Points of significance: Power and sample size

Points of significance: Power and sample size

    Martin Krzywinski  
    & Naomi Altman  

    Nature Methods
    10,
    1139–1140
    (2013)
    doi:10.1038/nmeth.2738

http://www.nature.com/nmeth/journal/v10/n12/full/nmeth.2738.html

Figure 3: Decreasing specificity increases power.

(a) Observations are assumed to be from the null distribution (H₀) with mean μ₀. We reject H₀ for values larger than x^* with an error rate α (red area). (b) The alternative hypothesis (H_A) is the competing scenario with a different mean μ_A. Values sampled from H_A smaller than x^* do not trigger rejection of H₀ and occur at a rate β. Power (sensitivity) is 1 − β (blue area). (c) Relationship of inference errors to x^*. The color key is same as in Figure 1.

Figure 4: Impact of sample (n) and effect size (d) on power.
 

H₀ and H_A are assumed normal with σ = 1. (a) Increasing n decreases the spread of the distribution of sample averages in proportion to 1/√n. Shown are scenarios at n = 1, 3 and 7 for d = 1 and α = 0.05. Right, power as function of n at four different α values for d = 1. The circles correspond to the three scenarios. (b) Power increases with d, making it easier to detect larger effects. The distributions show effect sizes d = 1, 1.5 and 2 for n = 3 and α = 0.05. Right, power as function of d at four different a values for n = 3.