Compare the mean of a continuous measurement in two samples. This calculator determines sample size given clinically significant effect size and allows for clustered sampling. Although the t-test will be used to compare the means, this calculator approximates the t-statistic with the z-statistic.
Instructions: Enter parameters in the red cells. Answers will appear in blue below.
Step 1: Calculate sample sizes without adjustment for clustering
Step 2: Calculate sample sizes with adjustment for clustering
Your study has either:By fixing the number of clusters (C_{1}), you limit the value of ρ. The larger C_{1}, the larger ρ can be.
q_{1} = | 0.500 | Proportion of subjects that are in Group 1 (exposed) |
N_{1} = | 0.00 | Size of group 1 (without adjustment) |
C_{1} = | Number of clusters in Group 1 (must be at least 1 and less than N_{1}) | |
ρ = | Within-cluster correlation coefficient (must be greater than 0 and less than C_{1}/N_{1} = 0.000) |
Cluster size = m = (1-ρ)/((C_{1}/N_{1})-ρ) =
Design Effect = 1+(ρ(m-1)) =
m (rounded):
N'_{1}:
N'_{0}:
N'_{total}:
With a fixed cluster size, ρ can take any value between 0 and 1.
N_{total} = | Total group size (without adjustment) | |
q_{1} = | 0.500 | Proportion of subjects that are in Group 1 (exposed) |
m = | Cluster size | |
ρ = | Within-cluster correlation coefficient (must be greater than 0 and no greater than 1) |
Design Effect = 1+(ρ(m-1)) =
Clusters in Group 1 = C_{1} = N_{total} * Design Effect * q1 / m =
Clusters in Group 0 = C_{0} = N_{total} * Design Effect * q0 / m =
N'_{1}:
N'_{0}:
N'_{total}:
Because the formula used here is based on approximating the t statistic with a z statistic, it will slightly underestimate the sample size when N is less than about 30.
Reference:
Donner A, Birkett N, Buck C. Randomization by cluster. Sample size requirements and analysis. Am J Epidemiol 1981;114:906-14.