## Test statistic for weighted average estimates

questions concerning analysis/theory using program MARK

### Test statistic for weighted average estimates

Hello everyone,

I have 29 year-to-year estimates (model averaged) of phi for 7 species in total.
What test statistics could I use to look for statistical differences in survival? Because I guess a simple t-test or anything is not possible. Anyway, I guess there are no differences (because of sparse data) but of course it would be nice to "proof" this in a adequate way.

Up to now I am restricted to compare the confidence intervals for each estimate and searched for non-overlapping pairs. So that I at least can tell for a certain year, that there is (or is not) a statistical difference between species.

But I guess you might know of some better way or at least give me a hint for literature (maybe even a chapter in the book?)

Thank you very much
Hannes
constant survivor

Posts: 31
Joined: Wed Dec 11, 2019 12:20 pm

### Re: Test statistic for weighted average estimates

Program CONTRAST, available at http://www.mbr-pwrc.usgs.gov/software/constrast.shtml can be used to compare groups of estimates. It will allow you to test different hypotheses (eg., H0: all estimates come from similar distribution vs H1: at least one estimate is different) .
jhines

Posts: 507
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

### Re: Test statistic for weighted average estimates

wow. never thought it could be that easy.
thank you!
constant survivor

Posts: 31
Joined: Wed Dec 11, 2019 12:20 pm

### Re: Test statistic for weighted average estimates

An alternative in the model selection ground would be comparing the AIC of models with a different structure relative to the "effect" of the species on the apparent survival. By the way this is not a test statistic but is another perspective to evaluate your question. You can compare the AIC of two models with different and equal survival. Also, if you have some biological reason to think that survival within some species is similar, you can build the corresponding models and "test" this hypothesis using the CONTRAST program or the model selection strategy.
simone77

Posts: 176
Joined: Mon Aug 10, 2009 2:52 pm

### Re: Test statistic for weighted average estimates

Hi,
I got one further question concerning CONTRAST.

I got significant results for a test of weighted average estimates of Species x vs. Species y. Say, two groups, right?
On the web page it says:
"Contrast then tests the null hypothesis that the average survival for each group is the same"

What irritates me, is that when I tried to calculate the mean survival for the same two species with the Method of Moments approach (VC estimation and so on... ; see other thread) I had strong difficulties to estimate a mean because of obviously sparse data. My aim of this surely was, to compare those means.

In terms of interpretation this brings me into the situation that I am on the one hand must admit, that calculation of mean survival for Species x and/or Species y is not possible because of sparse data (MOM approach).
On the other hand I am telling that there is a significant difference between the average survival of both species (CONTRAST).

I am aware about, that CONTRAST only compares the weighted average estimates I am feeding into it and that the MOM approach is based on the 'raw data' which surely is some different thing.

But how much certainty can this give me about real survival differences of both species? When the MOM approach is hardly even feasible and the result of CONTRAST is highly significant...
Is it just as simple as that one could say: it is not possible to calculate the 'true' mean so I made a compromise and compared the weighted average estimates?

Any thoughts on that are highly appreciated.
Thanks
Hannes
constant survivor

Posts: 31
Joined: Wed Dec 11, 2019 12:20 pm