Editing Statistics and Statistical Programming (Winter 2021)/Problem set 16 (section)

==== PC3: Fit a model to test for treatment effects ====

Now, let's construct a test for treatment effects. For a between-groups randomized-controlled trial (RCT) like this, that means we'll focus on the fitted parameter for the treatment assignment variable (<math>\beta_1\mathrm{obama}</math>) which will provide a direct estimate of the causal effect of exposure to the treatment (compared against the control) condition. That said, here are a few tips, notes, and requests:

* The outcome is dichotomous, so you can/should use logistic regression to model this data (we can discuss this choice in class). You may want to evaluate whether the conditions necessary to do so are met.
* You may want/need to convert some of these variables to appropriate types/classes in order to fit a logistic model. I also recommend at least turning <code>year</code> into a factor and creating a "centered" version of the <code>age</code> variable. Centering a variable means setting a new baseline by subtracting some amount from every value for a variable (often the mean of the variable) so that the new "centered" variable is 0 at the mean, negative below it, and positive above it. It's can make interpreting regressions much easier. We can discuss this in class too.
* Be sure to state the alternative and null hypotheses related to the experimental treatment under consideration.
* It's a good idea to include the following in the presentation and interpretation of logistic model results: (1) a tabular summary/report of your fitted model including any goodness of fit statistics you can extract from R; (2) a transformation of the coefficient estimating treatment effects into an "odds ratio"; (3) model-predicted probabilities for prototypical study participants. (''please note that examples for all of these are provided in this week's tutorial'')
* For the model-predicted probabilities, please estimate the treatment effects for the following hypothetical individuals: 
** a 9-year old girl in 2015.
** a 7-year old boy in 2012.