2.17 Unit 2 summary

2.17.1 You should be able to

Use Monte Carlo simulation to explore patterns in a random process:

  • Model: Translate real life phenomena into a model to be used in the simulation process.
  • Simulate: Use TinkerPlots™ to generate random outcomes from a model.
  • Evaluate: Determine the “typical” result from a Monte Carlo model, and a range of likely results

Conduct a statistical hypothesis test of an observed result, including:

  • Write an appropriate null hypothesis that specifies a “no effect” probability model and a source of variation
  • Use Monte Carlo simulation in TinkerPlots™ to simulate a study if the null hypothesis were true
    • Model: Use a sampler to model the study if the null hypothesis were true
    • Simulate: Run the simulation hundreds of times and collect the result of interest.
    • Evaluate:
      • Find a range of likely results if the null hypothesis were true
      • Determine whether the observed result is compatible with the null hypothesis
  • Calculate a p-value
  • Formulate a conclusion

2.17.2 You should understand

The logic behind statistical hypothesis testing, including:

  • Regularity in randomness
  • The role of the null hypothesis as specifying a baseline to compare the observed result to
  • Why we use Monte Carlo simulation
  • Why we need to run multiple trials and when we have run enough
  • What the distribution of results represents
  • What we are checking for, in order to determine whether the observed result is compatible with the null model
  • What a p-value represents
  • The sort of conclusions we can (and can’t) make from a statistical hypothesis test.

2.17.3 TinkerPlots™ skills

  • Create a new sampler and use different devices to model a null hypothesis
  • Plot values from a table and organize (by separating) the the plotted values.
  • Numerically summarize values in a plot (e.g., Count (N), Count (%)).
  • Automatically collect the results from many trials.
  • Use the Reference line and Divider tools to count the values in a distribution that are as or more extreme than a given value

2.17.4 Vocab

  • Monte Carlo simulation
  • Hypothesis test
  • Model
  • Trial
  • Result
  • Null hypothesis
  • “No effect” probability model
  • p-value
  • Statistical significance