t-test for means from VC estimation vs. CONTRAST

questions concerning analysis/theory using program MARK

t-test for means from VC estimation vs. CONTRAST

Postby constant survivor » Fri Nov 27, 2020 10:39 am

Hello,
every answer to one question, raises at least two new ones.

1.) Is it possible to do a unpaired, 2-tailed t-test on two Means that where calculated with the VC approach? I thought it may be possible to use the estimated mean (beta-hat), the SD (sigma, process variation only) and the sample size (number of estimates in VC output) to do that?

2.) If this is possible: What is actually the difference (except from the input data) compared to the approach with program CONTRAST? Because CONTRAST also tests the null hypotheses that the mean of two groups is different... Which method is preferred?

Thanks
Hannes
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Re: t-test for means from VC estimation vs. CONTRAST

Postby cooch » Fri Nov 27, 2020 11:38 am

You seem to be (overly) focussed on significance testing. A statistically significant test between 2 means (ignoring for the moment that the choice of a nominal alpha level is arbitrary and subjective) may or may not mean anything even remotely interesting biologically. One of the larger messages from Anderson & Burnham was the reminder that the more defensible focus should be on estimating and evaluating the 'effect size' -- the magnitude of difference, and whether or not said difference is bigger than some value that you (biologist) thinks is important. And that importance is determined by the biology of the organisms in question.

For simple linear models, you can consider effect size by looking at the estimates of the beta parameters (given the appropriately designed design matrix). This is covered in some detail in Chapter 6. For RE models, you can't easily get there from here using the MOM approach. You can, however, do this in a fairly straightforward way using the MCMC capabilities in MARK (Appendix E), which are in fact more flexible than the MOM approach (albeit slwer, with slightly more complications concerning model selection). A demonstration of this applied to a similiar problem is in the first Addendum to Chapter 14. There are other examples scattered throughout the book.
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Re: t-test for means from VC estimation vs. CONTRAST

Postby constant survivor » Fri Nov 27, 2020 12:01 pm

You seem to be (overly) focussed on significance testing. A statistically significant test between 2 means (ignoring for the moment that the choice of a nominal alpha level is arbitrary and subjective) may or may not mean anything even remotely interesting biologically. One of the larger messages from Anderson & Burnham was the reminder that the more defensible focus should be on estimnating and evaluating the 'effect size' -- the magnitude of difference, and whether or not said difference is bigger than some value that you (biologist) thinks is important. And that importance is determined by the biology of the organisms in question.


I totally agree and understand that. And it's not necessarily urgent for me to test for significance. I just want to tie together all the loose ends that keep hangin around in my head. I asked this question more in terms of understanding the connections/differences/suitabilities of both approaches.

For simple linear models, you can consider effect size by looking at the estimates of the beta parameters (given the appropriately designed design matrix). This is covered in some detail in Chapter 6. For RE models, you can't easily get there from here using the MOM approach. You can, however, do this in a fairly straightforward way using the MCMC capabilities in MARK (Appendix E), which are in fact more flexible than the MOM approach (albeit slwer, with slightly more complications concerning model selection). A demonstration of this applied to a similiar problem is in the first Addendum to Chapter 14. There are other examples scattered throughout the book.


Thanks for the tip. I will have to see if I can manage to get through it because time is running (MSc thesis). Will surely come back with questions...
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Re: t-test for means from VC estimation vs. CONTRAST

Postby constant survivor » Fri Nov 27, 2020 9:02 pm

For simple linear models, you can consider effect size by looking at the estimates of the beta parameters (given the appropriately designed design matrix). This is covered in some detail in Chapter 6.


As far as I understand, this means that, if I want to consider the effect size of the factor 'species', I'd have to put two (or more) species into a joint analysis and coding the species as 'groups' in the inp file, right?

Because up to now I treated every single species in it's own analysis for 'simply' calculating species survival (which in fact was all I wanted).
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Re: t-test for means from VC estimation vs. CONTRAST

Postby cooch » Sat Nov 28, 2020 9:02 am

My comment was 'for simple linear models', which you don't seem to have. If in fact you had a set of species,sampled on the same occasions, with the same sampling interval, then in theory, each species would be a group.

Failing that, you're doing post hoc means comparisons, which should be adjusted for the number of tests (paired comparisons) you do -- sequential Bonferroni is one option. Where you use a t-test or CONTRASST isn't really at issue (they'll likely yield equivalent 'results').
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Re: t-test for means from VC estimation vs. CONTRAST

Postby cooch » Sat Nov 28, 2020 8:22 pm

constant survivor wrote:As far as I understand, this means that, if I want to consider the effect size of the factor 'species', I'd have to put two (or more) species into a joint analysis and coding the species as 'groups' in the inp file, right?
.


This would also apply to the MCMC approach. You'd need to be able to generate the difference in means between the two groups (i.e., between the two species) as a derived parameter, and then calculate the credible interval for this derived parameter.
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Re: t-test for means from VC estimation vs. CONTRAST

Postby constant survivor » Mon Nov 30, 2020 6:06 am

Failing that, you're doing post hoc means comparisons, which should be adjusted for the number of tests (paired comparisons) you do -- sequential Bonferroni is one option.


Should the Bonferroni correction also be applied to test results from CONTRAST?

I dont think that I will manage to work through the MCMC thing so I have to stick to significance testing I guess.
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Re: t-test for means from VC estimation vs. CONTRAST

Postby cooch » Mon Nov 30, 2020 9:45 am

CONTRAST generates probabilities for a given comparison. Bonferroni adjust probabilities for number of total comparisons. Do some reading on your own...
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