How to compare more than 2 percentages

[hianghao]

CONTENTS DELETED

The author has deleted this message.

[Rich Ulrich]

I think you need to study more about experimental design and testing,
because here are multiple problems.

1) If you had some samples you compared with mortalities of
2% vs 51% with "no significant diff" -- then your *power* was
apparently so small that you should not have bothered mentioning
the analysis. However, "2%"  implies an N of 50 or so.  Unless the
other group at 51% was tiny, you seem to have been doing a
ridiculous amount of "correcting for testing", or you screwed up
your testing.


2) If you bother to collect replications, you certainly should look
at them to see that they are equivalent.  Unless there is special
gain from the simplification, you could use the separate numbers
in an analysis.  You have an N of 6+12=18  as proportions or
logits, that might be entered into some sort of ANOVA... as one
simple way of constructing the problem.  Or, that seems to be
2*18= 36, if your second experiment with Predator was the same
design.


3) The total number of tests to correct for is not the same as the
total number of tests.  You correct for the "interesting hypotheses"
that exist as the purpose of the experiment.

It hardly seems to be an interesting hypothesis - certainly, it
is an hypothesis of a different kind - that the mortality is higher
with a predator versus without.  You want to confirm that this
is true, as a simple, rational validation of the basic condition for
considering the  *difference* in surviving.  So, you don't have
as many "main tests" as you are counting. 

The test on Predator is uninteresting, except as confirmation
that you have data to analyze further.

The test on Species is (probably) relatively uninteresting.
Whether they are the same or different seems dull, compared
to the questions about relative survivorship under different
conditions of Predator or Density. I think that the three
actual, interesting hypotheses are the interactions of species
with P, with D, and with PxD.

Hope this helps.

--
Rich Ulrich

> Date: Thu, 25 Oct 2012 20:21:40 -0700

> From: [hidden email]
> Subject: How to compare more than 2 percentages
> To: [hidden email]
>
> I have 2 strains of mosquito: A & B. I reared both of them under low density
> and high density conditions (3 reps for high density, 100 larvae per rep/
> strain; 6 reps for low density, 50 larvae/rep/strain), and recorded total
> percentage (not the percentage of each replicate) of them which reach
> adulthood. At first i assigned "1" for each larva survived and 0 for dead,
> then i conducted Mann Whitney test. Because i have 4 grps, I need to do 6
> comparison and there'll be familywise error. Correction (Bonferroni/Sidak)
> caused most of the analysis to accept null hypothesis, including another
> experiment where i calculate the mortality with and without predator for
> both strain A & B. FYI the mortality with predator was 51% and the one
> without was 2 %, yet it became no significant diff btwn the mortality.
>
>
> I also want to compare percentage mortality of 4 groups of treatment (strain
> A of insect with predator, strain A without predator; strain B with
> predator; strain B without predator). I found that percentage can be
> compared using 2x2 contingency table. but i have 4 groups instead of 2. Or i
> should conduct 6/4 chi square tests and divide the alpha with 6 or 4
> (because i don't want to compare A+predator vs B-predator & A-predator vs
> B+predator)?
>
> Something came into my thought: do i need to correct the mortality in
> predator grp with mortality without predator grp?? How? Abott's correction?
>
> ...

[Ian Martin-2]

It sounds to me as though Hianghao has not collected replicate data, but rather pooled the mortalities for the reps before calculating the percentages.  Viz:

> recorded total
> > percentage (not the percentage of each replicate) of them which reach
> adulthood.

This is unfortunate, if true.  What was the point of the replicates? Assuming it is indeed the case, the data reduce to a simple 2x2 frequency table.

regards,
Ian

Ian D. Martin, Ph.D.
Aquatic Ecologist


On Oct 26, 2012, at 12:38 AM, Rich Ulrich wrote:

> I think you need to study more about experimental design and testing,
> because here are multiple problems.
>
> 1) If you had some samples you compared with mortalities of
> 2% vs 51% with "no significant diff" -- then your *power* was
> apparently so small that you should not have bothered mentioning
> the analysis. However, "2%"  implies an N of 50 or so.  Unless the
> other group at 51% was tiny, you seem to have been doing a
> ridiculous amount of "correcting for testing", or you screwed up
> your testing.
>
>
> 2) If you bother to collect replications, you certainly should look
> at them to see that they are equivalent.  Unless there is special
> gain from the simplification, you could use the separate numbers
> in an analysis.  You have an N of 6+12=18  as proportions or
> logits, that might be entered into some sort of ANOVA... as one
> simple way of constructing the problem.  Or, that seems to be
> 2*18= 36, if your second experiment with Predator was the same
> design.
>
>
> 3) The total number of tests to correct for is not the same as the
> total number of tests.  You correct for the "interesting hypotheses"
> that exist as the purpose of the experiment.
>
> It hardly seems to be an interesting hypothesis - certainly, it
> is an hypothesis of a different kind - that the mortality is higher
> with a predator versus without.  You want to confirm that this
> is true, as a simple, rational validation of the basic condition for
> considering the  *difference* in surviving.  So, you don't have
> as many "main tests" as you are counting.
>
> The test on Predator is uninteresting, except as confirmation
> that you have data to analyze further.
>
> The test on Species is (probably) relatively uninteresting.
> Whether they are the same or different seems dull, compared
> to the questions about relative survivorship under different
> conditions of Predator or Density. I think that the three
> actual, interesting hypotheses are the interactions of species
> with P, with D, and with PxD.
>
> Hope this helps.
>
> --
> Rich Ulrich
>
>
> > Date: Thu, 25 Oct 2012 20:21:40 -0700
> > From: [hidden email]
> > Subject: How to compare more than 2 percentages
> > To: [hidden email]
> >
> > I have 2 strains of mosquito: A & B. I reared both of them under low density
> > and high density conditions (3 reps for high density, 100 larvae per rep/
> > strain; 6 reps for low density, 50 larvae/rep/strain), and recorded total
> > percentage (not the percentage of each replicate) of them which reach
> > adulthood. At first i assigned "1" for each larva survived and 0 for dead,
> > then i conducted Mann Whitney test. Because i have 4 grps, I need to do 6
> > comparison and there'll be familywise error. Correction (Bonferroni/Sidak)
> > caused most of the analysis to accept null hypothesis, including another
> > experiment where i calculate the mortality with and without predator for
> > both strain A & B. FYI the mortality with predator was 51% and the one
> > without was 2 %, yet it became no significant diff btwn the mortality.
> >
> >
> > I also want to compare percentage mortality of 4 groups of treatment (strain
> > A of insect with predator, strain A without predator; strain B with
> > predator; strain B without predator). I found that percentage can be
> > compared using 2x2 contingency table. but i have 4 groups instead of 2. Or i
> > should conduct 6/4 chi square tests and divide the alpha with 6 or 4
> > (because i don't want to compare A+predator vs B-predator & A-predator vs
> > B+predator)?
> >
> > Something came into my thought: do i need to correct the mortality in
> > predator grp with mortality without predator grp?? How? Abott's correction?
> >
> > ...

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[Valerie Villella]

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[Peter Løvgreen (101plg)]

Jeg er på ferie.
Jeg er tilbage torsdag d. 5. november 2012.
Med venlig hilsen Peter Løvgreen

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