Discussion Solution — N and CO2 effects on pine seedling growth

General approach These data are best analyzed by multiple regression, which can address all three hypotheses in one analysis. The first two hypotheses assert positive effects of the two independent variables separately, while the third hypotheses posits a positive (“reinforcement”) interaction between them; testing the latter therefore requires a multivariable analysis. The first two hypotheses could be addressed by separate simple linear regressions using only the relevant independent variable. This would require, though, that only data for one level of the other variable be used in each analysis. If the other variable were simply ignored, this would inflate the ‘error’ term, and more important, would violate the assumption of independence (the observations at a given level of the variable being analyzed would be three distinct groups rather than nine random replicates). For the hypothesis about CO2 it actually would make sense to use only the data for 0 N, since the focal question is whether there is a CO2 effect even when the trees are nitrogen limited. Since multiple regression using all the data is the best approach for the other hypotheses, though, I would prefer to address the CO2 hypothesis as part of this same analysis. Because only a few levels of each independent variable were used, with replication, ANOVA could be used instead of regression. This approach, though, would not use the quantitative information about the experimental treatments, and would test more diffuse alternative hypotheses, and therefore would be less powerful and informative than regression.