NCEA Level 2Relative riskAS 91267

Relative risk: above 1, below 1, and evaluating a claim

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

Comparing risk between groups

  • Risk is a probability of something bad.
  • Relative risk compares two groups.
  • Divide one risk by the other.
Worked example

Phones and crashes

  • 2000 drivers, followed for a year.
  • 400 used a phone while driving.
  • 36 of them crashed; 48 of the other 1600 did.
CrashedDid notTotal
Used a phone36364400
Did not4815521600
Worked example

Two risks, then divide

  • Each group, its own total.
  • Then divide the risks.
  1. others: 2000 − 400 = 1600group total
  2. risk, phone = 36 ÷ 400crashed ÷ group
  3. = 0.09
  4. risk, others = 48 ÷ 1600crashed ÷ group
  5. = 0.03
  6. RR = 0.09 ÷ 0.03phone ÷ others
  7. = 3
Worked example

Three times the risk

  • Phone users: 9 in every 100 crashed.
  • Others: 3 in every 100.
  • Three of the small bars make the tall one.
Three times the risk
Key idea

"Three times as likely", not "3% more"

  • RR 3: three times as likely.
  • Not "3% more".
  1. RR = 0.09 ÷ 0.03 = 3times as likely
  2. difference = 0.09 − 0.03absolute
  3. = 0.06: 6 in every 100
  4. no crash: 400 − 36 = 364phone users
  5. 364 ÷ 400 = 0.9191% did not crash
Worked example

A relative risk below 1

  • Helmet ÷ no helmet.
  • Below 1: a lower risk.
  1. risk, helmet = 10 ÷ 500injured ÷ group
  2. = 0.02
  3. risk, no helmet = 20 ÷ 250injured ÷ group
  4. = 0.08
  5. RR = 0.02 ÷ 0.08helmet ÷ no helmet
  6. = 0.25
  7. 1 − 0.25 = 0.7575% lower risk
Key idea

Reading a relative risk below 1

  • 0.25: a quarter of the risk.
  • Or: the risk is 75% lower.
  • The group on top is the one being described.
Relative riskMeansExample
RR > 1first group at higher risk3: three times as likely
RR = 1same riskno difference
RR < 1first group at lower risk0.25: a quarter of the risk
Key idea

Which group goes on top?

  • Name both groups.
  • Same order as the division.
  1. helmet vs none: 0.02 ÷ 0.08
  2. = 0.25a quarter of the risk
  3. none vs helmet: 0.08 ÷ 0.02
  4. = 4four times as likely
  5. 1 ÷ 0.25 = 4the same fact
Worked example

Evaluating "phones triple your crash risk"

  • The number supports it, in this sample.
  • But how were drivers chosen? Is it cause?
  • And 91% of phone users did not crash.
CheckHereSo
The numberRR = 3 in this samplesupports "three times"
The samplewhich drivers, how chosen?may not represent all
Causeobservational datacannot prove cause
Absolute9% against 3%91% did not crash
Key idea

Where the marks are

  • Achieved: calculate risks from a table.
  • Merit: the relative risk, interpreted.
  • Excellence: evaluate the claim itself.
Summary

What to take away

  • Divide the risks, name the groups, question the claim.
Riskcases ÷ group total
Relative riskrisk in group 1 ÷ risk in group 2
Above 1first group more at risk
Below 1first group less at risk
Say"times as likely", not "% more"
Evaluatesample, cause, absolute risk
Your turn

Your turn: four questions

  • Pause here and answer each one.
  • Each risk uses its own group total.
  • Question 4: interpret, and give a limitation.
Question
DataExercisers: 30 of 200 had a cold. Others: 75 of 300.
1Find the risk of a cold for people who exercise.
2Find the risk for people who do not.
3Find the relative risk, exercisers compared with others.
4Interpret it in a sentence, with one limitation.
Show answer

1. 30 ÷ 200 = 0.15. 2. 75 ÷ 300 = 0.25. 3. 0.15 ÷ 0.25 = 0.6. 4. In this sample, people who exercise were 0.6 times as likely to catch a cold (a 40% lower risk). The data cannot show exercise causes it; other factors may differ between the groups.

Worked example

The answers: questions 1 to 3

  1. 1. risk = 30 ÷ 200exercisers
  2. = 0.15
  3. 2. risk = 75 ÷ 300others
  4. = 0.25
  5. 3. RR = 0.15 ÷ 0.25exercisers ÷ others
  6. = 0.6
Worked example

The answers: question 4

  1. 4. RR = 0.6, below 1a lower risk
  2. 1 − 0.6 = 0.440% lower
  3. In this sample, exercisers were
  4. 0.6 times as likely to get a cold
  5. Limitation: not an experiment,
  6. so it cannot show cause.
  7. Other factors may differ.

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