Week 06 · Thursday: Samples, Surveys and Studies (Statistics 9-12)

Thursday: Fair Samples and Unfair Ones

"Shortcut," Comet says. "I will just ask the first 10 runners through the gate."

"The early birds," Wren says. "They are the ones who like morning starts. Your sample would lean. What do you notice?"

"A convenience sample," Comet says. "Easy to grab, but it misses the late arrivals."

"Or we post a sheet and let runners write their views," Wren says. "Then only the ones with strong feelings bother."

"Voluntary response," Comet says. "Also leaning. And the question matters too. 'Don't you agree the loop is too long?'"

Nova glows the word "leading" over the card. "Would you like a hint? A fair question does not push."

"So: the bag picks, everyone has the same chance, and the question is plain," Wren says. "That is a simple random sample."

How a sample goes wrong

A convenience sample takes whoever is easy to reach. It can miss whole kinds of people, so it may lean.

Voluntary response lets people choose to answer. Strong feelings are overcounted, because those people bother to reply.

A leading question pushes the answer one way. "Don't you agree..." is not a question, it is a nudge.

A random sample fixes the first two. Plain, neutral wording fixes the third. A fair survey needs both.

The crew's plan	Problem	Why it leans
ask the first 10 runners at the gate	convenience sample	early arrivals are not like everyone
post a sheet and let runners write	voluntary response	only strong feelings reply
"Don't you agree the loop is too long?"	leading question	the wording pushes toward yes
draw 10 tokens from 40 and ask a plain question	none clear	chance picks, wording is neutral

How to draw a simple random sample

The crew's procedure with the bag. Read the steps, then put them in order below.

List the whole population and number each member, 1 to 40.
Put one token for each number in the bag. Every member now has exactly one token.
Shake the bag so no one can tell which token is which.
Draw 10 tokens without looking. Do not put any back until the sample is complete.
Match the drawn numbers to the list. Those members are the sample, and every member had the same chance.

DRAWING A SIMPLE RANDOM SAMPLE, IN ORDER

?Match the numbers to the list to name the sample
?Number every member of the population
?Draw the sample without looking, no tokens put back
?Put one token per member in the bag
?Shake the bag so no token can be told apart

WHY THIS EXERCISEEvery step protects the same thing: each member gets exactly the same chance of being picked.

A sample where chance, not a person, picks every member is called a this sample. Type one word.

A question whose wording pushes the answer one way is called a this question. Type one word.

WHICH CONCLUSION IS JUSTIFIED?

Read the question.
Tap your answer.

Comet asks the first 10 runners through the gate whether they want a morning start. What is the main problem, if any?

The crew posts a sheet at the water table and reads whatever runners choose to write. What is the main problem, if any?

The survey card asks, "Don't you agree the loop is far too long for most runners?" What is the main problem, if any?

Wren draws 10 tokens from a bag of 40 and asks each runner, "Which start time do you prefer?" What is the main problem, if any?

Statement	True or false?
A convenience sample can miss whole kinds of people.	?
Voluntary response overcounts people with strong feelings.	?
A leading question is fine as long as the sample is random.	?
In a simple random sample every member has the same chance of being picked.	?

WHY THIS EXERCISESpotting these three problems is most of what it takes to read a survey critically.

Try it

Rewrite the leading question "Don't you agree the loop is too long?" as a plain, neutral question.
Then describe one convenience sample you could have taken today, and who it would miss.

Draw the five steps of the bag procedure as five small pictures in a row.

Run Log: write the three ways a sample goes wrong, each with the crew's example.Write the five steps for a simple random sample in your own words.Write one question you have been asked that was leading, and how you would fix its wording.

Fair picks and fair questions. Tomorrow you read a report the way a statistician does, and review the week.