# Statistical power

This chapter answers parts from Section A of thePrimary Syllabus, even though study power is not specifically mentioned in any of the "abilities" there.  This topic was examined in Question 19 from the second paper of 2011.  It is revisited in the Required Reading chapter for the Part II exam ("Study power, population and sample size"); in the Fellowship Exam Question 23 from the second paper of 2008  and Question 25 from the first paper of 2006 both asked the candidates to define "study power".

In summary,  the commonest reason for a negative result is a small sample size. You need a sufficiently large sample to detect a given size of effect. The large the sample, the more likely you are to detect a true treatment effect. The point of calculating power is that you can use it to calculate a sufficient sample size, and not run the risk of performing a pointless negative study (thus exposing patients to risk), nor performing a pointlessly expensive study (collecting data from an unnecessarily large group of patients)

### Power

• The power of a statistical test is the probability that it correctly rejects the null hypothesis, when the null hypothesis is false.
• The chance of a study demonstrating a "true" result
• Power = (1 - false positive rate)
• Power = (1- beta error)
• Normally, power is 80% (i.e. a 20% chance of a false negative result)

Power nearly always depends on the following three factors:

• The statistical significance criterion: a statement of how unlikely a positive result must be, if the null hypothesis is true, for the null hypothesis to be rejected. I.e. for a value of 0.05, in 5% of cases the study would find a positive result even though there really is no treatment effect.
• The magnitude of the effect of interest in the population: if the effect size is small, power will also be small.
• The sample size used to detect the effect: small sample sizes make effects harder to detect

## References

Cohen, Jacob. "Statistical power analysis." Current directions in psychological science 1.3 (1992): 98-101.