Fig. 7

Measurement of effect sizes across select proteins. A Distributions of normalized protein abundance. The mean and standard deviation for each distribution is marked by the center dot and line, respectively (note that these proteins were selected to illustrate relevant patterns that impact statistical power). The power for each of these proteins is determined by the overlap of distributions between PDR and control groups. Assuming both groups follow normal distributions, one can compare them quantitatively by considering (a) difference in means (delta PDR vs. control) and (b) a pooled standard deviation that characterizes their dispersions. B Scatter plot of protein delta (PDR vs. control) and dispersion. The product of these two coordinates defines the estimate of Hedges’ g relative effect size for each protein (absolute value of the delta considers only the magnitude of the effect). Highlighted proteins illustrate distinct patterns in protein delta and dispersion. C Estimated Hedges’ g effect size. The 95% confidence interval of the estimated effect is shaded in gray. As stated above, effect size estimators make specific assumptions about the data. In the Hedges’ g effect estimator, data from each group are assumed to be from a normal distribution where the standard deviations are free from systematic differences. For that reason, effect sizes and power calculations for a specific protein should also include a detailed examination of the actual distributions. Note that the distributions in A for protein CA2 appear to violate both these assumptions, so while these distributions appear to be distinct, the calculated effect size for this protein should be treated with skepticism (see Additional file 1). Effect size estimations were performed with the R library effsize (v0.8.1) [125]