Guiding questions

  1. ANOVA is a type of linear model. In ANOVA, we are often interested in comparing the mean of more than two groups. Please simulate data for 4 groups under the assumptions of a linear model.

  2. Once you have simulated these data, let’s fit a linear model. To this end, we will need to create Ng1 binary covariates, where Ng is the number of groups. In our example, this means that we will need to create 3 binary covariates because we have 4 groups/treatments. Creating these 3 binary variables might seem very exoteric but this is exactly what R does when you specify a variable to be a factor with 4 levels.

  3. Fit a linear model in a frequentist framework using the “lm” function

a - What is the p-value of the model? This is shown at the very bottom together with the F-statistic and should be identical to the one we get using the “aov” function.

b - Estimate the mean of each group by summing the appropriate parameters.

  1. Fit a linear model in a Bayesian framework using our JAGS code. Do our parameter estimates from the Bayesian model match those estimated using a frequentist framework?



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