I have a question about the dataset below which is for one of a number of variables in a study. The observations ("Total") are the averages of spatially distributed sample units collected in a single sample period. For example, there were 4 sample periods in the control area before the perturbation took place and the sample units (transects) in each period were averaged to get the sample unit means shown. Sampling was twice per year sampled but did not happen every year (some years were not sampled). In the data set they are arranged in chronolocial order.
I'm using the data in a before-after-control-impact analysis using ANOVA. A reviewer has said that because the data are sequences of observations in time, serial correlation should be evaluated to test the assumptions of independence and additivity. She compared the issue to a similar problem in the Stewart-Oaten type of analysis where you compare control-impact differences before and after (which I also want to try but that's another question).
I've looked at the Durbin-Watson statistic from linear regressions done as follows:
a. I used separate regressions for the control and impact since they are separate series of observations.
b. I used the value of "Total" as the dependent variable
c. I used a sequential number for the independent variable.
RESULT: The impact area passes the D-W test. Control does not.
MY QUESTIONS ARE:
1. Am I doing this correctly? Or should I be using the raw data (from sample units) instead of the sample period means for the regressions?
2. Is a sequential number the right thing to use for the independent variable? Should it be a series of numbers (1,2,3,4 . . .) or should it reflect gaps among years (1, 4, 5, 7, 13 . . .), or does it matter?
3. What to do when the D-W fails? Comments on practical considerations (can the violation be ignored?) would be appreciated in addition to recommendations for statistical solutions like transformations.
4. Does using nonparametric tests instead of ANOVA resolve the issue of the failure of the independence assumption?
5. How to test for additivity?
Thanks!
DATA:
Period Area Total
Before CONTROL 12.5
Before CONTROL 13.3
Before CONTROL 10.2
Before CONTROL 12.5
Before IMPACT 9.3
Before IMPACT 10.5
Before IMPACT 8.4
Before IMPACT 10.0
After CONTROL 8.8
After CONTROL 12.3
After CONTROL 11.2
After CONTROL 11.0
After CONTROL 10.6
After CONTROL 13.0
After CONTROL 10.6
After CONTROL 11.5
After IMPACT 4.3
After IMPACT 4.0
After IMPACT 2.0
After IMPACT 2.7
After IMPACT 1.3
After IMPACT 2.5
After IMPACT 1.2
After IMPACT 1.1
Last edited by suobs; 07-19-2010 at 08:36 AM.
Hi all, I notice there have been a lot of views of my question, but nobody has replied. Should I tighten up the question or shorten it?
The main question is about what to use as the independent variable in a regression being run only to get the Durbin-Watson statistic.
The other big question is what to do about serial correlation (autocorrelation) if it does exist.
Of course, I'm also wondering if you agree with the reviewer who said that serial correlation violates independence in the ANOVA.
To be quite honest a lot of times I skip over threads that have a really long initial first post. I just don't feel like mucking through a newer users really long post to see if I can understand the question they're trying to ask and then figuring out if I know how to answer the questions they're asking.
Sorry, I was just trying to provide the needed background and a visualization of the data.
I think I tightened up the question in my followup and anyone wondering could refer back to the first post for details...
Steve
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