Autocorrelation and comparing means......

#1
Hi All,
I might be totally missing a key point here - or making a mountain out of a molehill, but I have been reading around and trying to find the answer to this question for a day or so now, so figured I might as well ask!
I have counts of birds per hour in a effort-based monitoring survey which took place each summer over a 4 year period. It looks like the average annual number of birds sighted per hour increased in the last year of the survey and all I am trying to do is show whether this 'increase' seems to be significant.
I have averaged all the hourly counts from each year to get a mean 'birds per hour' value for each year and then carried out an ANOVA, with year as the factor/grouping variable. The results show the there are differences between mean counts per year. Post-hocs indicate the last year of the survey is sig. diff. to the other 3 years. Ok - sounds fine........
My concern is that the data within each year group are autocorellated (I have tested this and found they are). BUT, I can't work out if this is a problem or not!
I know that IF the annual mean values were correlated (i.e. observations across groups are corellated), then this would definitely be a problem. But does it matter that the within year data is correlated? If it does matter, what is the solution??
I have investigated non-parametric tests for differences between means (Kruskal-Wallis for example). But it seems that these can get around issues of non-constant variance and non-normality, BUT can't deal with dependence.
I just can't work out if the within-year dependence in my data is an issue, or whether it doesn't matter because I am only comparing the mean values from each year with each other (and these are not corellated).
Thanks in advance for any help!
Ally
 

trinker

ggplot2orBust
#2
When I read your post two things jump out at me:

  1. Ecological Count Data
  2. Repeated Measures

The count data may best be handled using negative binomial or Poisson regression (possibly zero truncated as you may have a lot of zero counts). Second you should be worried about the autocorrelation. The ANOVA design you used won't take this into account. You will want to use some sort of model that handles repeated measures.

So the two key terms you'll want to use in your search are count data and repeated measures.