Statistics for critical appraisal made easy.

1. Stats made easy!
Let's imagine a very unscientific study looking at whether chocolate reduces stress in
librarians.
Population: busy librarians
Intervention: a bar of chocolate
Comparison: no chocolate
Outcome: Reduction in stress symptoms
Control group Treatment group
Total participants 50 50
Number of participants
reporting symptoms of stress
30 15
Mean number of days per
month with stress symptoms
8 4
Absolute risk
Probability that a specified event will occur in a specified population
Absolute risk (AR) = no. of patients with events / total no. of patients in group
Control group = 30/50 = 0.6 = 60%
Treatment group = 15/50 = 0.3 = 30%
In other words 60% of the control group were stressed compared to only 30% of the
treatment group
Relative risk
The ratio of risk in the treated group to risk in the control group
Relative risk (RR) = AR (treatment) / AR (control)
= 0.3 / 0.6 = 0.5
In other words those in the treatment group are half as likely to be stressed as those in the
control group

2. Relative risk reduction
The proportional reduction comparing the risk in the control group against the risk in the
treatment group.
Relative risk reduction = (1 – RR) x 100
(RRR)
= (1 – 0.5) x 100 = 50
In other words giving chocolate to librarians reduces the risk of stress by half (or 50%)
Absolute risk reduction
The size of a difference between two treatments in terms of the actual numbers of people
who experience the outcome.
Absolute risk reduction = AR(control) – AR(treatment)
(ARR)
= 0.6 – 0.3 = 0.3 = 30%
In other words chocolate will prevent 30% of librarians suffering from stress
Both relative risk and absolute risk can be inverted to express increase rather than reduction
if you’re looking at a study where events occur more times in the treatment group than the
control group.
Number needed to treat
The number of patients you need to treat with a specific intervention to get one additional
positive outcome (or one less negative outcome).
Number needed to treat = 1/AAR
= 1/03 = 3.3
In other words you’d need to give three librarians chocolate in order for one of them to see
the benefit

3. Odds ratio
The likelihood of an outcome occurringwith a particular exposure, compared to the
likelihood of the outcome occurring without that exposure.
Odds = no.with events / no.without
= 30/20 (control) = 1.5
= 15/35 (treatment) = 0.43
Odd ratio = odds (treatment) / odds (control)
= 0.43 / 1.5 = 0.29
In other words the odds of getting stressed are 30% less in librarians who eat chocolate
Mean difference
The average difference between the intervention group and the control group. Used when
combining or comparing measures on continuous scales, such as weight.
Mean difference = Mean value in control group - mean value in treatment group
= 8 days – 4 days
= 4
In other words librarians eating chocolate will, on average, have four less days of stress per
month than those who don’t.
Some things to bear in mind
Odds ratio and risk ratio will be similar when an event is rare, but very different when the
event is common. Be aware that the odds ratio can often show an intervention in a more
positive light.
Relative risk reduction and absolute risk reduction both show the decrease (or increase) of
risk. However, because of the way they are calculated, the values can be quite different. Be
aware that relative risk reduction tends to look more impressive so drug companies are
likely to use this measure to make their drugs look more effective. Absolute risk reduction is
a more accurate measure.