Study design: 7 exam questions solved step by step

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What this lesson covers

  • Only a randomised experiment supports a causal claim; an observational study supports an association.
  • Random allocation balances confounders; random selection lets results extend to a population.
Key idea

7 questions, one method

  • 1. Who chose the treatment? Name the type.
  • 2. Explanatory and response variables.
  • 3. Allocation: cause. Selection: who.
  • 4. Claim no more than the design allows.
Your turn

Question 1 · Achieved

  • An invented study of 500 Year 13 students
  • recorded weekly social media hours and
  • exam marks: over 15 hours averaged 54%,
  • the rest 62%. Name the study type.
Worked example

Q1: social media and marks

  • Who chose the hours?
  • Then the two variables.
  1. 62 − 54 = 8 points lowerover 15 hours
  2. students chose their hoursnobody assigned
  3. observational study
  4. explanatory: social media hours
  5. response: exam mark
  6. an association onlyno random allocation
Your turn

Question 2 · Achieved

  • An invented orchard trial: 60 kiwifruit
  • vines split at random, 30 given a new
  • fertiliser, 30 the usual one. Mean yield:
  • 41 kg v 36 kg a vine. What can it claim?
Worked example

Q2: the fertiliser trial

  • The grower assigned it.
  • At random: a cause.
  1. grower assigned the fertiliser
  2. experimenttreatment assigned
  3. explanatory: fertiliser type
  4. response: yield per vine (kg)
  5. 41 − 36 = 5 kg more a vine
  6. split at randombalances confounders
  7. caused about 5 kg morefor vines like these
Your turn

Question 3 · Merit

  • An invented gym: 80 volunteers split at
  • random between two warm-ups. Injured in
  • 6 weeks: 3 of 40 (A), 9 of 40 (B). Does A
  • cut injuries for all members?
Worked example

Q3: allocation, then selection

  • Allocation: cause?
  • Selection: for whom?
  1. A: 3 ÷ 40 = 0.075 = 7.5%
  2. B: 9 ÷ 40 = 0.225 = 22.5%
  3. 22.5 − 7.5 = 15 points
  4. split at randomrandom allocation
  5. A caused fewer injuriesa causal claim
  6. volunteers, not chosen at random
  7. only members like theseno random selection
Your turn

Question 4 · Merit, in context

  • An invented random survey of 1200 adults:
  • 64% of dog owners meet the activity
  • guideline; 41% of non-owners do.
  • Headline: "A dog makes you fitter."
Worked example

Q4: does a dog make you fitter?

  • Who chose the dog?
  • What else differs?
  1. 64 − 41 = 23 points
  2. people chose to own a dogobservational
  3. "a dog makes you fitter"a causal claim
  4. confounders: age, health, time
  5. active people may get dogs
  6. random selection: all adults
  7. an association in all adults
Your turn

Question 5 · Merit

  • An invented double-blind trial: of 120
  • volunteers, 60 at random get a sleep
  • supplement, 60 a look-alike placebo.
  • Extra sleep a night: 34 min v 21 min.
  • Why the placebo and blinding? Pause.
Worked example

Q5: placebo and blinding

  • The placebo group improved.
  • So what did it add?
  1. placebo: +21 minno active ingredient
  2. supplement: +34 min
  3. 34 − 21 = 13 minthe supplement itself
  4. placebo: same expectationboth groups
  5. volunteers do not knowblind
  6. researchers do not knowdouble blind
  7. about 13 extra minutes a night
Your turn

Question 6 · Excellence

  • An invented study: 30 students did a
  • memory test in silence, then again with
  • music. Mean: 14.2 v 12.6. "Music harms
  • memory." Evaluate the design.
Worked example

Q6: the order of the tests

  • Music was always second.
  • Randomise the order.
  1. 14.2 − 12.6 = 1.6 marks
  2. everyone: silence, then music
  3. second test: tired or boredorder effect
  4. music and order mixed upconfounded
  5. "music harms memory"could be the order
  6. half at random: music first
  7. order hits both alikein the comparison
  8. reduced, not removed
Your turn

Question 7 · Excellence

  • An invented random sample of 800 homes:
  • with a heat pump, 1.4 colds a person last
  • winter; without, 2.0. "Heat pumps prevent
  • colds." Evaluate, then design a test.
Worked example

Q7: what the survey shows

  • Check the numbers.
  • Then the study type.
  1. 2.0 − 1.4 = 0.6 colds a person
  2. 0.6 ÷ 2.0 = 0.3 = 30% fewer
  3. households chose heat pumpsobservational
  4. confounders: income, newer homes
  5. "heat pumps prevent colds"a causal claim
  6. association in all homesrandom selection
Worked example

Q7: a study that could test it

  • Select at random: who.
  • Allocate at random: cause.
  1. homes without a heat pumpthe population
  2. select homes at randomextends to them all
  3. allocate pumps at randombalances confounders
  4. the rest: no heat pump yetcomparison group
  5. count colds next winterresponse variable
  6. then a causal claim
Summary

The method that solved all seven

  • Name the type, then claim no more than the design allows.
StepHow
Study typewho chose the treatment?
Variablesexplanatory, then response
Allocationrandom: a causal claim
Selectionrandom: the population
Placebossame expectation, both groups
Order effectrandomise it: reduced

More in AS 91584

Margin of error: the three rules of thumb6 minConfidence intervals, claims, and why overlap fails7 minExperiments vs observational studies: what you can conclude7 minSurveys and bias: sampling frames, non-response and wording6 minEvaluating a statistical report: the full answer7 minMargin of error: 7 exam questions solved step by step10 minConfidence intervals: 7 exam questions solved step by step10 minStudy design: 7 exam questions solved step by step10 minSurveys and bias: 7 exam questions solved step by step10 minEvaluating reports: 7 exam questions solved step by step10 min

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