I measure a continuous variable prior and after treatment allocation in a 3x4 factorial experimental design . The pre-treatment measurements are all unaffected by the treatment. There is no counter-balancing.
As far as I know, generally there are several way to approach this kind of data. For example, paired t-test or Wilcoxon signed-rank test, repeated measures ANOVA, ANCOVA, mixed models (random or fixed effects), and change scores as dependent variable. Some of these are answering slightly different research questions but are generally suited to the data at hand.
My general interest is in differences in changes from pre- to post-treatment measurements between the different factor combinations (factor interactions).
In general, can anyone recommend a source where to read up on these approaches relative to each other, in order to assess the merits of them?
More specifically, I wonder about how, e.g. coding the pre- and post-treatment variables as change scores, and using these change scores as a dependent variable in e.g. an OLS regression with the treatment interaction term as independent variables, performs relative to testing the treatment interaction in a repeated-measures ANOVA (or random/fixed effects model). Is using change scores like this somehow inferior to the repeated-measures approach (possibly due to a loss of information due to reducing two variables to one)?
I usually prefer Post score regressed on Pre score rather than a change score - with the latter a change of 10 from a base of 0 is very different from a change of 10 from a base of a 1000
Gelman and Hill explain this in more detail: .
Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. www.stat.columbia.edu/~gelman/arm/
In preference I would explicitly model the change choosing the value for the later visit as the response and the values for the earlier visit as a predictor and then including other predictors - including any treatments and covariates (usually from the first visit and any time invariant ones). By setting up the model in this way you are conditioning on the previous starting values and explicitly modeling change.
Taken from
What are the statistics for a cross sectional study? - ResearchGate. Available from: https://www.researchgate.net/post/What_are_the_statistics_for_a_cross_sectional_study [accessed Nov 22, 2016].
I usually prefer Post score regressed on Pre score rather than a change score - with the latter a change of 10 from a base of 0 is very different from a change of 10 from a base of a 1000
Gelman and Hill explain this in more detail: .
Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. www.stat.columbia.edu/~gelman/arm/
In preference I would explicitly model the change choosing the value for the later visit as the response and the values for the earlier visit as a predictor and then including other predictors - including any treatments and covariates (usually from the first visit and any time invariant ones). By setting up the model in this way you are conditioning on the previous starting values and explicitly modeling change.
Taken from
What are the statistics for a cross sectional study? - ResearchGate. Available from: https://www.researchgate.net/post/What_are_the_statistics_for_a_cross_sectional_study [accessed Nov 22, 2016].
Dear Mr. Jones,
thank you very much for your answer. I have a question directly related to the approach of including pre-treatment measurements as an independent variable.
Doesn't this suffer from the problem that both the independent variable (baseline) and dependent variable are influenced by unobserved effects that are captured in the error term, resulting in endogeneity? With this approach, the independent variable is likely to be significant because it captures unobserved effects from the error term, with which it correlates. This may bias other estimates of independent variables as a result.
The treatment is randomized and subjects are randomly allocated to the treatment groups. I see, in that case there should be no correlation between the error term and the treatment variable, because they are uncorrelated per design/ randomized allocation.
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