Determining the Appropriate Transformation of Data from Insect Control Experiments for Use in the Analysis of Variance

Abstract

The procedure used to determine the appropriate transformation of insect control data consisted of testing the untransformed data for fulfillment of the basic assumptions underlying the analysis of variance procedure and its related tests of significance. The data were tested two more times, once when the data were transformed to the square-root scale and once when transformed to the log scale. A nonparametric, rank-correlation coefficient was computed for the ranges and means of each set of data for evidence of normality. A nonsignificant coefficient was an indication that the ranges and means were independent of each other, thus indicating normality of the data. After normality had been established, Bliss and Calhoun’s modification to Hartley’s test for heterogeneity of variance and Tukey’s test for nonadditivity were computed for each set of data. A set of data was considered appropriate for use in the analysis of variance when the data fulfilled the basic assumptions of the analysis procedure. For illustrative purposes this procedure was used on two control experiments, one on the potato leafhopper ( Ernpoasca fabae (Harris)) and one on the alfalfa snout beetle ( Brachyrhinus ligustici (L)) larva. The leafhopper data transformed both to the square-root and log scales were found to fulfill the assumptions while a log transformation appeared to be the best scale to use for the snout beetle data.