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Example 1: Helper/hinderer?

  • https://campuspress.yale.edu/infantlab/media/
  • Sixteen pre-verbal infants were shown two videos of a toy trying to climb a hill
    • One where a “helper” toy pushes the original toy up
    • One where a “hinderer” toy pushes the toy back down
  • Infants were then presented with the two toys from the videos
    • Researchers noted which toy then infant chose to play with

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Example 1: Helper/hinderer?

  • Data: 14 of the 16 infants chose the “helper” toy
  • Two possible explanations
    • Infants choose randomly, no genuine preference, researchers just got lucky
    • Infants have a genuine preference for the helper toy
  • Core question of inference:
    • Is such an extreme result unlikely to occur by chance (random choice) alone …
    • … if there were no genuine preference (null model)?

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Analysis options

  • Could use the normal approximation to the binomial, but sample size is too small for CLT
  • Could use a binomial probability calculation
  • We prefer a simulation approach
    • To illustrate “how often would we get a result like this just by random chance?”
    • Starting with tactile simulation

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Strategy

  • Students flip a fair coin 16 times
    • Count number of heads, representing choices of helper and hinderer toys
    • Under the null model of no genuine preference
  • Repeat several times, combine results
    • See how surprising it is to get 14 or more heads even with “such a small sample size”
    • Approximate (empirical) p-value
  • Turn to applet for large number of repetitions: www.rossmanchance.com/ISIapplets.html (One Proportion)

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Results

  • Pretty unlikely to obtain 14 or more heads in 16 tosses of a fair coin, so …
  • Pretty strong evidence that pre-verbal infants do have a genuine preference for helper toy and were not just choosing at random

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Exact p-value?

  • Binomial distribution

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  • Two-sided p-value?

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Activity 2: Facial Prototyping

  • Who is on the left – Bob or Tim?

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Activity 2: Facial Prototyping

  • Facial prototyping
    • Does our sample result provide convincing evidence that people have a genuine tendency to assign the name Tim to the face on the left?
    • How can we use simulation to investigate this question?
    • What conclusion would you draw?
    • Explain reasoning process behind conclusion.

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Six-Step Process

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Note:

The goal is not to have them memorize these steps but to introduce an organized way of thinking, where all the steps are important!

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3S Strategy

  • Statistic
  • Simulate
    • “Could have been” distribution of data for each repetition (under null model)
    • “What if” distribution of statistics across repetitions (under null model)
  • Strength of evidence
    • Reject vs. plausible

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Summary

  • Use real data/scientific studies
    • Emphasize the process of statistical investigation
  • Stress conceptual understanding
    • Idea of p-value on day 1/in one day!
  • Foster active learning
    • You are a dot on the board
  • Use technology
    • Could this have happened “by chance alone”?
    • What if only 10 infants had picked the helper?

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