NCEA Level 2Relative riskAS 91267

Relative risk: 7 exam questions solved step by step

What this lesson covers

  • Relative risk compares the risk in one group with the risk in another by dividing.
  • A relative risk above 1 means higher risk for the first group; below 1 means lower.
Key idea

7 questions, one comparison

  • 1. Risk = cases ÷ that group's total.
  • 2. RR = risk ÷ reference risk.
  • 3. Say it as "times as likely".
  • 4. Question the claim.
Your turn

Question 1 · Achieved, in context

  • 600 people at a beach on a hot day.
  • Find the risk of sunburn for
  • people with no sunscreen.
GroupSunburntNotTotal
No sunscreen84156240
Sunscreen36324360
Total120480600
Worked example

Q1: one risk

  • Use the row total.
  • Not the grand total.
  1. risk = sunburnt ÷ group total
  2. risk(none) = 84 ÷ 240
  3. = 0.35
  4. 84 ÷ 600 = 0.14grand total: wrong group
  5. 35% of non-users got sunburnt
Your turn

Question 2 · Achieved

  • Same table.
  • Find the relative risk of sunburn,
  • no sunscreen compared with sunscreen.
GroupSunburntNotTotal
No sunscreen84156240
Sunscreen36324360
Total120480600
Worked example

Q2: RR above 1

  • Reference: sunscreen users.
  • Say it in a sentence.
  1. risk(sunscreen) = 36 ÷ 360
  2. = 0.1
  3. RR = risk(none) ÷ risk(sunscreen)
  4. = 0.35 ÷ 0.1reference: sunscreen
  5. = 3.5
  6. no sunscreen: 3.5 times as likely
Your turn

Question 3 · Merit

  • Same table, the other way round:
  • sunscreen compared with none.
  • Find the RR and interpret it.
GroupSunburntNotTotal
No sunscreen84156240
Sunscreen36324360
Total120480600
Worked example

Q3: RR below 1

  • Reference: no sunscreen.
  • Below 1: lower risk.
  1. RR = risk(sunscreen) ÷ risk(none)
  2. = 0.1 ÷ 0.35reference: no sunscreen
  3. = 0.285714…calculator
  4. = 0.292 d.p.
  5. 1 ÷ 3.5 = 0.29flip of question 2
  6. 1 − 0.29 = 0.71
  7. sunscreen: 0.29 times as likely
  8. a 71% lower risk
Your turn

Question 4 · Merit

  • 600 office workers, back pain or not.
  • Some cells are missing.
  • Find the RR of back pain,
  • sitting compared with standing.
DeskBack painNo painTotal
Standing18?150
Sitting?315450
Total??600
Worked example

Q4: fill the gap, then divide

  • Find only the cell you need.
  • Reference: standing.
  1. sitting, pain: 450 − 315 = 135
  2. risk(standing) = 18 ÷ 150 = 0.12
  3. risk(sitting) = 135 ÷ 450 = 0.3
  4. RR = 0.3 ÷ 0.12reference: standing
  5. = 2.5
  6. sitting: 2.5 times as likely
Your turn

Question 5 · Merit, in context

  • Netball ankle injuries in a season.
  • No balance training: RR = 1.6
  • Training: risk 0.15. 40 players skip it.
  • How many injuries among them?
Worked example

Q5: risk from a relative risk

  • 1.6 times: multiply.
  • Then expected = n × risk.
  1. RR = 1.6, reference: training
  2. risk(no training) = 1.6 × 0.15
  3. = 0.24
  4. 0.15 + 0.6 = 0.75adds; should multiply
  5. expected = 40 × 0.24 = 9.6
  6. about 10 injured playerswhole people
Your turn

Question 6 · Excellence, in context

  • Headline: "Gaming over 3 hours a day
  • doubles a child's chance of glasses."
  • Glasses: 45 of 150 heavy gamers,
  • 60 of 400 other children. Evaluate.
Worked example

Q6: check the number

  • Calculate before judging.
  • Reference: other children.
  1. risk(heavy) = 45 ÷ 150 = 0.3
  2. risk(others) = 60 ÷ 400 = 0.15
  3. RR = 0.3 ÷ 0.15 = 2reference: others
  4. "doubles": RR = 2 fits the data
Worked example

Q6: check the words

  • "Doubles" claims a cause.
  • A study like this cannot show one.
  1. observational: no proof of cause
  2. other factors may differ
  3. one sample of 550 children
  4. 150 − 45 = 105 did not: 70%
  5. 2 times as likely, cause unproven
Your turn

Question 7 · Excellence, in context

  • No app: 60 of 400 patients forgot a dose.
  • 250 used a reminder app. RR = 0.4
  • How many app users forgot?
  • Is "60% lower risk" right?
Worked example

Q7: work back from the RR

  • Reference: no app.
  • Risk × group size = count.
  1. risk(no app) = 60 ÷ 400 = 0.15
  2. RR = risk(app) ÷ risk(no app)
  3. 0.4 = risk(app) ÷ 0.15reference: no app
  4. risk(app) = 0.4 × 0.15 = 0.06
  5. forgot = 0.06 × 250 = 15
  6. check: 15 ÷ 250 = 0.06
  7. 15 app users forgot a dose
Worked example

Q7: relative and absolute

  • Below 1: 1 − RR is the drop.
  • Give the absolute change too.
  1. 1 − 0.4 = 0.6
  2. "60% lower risk": correct
  3. 0.15 − 0.06 = 0.09absolute drop
  4. 9 fewer in every 100 patients
  5. 60% relative, 9 in 100 absolute
Summary

The method that solved all seven

  • Name the reference group, then divide.
StepHow
Riskcases ÷ that group's total
RRrisk ÷ reference risk
Above 1say "times as likely"
Below 11 − RR is the drop
Missingrisk = RR × reference risk
Claimcause, sample, absolute risk

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