Pairwise Comparison Study Stats

[Jazzey]

Hi,

I'm looking to carry out a study which will involve a pairwise choice comparison. I am aiming to identify any patterns of preference by wild individuals (measured by abundance) when presented with four different types of refuge. I will be conducting it in the form of pairwise choice comparisons, e.g.

R1 vs R2
R1 vs R3
R1 vs R4
R2 vs R3
R2 vs R4
R3 vs R4

There will be four replicates of each of the six pairs, (i.e. R1 vs R2 x 4, etc.), and I will survey each pair and their replicates 19 times over a set period.

So, hoping this makes sense, can anyone help me with getting my head round the appropriate statistical test to use to analyse this data? If anyone can go one further and also tell me if my current methodology has a sufficient sample size for the suggested test, that would be amazing. I'm concerned that the subsequent sampling (18 re-visits) is pseudoreplication....

 

[obh]

Hi Jazzey,

"Pairwise comparison" deal of comparison of the averages of several groups
Are you comparing the averages of the groups?

If the answer is yes, you may run:
You may start or not with the One way ANOVA.
Then you have two options:
1. Tukey HSD/Tukey Cramer
2. Pairwise t-test with a significance level correction (Bonferroni/Sidak/Holm)

 

[Jazzey]

Hi obh,

Thanks for the speedy reply.

Yes, I was hoping to do an ANOVA, with it being the most powerful and seemingly appropriate test, but I was unsure whether it actually was appropriate with my methodology.

Using the mean abundance of the four replicates for each group seems right to me, but would it be right to take the sum of each group and their replicates, and then take the mean?

To add a bit more detail, it will be the abundance of a specific species using the refugia, which is why I'm worried about pseudoreplication if I end up sampling the same individuals. I should be able to identify between individuals, so would it be right to exclude previously counted individuals if they 'choose' the same refuge? Or does their presence within that group indicate another independent 'choice'?

Furthermore, power analysis for a One-Way ANOVA with four groups suggests I need a sample size of 45. Would this mean I need 45 replicates as opposed to my 4? Or do my re-visits contribute to this number?

Thanks for your help already.

 

[obh]

I don't think I understand the study.
So you treat any combination like R1 vs R2 as one group?
Can you please explain more what is R1? what is R2 and what is R1 vs R2?
Can you please add example data?

 

[Jazzey]

"So you treat any combination like R1 vs R2 as one group?" - This is what I am unsure about. It is a comparison of two refuge types placed next to each other to see if a choice is made by the reptile as to which refuge type to utilise, so I'm unsure if the two refuges placed next to each other is one group, or two groups.

So I just realised I was wrong with saying I have 4 replicates of each refuge type (if they are counted as distinct groups), as I would then actually have 12 replicates of each group (as I have 4 replicates of each pairing).

"Can you please explain more what is R1? what is R2 and what is R1 vs R2?" - I will be using four refuge types, and I am simplifying them by numbers. R1 will be felt, R2 will be tin, R3 will be insulated tin, R4 will be insulted felt. So a felt refuge will be placed next to a tin refuge (i.e. R1 vs R2) and at another location felt will be placed next to insulated felt (R1 vs R4), and so on for the other pairings.

"Can you please add example data?" - Please see below. The shaded columns indicate pairings, whilst the red and black i-iv's represent the four replicates of each pairing, whilst the "Sampling Day" row numbers indicate the repeat observations (over time, e.g. once a day).

I hope this is clear - I'm asking for help in statistical analysis of the data because it confuses me - and it's my study, hah.

Thanks again.

 

[obh]

Hi Jazzey,

Sorry for the late response, but I still not sure I understand...
Is the following table describe the experiment?

R1, R2, R3, Y
1, 1, 0, R1
1, 1, 0, R2
0, 1, 1, R3

row1: let the reptile choose between R1 and R2 and it chose R1
row2: let the reptile choose between R1 and R2 and it chose R2
row3: let the reptile choose between R2 and R3 and it chose R3

If the answer is yes you may check if your experiment meets the assumptions of multinomial logistic regression ??
The answer may be the probability to choose Ri when letting the reptile choose between Ri and Rj.
You may also consider just calculate separately the probability to choose Ri in any pair of Ri and Rj

 

[obh]

On second thought, since you give the reptile option to choose only between 2 Ri
Say you don't let it choose between R1 R3 and R4, and you don't have other predictors.
Probably a simple probability between Ri and Rj will be better...