Week 09 · Friday: Comparing Two Treatments (Statistics 9-12)

Friday: Everyday Comparisons

"My cousin says the runners who stretched longer finished faster last year," Comet says. "So stretching works?"

"Who decided how long each one stretched?" Wren asks.

"They did," Comet says. "Oh. The keen runners stretched longer and were faster anyway."

Nova hovers up two pictures: a shuffled deck and a sign-up sheet. "Would you like a hint? Only one of these earns the word cause."

"The deck," Wren says. "What do you notice about our own experiment? Twelve runners, one lap each, one day."

"So our answer is about those twelve on that day," Comet says. "Not about every runner in the world."

"Still a real answer," Wren says. "Significant, random, honest about its limits. That is what the Run Log says."

"And the start cue stays a tie until we test more runners," Comet adds.

Comparisons in everyday life

Everyday life is full of two-group comparisons: this shoe or that, this path or that, this warm-up or that.

Ask three questions. Who decided the groups? How big is the gap? What could chance alone do?

If chance decided the groups and the gap is beyond what chance alone does, the treatment is the best explanation.

If people chose their own groups, a gap may come from the people, not the treatment. Then no cause is justified.

Everyday comparison	Who decided the groups?	Can it point to a cause?
the crew's warm-up experiment	a shuffled deck	yes, for these runners
runners who chose to stretch longer last year	the runners themselves	no
the crew's start-cue experiment	a shuffled deck	yes, but the gap was not significant
the first six to arrive jog, the rest stretch	arrival order	no, early arrivers may differ

JUDGE THE COMPARISON

Read the question.
Tap your answer.

The first six runners to arrive jog and the rest stretch. The jog group is faster. What is the problem?

The crew looked at last year's log and compared runners who stretched longer with those who stretched less. What kind of study is this?

How does randomization work in an observational study?

Which experiment would make the crew trust its warm-up answer more?

Review: the week in one list

An experiment assigns treatments. Random assignment lets chance choose the groups.
The difference of means measures the gap between the groups.
Re-randomize: write every result on a card, shuffle, deal, find the difference, repeat, plot.
The 5% rule: fewer than 5% of shuffles at or beyond the gap means significant.
Significant points to a cause for the runners in the experiment. Not significant means chance could explain the gap.

MIXED REVIEW

Read the question.
Tap your answer.

Jog group: 88, 91, 86, 93, 90, 92 seconds. Stretch group: 95, 92, 97, 94, 96, 90 seconds. What is the difference of the means, jog minus stretch? (Round to 1 place.)

In the crew's 25 warm-up shuffles, 4 gave a difference of 3 or more. What percent is that? (Round to 1 place.)

In a dot plot of shuffled differences, where does the pile sit?

By the crew's rule, a difference is significant when the shuffles at or beyond it are under what percent? Type the number.

WHY THIS EXERCISEThe line is agreed before the data arrives. That is what makes the judgment fair.

Statement	True or false?
90 - 94 = -4	?
People choosing their own groups can make a gap that has nothing to do with the treatment.	?
A significant result about twelve runners proves the same for every runner.	?
Shuffling cards is a fair model of chance only when the groups were randomly assigned.	?

WHY THIS EXERCISEThe three questions, who decided, how big, what could chance do, work on any comparison you meet.

Try it

Find one comparison you have heard this week ("this is better than that"). Write down who decided the groups.
Write whether it could point to a cause, and what experiment would settle it.

Draw the table of everyday comparisons as a two-column chart: who decided the groups, and cause or no cause.

Run Log: write the three questions for any comparison and answer them for the cousin's stretching claim.Write what the crew's warm-up result does and does not say, in two sentences.Plan Track Day: a two-treatment experiment at home with a coin to assign groups and cards to shuffle.Write the five review points in your own words, one line each.

A clear-headed week. Tomorrow is Track Day: your family runs a tiny experiment and shuffles the cards.