We will perform assays on 56 participants who contributed blood samples at waves 1, 3, and 4. We will select two groups (n=28) below and above poverty matched by 5-year age group (30-34, 35-39, etc), sex, and race.
Metabolomics & lipidomics are new areas. There's no literature to guide us in establishing an expected effect size. Consequently, we need to make some assumptions. There are two crucial parameters in calculating power for longitudinal comparisons: the expected effect size and the correlation of measures over time.
There's general agreement that 0.2 is a small effect, 0.5 is a medium-sized effect, and 0.8 is a large effect based on Cohen (1988).
Although these adjectives are subject to misinterpretation, the levels are widely accepted in most areas.
Effect size describes the size of the difference between two groups in standardized units. Unlike statistical significance, effect size does not depend on sample sizes.
Sample size requirements increase as the correlation over time increases. Put another way, fewer samples are required when correlations over times are smaller.
Oddly, power and sample size does not depend on the time interval between measures.
Diggle et al (2002) derived the method for computing sample size per group in a longitudinal study.
For assays somewhat weakly correlated over time (r = .25), we would require 31 participants per group for 80% power. For assays more highly correlated over time (r = .50), we would require 41 participants per group for 80% power.
The plot below shows power as effect sizes and correlation between times vary. We're unlikely to detect small effects (blue lines). We have better chances at detecting medium-sized effects particularly if the correlation over time is no greater than .5.
For 28 participants per group (gray line), we have about .7 power to detect a medium-sized effect with measures correlated <.5 over time.
Cohen, J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale, NJ.: L. Erlbaum Associates; 1988.
Diggle PJ, Heagerty PJ, Liang KY. Analysis of Longitudinal Data. 2nd ed. Oxford University Press; 2002.