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I have 2 sites with 15 trees on each site. I plan to treat all 15 trees in site 1 with a new pesticide and leave all 15 trees in site 2 untreated. The total number of bugs on each tree is measured before treatment and after treatment on both sites, even though the second site is untreated, we still measure the bugs at the same time we measure the post treated trees on site 1.

Limitation of this study is that randomly assigning trees to treatment is not possible.

I'm interested to know the effectiveness of the new pesticide. What model would be suitable to answer this research question?

Any help is appreciated!

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  • $\begingroup$ You cannot discriminate the effectiveness of the new pesticide from any effects due to other systematic differences between the two sites. Thus, you don't need a model: you need a better experimental design. $\endgroup$ – whuber Jun 18 '18 at 1:47
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To my knowledge there is no statistical model that corrects for that weakness in research design. The answer to your question is thus how to analyze the difference in bugs on each group of trees. This would be a simple T-test.

To strengthen the causal inference in your analysis, you could try to wait for some time and count the bugs again, then spray the pesticide on trees in group 2 also. Then count the bugs in each group again. This would change your statistical analysis to a repeated measures design. You could use an repeated measures ANOVA in this case.

I would advise you to read: Shadish, W., Cook, T., & Campbell, D. (2002). Experimental and quasi-experimental designs for generalized causal inference. Boston [etc.]: Houghton Mifflin.

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  • $\begingroup$ Thanks for your prompt response! I changed the setting to treat trees in site 2 as well. A "pre-test post-test" ignores the site effect. Would that make sense to use a regression model with response: # bugs on each tree & independent variables: 1) site (2 levels) & treatment (2 levels pre/post)? (I know you mentioned that the effect of site cannot be captured?? not sure if it's still the case). $\endgroup$ – soshelp Jun 18 '18 at 16:51
  • $\begingroup$ If you insist on using the design you proposed you could use a regression or an one way anova. I really encourage you to look at the book i mentioned before you set off to do your experiment. Your current design is pretty weak for the type of causal inference you try to achieve in your thesis. $\endgroup$ – SK4ndal Jun 19 '18 at 9:00

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