Samples of 42 dura x pisifera progenies of Ekona, AVROS, Ghana and Nigeria oil palm varieties, each involving six pisifera, were used to determine the minimum sample size of their parents for obtaining statistical yield differences between varieties. The 95% confidence interval of differences between varieties decreased sharply and, hence, the precision of the test improved, when increasing the number of progenies from 6 to 30 and pisifera (involved) from 1 to 4 and then levelled off to a steady decrement. As a test of differences the confidence interval has only a power of 50%, being the probability that a false null hypothesis of zero difference between varieties is rejected. With a power of 80%, a sample of 60 progenies in three replications detects, depending on the variance of the pisifera parents, a significant yield difference of 4.5% between Nigeria and AVROS and 7% between Ghana and Ekona with 6 and 9 pisifera in the sample, respectively. The article argues to incorporate optimal planting density as a crucial trait in selecting oil palm varieties. This study offers a method to obtain unbiased progeny samples, along with a field lay out for bulk recording of progeny plots.