## Calculating p*(cumulative pdet on a site over all K surveys)

questions concerning analysis/theory using program PRESENCE

### Calculating p*(cumulative pdet on a site over all K surveys)

This is a pretty basic question but I just wanted to make sure I was calculating P* correctly (P*=(1- (single survey p)^K)). Am I correct in assuming that the single survey p is the Individual Site estimates of p from my model output? Looking at the Blue-lined salamander example it seems so.
Lea

Posts: 30
Joined: Thu Oct 24, 2013 1:09 pm

### Re: Calculating p*(cumulative pdet on a site over all K surv

That is correct for the model where the single-survey p does not change by survey (model p(.)). A more general formula is:

p* = 1 - product( 1-p(j)) {j=1,2,... K}

where p(j) is the detection probability for survey j.
jhines

Posts: 404
Joined: Fri May 16, 2003 9:24 am
Location: Laurel, MD, USA

### Re: Calculating p*(cumulative pdet on a site over all K surv

Thank you!
Lea

Posts: 30
Joined: Thu Oct 24, 2013 1:09 pm

### Re: Calculating p*(cumulative pdet on a site over all K surv

Hi Lea,
Note that your initial equation of:
P*=(1- (single survey p)^K)

isn't quite correct. It should be

P*=1- (1-p)^K

where p is the single-survey detection probability. Your P* would be the probability of not detecting the species in every survey (i.e., 1 minus the probability of detecting it in every survey), given presence.

Darryl
darryl

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Joined: Thu Jun 12, 2003 3:04 pm
Location: Dunedin, New Zealand