How does the performance of swimmers decline over long events?

Case Studies in Statistical Thinking

Justin Bois

Lecturer, Caltech

More swimming background

1 Photo by Chan-Fan, CC-BY-SA-4.0
Case Studies in Statistical Thinking

More swimming background

  • Split: The time is takes to swim one length of the pool
Case Studies in Statistical Thinking

More swimming background

Case Studies in Statistical Thinking

More swimming background

1 Image: Miho NL, CC-BY-3.0
Case Studies in Statistical Thinking

More swimming background

Case Studies in Statistical Thinking

Slowing down

Case Studies in Statistical Thinking

Quantifying slowdown

  • Use women's 800 m freestyle heats
  • Omit first and last 100 meters
  • Compute mean split time for each split number
  • Perform linear regression to get slowdown per split
  • Perform hypothesis test: can the slowdown be explained by random variation?
Case Studies in Statistical Thinking

Hypothesis tests for correlation

  • Posit null hypothesis: split time and split number are completely uncorrelated
  • Simulate data assuming null hypothesis is true
    scrambled_split_number = np.random.permutation(
  split_number
)
  • Use Pearson correlation, denoted rho, as test statistic
    rho = dcst.pearson_r(scrambled_split_number, splits)
  • Compute p-value as the fraction of replicates that have Pearson correlation at least as large as observed
Case Studies in Statistical Thinking

Let's practice!

Case Studies in Statistical Thinking

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