Probability model
Also enter your estimate of the p-value here and press Submit.
(g) After several people have submitted their results [Check back here until you see at least 15 entries.]: Did everyone obtain the same value for the p-value? Are they similar to each other?
Instead of using simulation, we can use probability rules to calculate the p-value. If we did enough repetitions of the simulation, all of the estimated p-values would converge to this exact probability.
Binomial Process
The "coin tossing model" that we have been using is a prototypical example of a binomial process, which has four key characteristics:
- Each trial results in "success" or "failures" (Which outcome we call success and which we call failure is often unimportant, we just need to be consistent.)
- The trials are independent: The outcome of one trial does not change the probability of success on the next trial.
- The probabilty of success is constant across the trials.
- There are a fixed number of trials.
So with coin tossing, we assume that each and every coin toss has a 0.50 probability of landing heads and that the outcome of the previous coin toss does not make us any more or less likely to find heads on the next toss.
(d) Explain in your own words how we can apply the binomial model to the toast dropping study. Explain any assumptions you need to make, including what the null model assumes about the probability of succes and the number of trials in the initial study.
