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Magic of Statistics

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The Magic of Statistics… Revealed!
Michael A. Posner, Ph.D.
Assistant Professor of Statistics Department of Mathematical Sciences Villanova University michael.posner@villanova.edu http://homepage.villanova.edu/michael.posner

It’s MAGIC!!!
• Spend 15 minutes entertaining your students while teaching or reviewing concepts including:
– Probability and Independence – The Binomial distribution – The Normal approximation to the binomial – Hypothesis testing

Semantics
• Remove all ACEs from the deck • Place one red ACE and one black ACE face up • Ask each student, in order, to guess the color of a card which they cannot see • Place card onto appropriate colored ACE stack • After 10 (or so) guesses, place opposite color ACE on each stack • Repeat second step above • Reveal to students their hidden psychic ability!

Probability
• Define “success” as guessing right • What is the probability of “success”?
– Bayesian? – Frequentist?

• What is the probability of getting all n right?

Independence
• What is the probability of getting all n right? • Does the guess of one student affect the next student?
– Series of reds often forces the next guess to be black – Does the probability of “success” change?

Binomial Distribution
• Recall requirements of
– Dichotomous event – Independence – N trials – Constant probability of success (50%)

• What is the probability of getting all n right? • What is the probability of getting n-1 out of n right (modification)?

Hypothesis Testing
• p-value: If the true probability of “success” is 50%, what is the chance you get all n right?
– Binomial calculation – Normal approximation to the binomial
• Only need n=10 until np and n(1-p) = 5

• In the end, students don’t need to understand how the trick works, just that their guesses were likely not random
– This is how hypothesis testing often works

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