Fig 1.
A. Distributions of observations and sample means across 8 observations for the African American actor condition (solid line) and White actor condition (dashed-line). B. Distribution of the measurement tool, the difference in sample means. The vertical line is the zero estimator. C. Distribution of the absolute error for the sample mean measurement tool. The root-mean-squared error is 7 times greater for the sample mean tool than the zero estimator.
Fig 2.
True values, data, sample means, and a Bayesian hierarchical shrinkage estimates are shown. The shrinkage estimates are more accurate in this case as well as on average across repeated samples from the true values.
Fig 3.
Mean-square error for the sample mean and the random estimator for 10 observations in each of four conditions.
Each point shows the result from a simulation repetition, and there are 10,000 such repetitions. Contours are bivariate kernel density estimates. The large point is the mean of MSEs across repetitions. This mean for sample means is 40% larger than the mean for the random estimator, and 63% of samples show larger MSE for the sample mean.
Fig 4.
A. Minimum sample size (per condition) for minimal acceptable accuracy of the sample mean as a function of effect size f2 and the number of conditions. One of the more noteworthy aspects is that the needed sample size per condition increases with the number of conditions. B. Minimum sample size (per condition) for a power of 50% at the 5% level. The needed sample size per condition decreases with the number of conditions. C. The power at the 5% level for the minimum sample size for minimal sample mean accuracy. Surprisingly, commonly powered designs often yield unacceptably accurate sample means.