Vol 120 (2007): Proceedings of the Florida State Horticultural Society

Power analysis of on-farm fertilizer trials with tomato

Eric Simmonne
University of Florida
Published December 1, 2007
  • best management practices,
  • alpha,
  • beta,
  • type I error,
  • type II error


With the development of best management practices for vegetables grown in Florida, fertilizer recommendations try to balance profitability with environmental stewardship. When analysis of variance fails to reject the null hypothesis in two-rate fertilizer trials, power analysis should be used to determine the level of risk taken in accepting the null hypothesis that yield are the same with two rates. Analysis of variance of yield components of five on-farm tomato (Solanum lycopersicum L.) trials found significant differences 25% and 36% of the time for single grade and cumulative yields, respectively. Single grade and cumulative yield variances were 75% and 15% of the time <5 25-lb boxes/acre, respectively. For cumulative yields, 80% of variances were 5 to 15 25-lb boxes/acre. Retrospective power analysis showed power overall ranged between 0.20 and 0.66 when variance was 5 to 10 25-lb boxes/acre, and when four replications and an economical yield difference of 10 25-lb boxes/acre were used. Under current field conditions (four replications, variance between 0 and 20 25-lb boxes/acre), a difference of 50 25-lb boxes/acre may be detected with a power of 0.80. Prospective power analysis showed that power may be increased to at least 0.80 when a yield difference of 50 25-lb boxes/acre and a variance <20 25-lb boxes/acre are used or when the number of replications is increased to six and the variance is <5 25-lb boxes/acre. Further discussion and consensus are needed to identify a power value that well balances type I and type II risks in fertilizer trials.