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Statistics 9-12 / Week 09 / Track Day
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Week 09 · Comparing Two Treatments

Track Day

Track Day: the family experiment
// Two warm-ups, one shuffled deck
⏱ about 20 min

Track Day: The Family Experiment

Saturday the kitchen table becomes the experiment. The task: sort twenty mixed playing cards into red and black.

"Standing or sitting," Comet says. "A coin flip decides each round. Heads, you stand. Tails, you sit."

Eight rounds, four each. Standing: 41, 38, 44, 40 seconds. Sitting: 39, 43, 37, 42.

"Difference 0.5," Wren says. "Standing minus sitting. Now shuffle the eight time cards and deal four and four."

The family shuffles ten times. The differences pile up around zero, and several land past half a second.

"So chance can make our gap easily," Comet says. "Standing or sitting, it is a tie. What do you notice?"

Nova hovers. "Would you like a hint? A tie found fairly is still a finding."

"Then we write it down," Wren says. "Not significant, eight rounds, one afternoon."

  1. An experiment assigns treatments, and random assignment lets chance choose the groups.
  2. The difference of means measures the gap.
  3. Re-randomize with cards to see what chance alone does: shuffle, deal, difference, repeat, plot.
  4. Under 5% of shuffles at or beyond the gap means significant; otherwise chance could explain it.
  5. Significant points to a cause for the people in the experiment, and only because chance chose the groups.
◇ FAMILY TWO-TREATMENT EXPERIMENT
Pick a short timed task and two treatments, such as sorting cards standing or sitting. Flip a coin before each round to assign it.
Run eight rounds, four of each, and time each one. Write the times on eight index cards.
Find the difference of means. Then shuffle the eight cards, deal four and four, and record the difference. Repeat ten times.
Plot the ten shuffled differences, mark your observed gap, and decide together: could chance alone make it?
For a grown-up
The coin must decide each round, even if someone prefers to sit. That is the whole point of random assignment.
Most family gaps will not be significant. Help the family hear "a fair tie" as a real result.
JUDGE THE FAMILY EXPERIMENT
  • Read the question.
  • Tap your answer.
Standing: 41, 38, 44, 40 seconds. Sitting: 39, 43, 37, 42 seconds. What is the difference of the means, standing minus sitting? (Round to 1 place.)
Why did the family flip a coin before each round instead of choosing?
How many rounds did the family run in all? Type the number.
WHY THIS EXERCISEA tiny experiment is still an experiment when chance chose the groups. Its answer is just about those eight rounds.
Draw the family dot plot of ten shuffled differences and mark the observed gap with a red line.

Track Day done. Next week the crew draws lane spots from the bag and builds the rules of probability from the sample space.

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