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

Marc Schwartz m@rc_@chw@rtz @end|ng |rom me@com
Mon Aug 9 16:53:29 CEST 2021

```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*
> *Graduate Coordinator*
>
> *Department of Mathematics and Statistics*
> *University of Southern Maine*
>

```

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