## 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