Lesson 2 ~35 min Data Analysis C · Path +85 XP

Gathering Data Ethically and Efficiently

Two things quietly determine whether an investigation works: whether people were willing and able to answer honestly, and whether the data was recorded in a shape you can actually analyse.

Today's hook: "Do you agree that the canteen should stock healthier food?" and "should the canteen change what it stocks?" are asked about the same thing and will not get the same answers. The first supplies its own conclusion. Wording is not presentation, it is part of the measurement.

0/5QUESTS

Think First

warm-up

You are asked to record, for thirty classmates, their year group, height and favourite sport. Sketch how you would lay the data out on paper or in a spreadsheet before reading on. Then ask yourself: if you later wanted the mean height of Year 9 students only, how much work would your layout require?

Record your answer in your workbook.

The Big Idea

+5 XP to read

Ethical collection means the people supplying the data understood what they were agreeing to, could decline, and cannot be identified from what you publish. Efficient collection means recording it once, in a shape that answers questions you have not thought of yet. Neither can be added afterwards.

Consent · Privacy · Neutral wording · One row per subject, one column per variable

The organisational half has a standard shape worth knowing: one row per subject, one column per variable, one value per cell. Data in that form can be sorted, filtered and grouped without being retyped. Data in any other form usually has to be rebuilt before the first question can be answered.

Wording is measurement

A leading question changes the answer, so it changes the data.

Consent must be informed

People need to know what is collected, why, and that they may decline.

One row, one subject

One value per cell. It is the layout every tool expects.

What You'll Master

objectives

Know

What informed consent requires, and what anonymity and confidentiality mean
The features of a neutral survey question
The standard data layout: one row per subject, one column per variable

Understand

Why the wording of a question is part of the measurement rather than presentation
Why a small identifying detail can breach privacy even without a name

Can Do

Identify and repair leading, loaded and double-barrelled questions
Design a collection method that respects consent and privacy
Organise raw data into a structure that can be sorted, filtered and grouped

Words You Need

vocabulary

Informed consentAgreement given by someone who understands what is collected, why, and that they may decline.

AnonymousCollected so that not even the researcher can link a response to a person.

ConfidentialThe researcher can link responses to people but undertakes not to reveal the link.

Leading questionOne whose wording suggests the answer expected.

Double-barrelled questionOne asking two things at once, so a single answer cannot address both.

Tidy layoutOne row per subject, one column per variable, one value per cell.

What Informed Consent Requires

+5 XP to read

Three things must be true before someone's data may be used.

They know what is being collected and why. "A survey for maths" is not enough. "How long you sleep each night for one week, to investigate whether sleep is related to test marks" is.

They can decline without consequence. If declining is awkward, embarrassing, or affects them in any way, the consent is not freely given.

They know what happens to the data. Who sees it, whether it is published, and whether it can be traced back to them.

Note the distinction between anonymous and confidential. Anonymous means even you cannot tell who gave which response. Confidential means you can, but undertake not to say. Both are legitimate; promising one while doing the other is not.

Privacy Survives the Removal of Names

+5 XP to read

Deleting the name column does not make data anonymous. What identifies someone is any combination of details that only one person matches.

Consider a table with columns for year group, sport played and hours of part-time work. "Year 12, water polo, 22 hours" may describe exactly one student in the school, and everyone who knows the water polo team will be able to say who. The name was never needed.

Two practical defences:

Group the rare values. Report sport as "team sport" or "individual sport" rather than naming it, so no cell isolates one person.

Report totals, not rows. Publishing "the mean was 12.4 hours across 40 students" reveals nothing about any individual. Publishing the raw table often does.

Test to apply

For each row you plan to publish, ask whether anyone in the school could work out who it is. If the answer is yes for even one row, the data is not anonymous.

Question Wording Is Part of the Measurement

+5 XP to read

Three faults account for most bad survey questions.

Fault	Example	Repair
Leading	Do you agree the canteen should stock healthier food?	Should the canteen change what it stocks? If so, how?
Loaded	How much do you enjoy mathematics?	How do you feel about mathematics? (options from strongly dislike to strongly enjoy)
Double-barrelled	Is the canteen cheap and fast?	Two questions, one about price and one about speed

The loaded example is the subtlest. "How much do you enjoy" assumes enjoyment and offers no way to express dislike, so a student who dislikes the subject must either misreport or skip the question. Either way the data is wrong, and it is wrong in a predictable direction, which is worse than being wrong at random.

Organising Data So It Can Be Used

+5 XP to read

The standard layout is one row per subject, one column per variable, one value per cell.

Student	Year	Height (cm)	Sport
1	9	162	netball
2	10	171	soccer
3	9	158	none

Three habits keep it usable. One value per cell: a cell reading "netball, soccer" cannot be counted, so use a second column or a second row. Consistent units and spelling: "162", "162 cm" and "1.62" in one column make the column unusable, and so do "Soccer", "soccer" and "footy". Record missing values as missing: an empty cell means "not collected"; typing $0$ means the value was zero, which is a different claim.

Laid out this way, the mean height of Year 9 students is a filter and a calculation. Laid out any other way, it is a retyping job.

Common Pitfalls

+5 XP to read

Assuming that deleting names makes data anonymous.

Fix: check whether any combination of remaining columns identifies one person. Group rare categories or report totals instead of rows.

Recording a missing value as zero.

Fix: zero is a measurement; missing is the absence of one. Averaging a column where absences were typed as zero pulls the mean down for no reason.

Writing a question whose options do not cover every honest answer.

Fix: read your options as a respondent who disagrees with the premise. If they have nowhere to go, the question is loaded.

Watch Me Solve It · 3 examples

Watch Me Solve It · Repairing three questions

+15 XP per step

PROBLEM

A survey contains: (i) "Don't you think homework is excessive?" (ii) "Rate how much you enjoy sport: 1 to 5." (iii) "Is the library quiet and well stocked?" Identify each fault and rewrite.

1

Question (i): leading

"Don't you think" invites agreement and supplies the conclusion. Rewrite neutrally: "How would you describe the amount of homework you are set? (far too little / too little / about right / too much / far too much)".
2

Question (ii): loaded

It assumes enjoyment and gives a student who dislikes sport nowhere honest to go. Rewrite: "How do you feel about sport?" with options from strongly dislike to strongly enjoy.
3

Question (iii): double-barrelled

Someone who finds the library quiet but poorly stocked cannot answer. Split it into one question about noise and one about stock.
4

Check each repair against the same test

Read each rewritten question as a respondent who holds the opposite view to the one the original assumed. If they can answer honestly, the repair worked.

AnswerLeading, loaded and double-barrelled, each split or reworded neutrally

Watch Me Solve It · Deciding what may be published

+15 XP per step

PROBLEM

A student has surveyed 30 classmates and wants to publish the full table, having deleted the names. The columns are year group, part-time job (yes or no), weekly hours worked, and suburb. Advise them.

1

Look for combinations that isolate one person

Suburb is the risk. In a school drawing from many suburbs, one student may be the only respondent from theirs, and that row is then identified regardless of the missing name.
2

Check the numerical column too

An unusually high value, such as 25 hours a week, may itself be recognisable to anyone who knows the person, since extreme values are memorable.
3

Apply the two defences

Group suburb into a broader region, or drop the column if the inquiry does not need it. Group the hours into intervals such as 0, 1 to 5, 6 to 10, over 10.
4

Prefer summaries to rows

If the aim can be answered with means and counts, publish those. "The 12 students with jobs worked a mean of 8.4 hours" reveals nothing about any individual.

AnswerDo not publish the raw table: group or drop suburb, band the hours, and report summaries

Watch Me Solve It · Restructuring a messy record

+15 XP per step

PROBLEM

A student has recorded data as: "Amy: yr9, 162cm, netball and soccer. Ben: yr10, 171, soccer. Cara: yr9, unknown, none." Restructure it and explain each decision.

1

One row per subject, one column per variable

Four columns: student, year, height in cm, sport. Every row then has the same shape and the columns can be sorted or filtered.
2

One value per cell

Amy plays two sports, which cannot share a cell. Either add a second sport column, or use one row per student-sport pair. Which is better depends on whether the inquiry counts students or counts sports.
3

Make units and spelling consistent

Record height as a bare number with the unit in the column heading, so "162cm" and "171" become $162$ and $171$. Fix any variation in the sport names before analysis, not during.
4

Distinguish missing from zero

Cara's height is unknown. Leave the cell empty and note it; entering $0$ would claim she has zero height and would drag any mean downwards.

AnswerA four-column table with one value per cell, consistent units, and the missing height left empty

Brain Trainer · 4 problems

Brain Trainer · Spot the fault

4 problems

Four quick problems. Work each one, then reveal the answer.

1 "Do you agree our uniform is uncomfortable?" What is wrong?

The wording supplies the conclusion and invites agreement.Leading
2 "Is the bus cheap and reliable?" What is wrong?

Someone who finds it cheap but unreliable cannot answer.Double-barrelled
3 A cell in the height column is empty because the student was absent. Enter $0$?

Zero is a measurement; absence is not.No, leave it missing
4 Names have been deleted, but one row reads "Year 12, water polo, 22 hours". Anonymous?

The combination may match exactly one person.No

Complete in your workbook.

Multiple Choice · 5 questions

MC1

Informed consent

+10 XP

Consent to take part in a survey is informed only if the respondent:

MC2

Anonymity

+10 XP

Deleting the name column from a data set:

MC3

Question faults

+10 XP

"Is the canteen cheap and fast?" is an example of a question that is:

MC4

The tidy layout

+10 XP

The standard layout for a data set is:

MC5

Missing values

+10 XP

A student was absent, so their height was not measured. The cell should contain:

Short Answer · 3 questions

Repair a survey

+15 XP

SHORT ANSWER

A student's survey reads:
1. "Don't you think the library should open longer?"
2. "How much do you like studying in the library? (1 to 5)"
3. "Is the library quiet and comfortable?"
(a) Name the fault in each question.
(b) Rewrite each one.
(c) Explain why a loaded question produces data that is wrong in a predictable direction, and why that is worse than random error.

Write your working in your book.

Ethics of a real collection

+15 XP

SHORT ANSWER

A student plans to record, for every member of their sports team: name, weekly training hours, and a self-rated fitness score, then publish the full table in a class report.
(a) State two consent requirements they must satisfy before collecting.
(b) Explain why removing the name column would not be enough to make the published table anonymous.
(c) Describe two changes that would let them report their findings without breaching privacy.

Write your working in your book.

Restructure the data

+15 XP

SHORT ANSWER

A student's raw record reads: "Dan yr10 175cm soccer+athletics, Elle yr9 1.61m netball, Finn yr10 168 none, Gia yr9 (absent) netball".
(a) Redraw this in the standard layout.
(b) State three problems with the original record and how your layout fixes each.
(c) The student wants the mean height of Year 9 students. Explain what your layout makes possible that the original did not.

Write your working in your book.

Stretch Challenge · The question that changed the answer

+25 XP

CHALLENGE

In a well-known pair of surveys, people were asked whether a country should "forbid" public speeches against democracy, and, separately, whether it should "allow" such speeches. Far more people were willing to not allow speeches than were willing to forbid them, even though the two positions are logically identical.
(a) Explain how this can happen if the two questions mean the same thing.
(b) A student concludes that survey data is worthless. Explain why this does not follow.
(c) Describe how you would design a survey to measure opinion on a contested issue at your school, given this effect.

Quick Review

recap

Consent

Understood, freely given, and revocable

Privacy

A combination can identify, even with no name

Wording

Leading, loaded and double-barrelled all distort

Layout

One row per subject, one value per cell

Your Badges

0 of 6

First Steps

3-Day Streak

3 in a Row

Lesson Ace

Stretch Seeker

Daily Warrior

Mark lesson as complete

Tick when you've finished Learn, Practice and the Stretch. Earns +85 XP and +25 coins.

Data Analysis C (Path) index · Maths subject page