which reflects the probability of finding a
> "statistically significant" result at a given alpha level, given that
> your a priori assumptions are valid.
>
> Regards,
>
> Marc Schwartz
>
>
> AbouEl-Makarim Aboueissa wrote on 8/9/21 9:41 AM:
> > Dear All: good morning
> >
> > *Re:* Sample Size Determination to Compare Three Independent Proportions
> >
> > *Situation:*
> >
> > Three Binary variables (Yes, No)
> >
> > Three independent populations with fixed sizes (*say:* N1 = 1500, N2 =
> 900,
> > N3 = 1350).
> >
> > Power = 0.80
> >
> > How to choose the sample sizes to compare the three proportions of “Yes”
> > among the three variables.
> >
> > If you know a reference to this topic, it will be very helpful too.
> >
> > with many thanks in advance
> >
> > abou
> > ______________________
> >
> >
> > *AbouEl-Makarim Aboueissa, PhD*
> >
> > *Professor, Statistics and Data Science*