R help - Aug 2021 - Sample size Determination to Compare Three Independent Proportions

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*
>

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*
*Graduate Coordinator*

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



On Mon, Aug 9, 2021 at 10:53 AM Marc Schwartz <marc_schwartz at 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*
> > *Graduate Coordinator*
> >
> > *Department of Mathematics and Statistics*
> > *University of Southern Maine*
> >
>
>
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