Exercises: Decide if a Model Is Consistent with Data Using Simulation
Work through each section in order. A "model" is an assumed chance
mechanism (for example, "this coin lands heads with probability 0.5").
To decide if data is consistent with a model, assume the model is true,
simulate the data-generating process many times, build the simulated
distribution, and see how often the model produces a result as extreme
as the one observed. Remember: a surprising result is EVIDENCE to
question a model, never proof the model is false; and an ordinary result
never proves a model true.
Fluency Practice
Apply the simulation framework: device, trial, statistic, repetitions, and reading distributions.
A simulation has these design choices. The model is "a die is fair." We want to know if getting four 6's in 12 rolls is surprising. Fill in each design choice: the chance device that matches the model is a fair ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ -sided die; one trial is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ simulated rolls; the statistic recorded is the number of ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ in those rolls.