Statistical methods have not been described for comparing estimates of family-mean heritability (H) or expected selection response (R), nor have consistently valid methods been described for estimating R intervals. Nonparametric methods, e.g., delete-one jackknifing, may be used to estimate variances, intervals, and hypothesis test statistics in estimation problems where parametric methods are unsuitable, nonrobust, or undefinable. Our objective was to evaluate normal-approximation jackknife interval estimators for H and R using Monte Carlo simulation. Simulations were done using normally distributed within-family effects and normally, uniformly, and exponentially distributed between-family effects. Realized coverage probabilities for jackknife interval (2) and parametric interval (5) for H were not significantly different from stated probabilities when between-family effects were normally distributed. Coverages for jackknife intervals (3) and (4) for R were not significantly different from stated coverages when between-family effects were normally distributed. Coverages for interval (3) for R were occasionally significantly less than stated when between-family effects were uniformly or exponentially distributed. Coverages for interval (2) for H were occasionally significantly less than stated when between-family effects were exponentially distributed. Thus, intervals (3) and (4) for R and (2) for H were robust. Means of analysis of variance estimates of R were often significantly less than parametric values when the number of families evaluated was 60 or less. Means of analysis of variance estimates of H were consistently significantly less than parametric values. Means of jackknife estimates of H calculated from log transformed point estimates and R calculated from untransformed or log transformed point estimates were not significantly different from parametric values. Thus, jackknife estimators of H and R were unbiased. Delete-one jackknifing is a robust, versatile, and effective statistical method when applied to estimation problems involving variance functions. Jackknifing is especially valuable in hypothesis test estimation problems where the objective is comparing estimates from different populations.