For more realistic descriptions, numerical solutions are required, although recent advances allowed for a unified model to describe the optical path change, regardless of the sample thickness, assuming a sample of infinite radius.
Assuming a sample of 600 subjects in each of the two arms, an intra-cluster correlation of 0.05 and an average cluster size of 55 resulted in an estimated design effect of 3.7, thus reducing the effective sample size to 162 for each arm.
Assuming a sample size of 80 per group, and r (correlations between waves of data)=0.5, 0.6 and 0.7, the resulting estimates of effect sizes are δ=4.71, 4.21 and 3.65, thus demonstrating that a medium effect size (Cohen's d=0.37 to 0.48) could be detected with this sample size.
We had 82 and 78%% power to detect an odds ratio of 1.12 and 1.25 for the effects of height and BMI on prostate cancer risk, assuming a sample size of 41,062 and that the genetic risk scores explained 6.31 and 1.46 % of the variation in height and BMI, respectively [ 29].
Assuming a sample size of 416 in each group, the trial will have in excess of 95% power for each pairwise comparison to detect a difference of 7.5% in the percentage of gingival sites that bleed on probing.
Assuming a sample size of 600 families (300 per arm), allowing for a 20% dropout, a two tailed α of 0.05 and no clustering effects, there is 95% power to detect a 25% change in tooth brushing frequency.
Computed statistical power for the reading (a) and spelling (b) analyses, given a certain β-coefficient and minor allele frequency (MAF) and assuming a sample size of 500 participants.
Assuming a sample volume of 4.5 × 10-5 l, 100% reverse transcription efficiency, and an average strand length of 1000 we calculate the rare species concentration as ~0.1 pM, intermediate species concentration ~1 pM and abundant species concentration ~20 pM.
After this new calculation, 68 very-severe patients were required, assuming a sample size of 128 patients with moderate and 128 with severe COPD (95% reliability, one-sided test, 10% dropout rate).
Assuming a sample size of 600 families (300 per arm) considered feasible for recruitment, and allowing for a 20% drop out, a two tailed α of 0.05 and no clustering effects, there was 95% power to detect a 25% change in tooth brushing frequency.
The total depth range was measured to be ~2.8 mm in air (which is equivalent to 2.1 mm in biological tissue, assuming a sample refractive index of ~1.35) and the power incidence on the sample was measured to be ~1mW.
