Coefficients of Variation, Error Variances, and Resource Allocation in Soybean Growth Analysis Experiments1

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Abstract
Treatment differences are usually difficult to detect in soybean (Glycine max (L.) Merr.) plant growth analysis studies because of large experimental errors. However, no estimates of error variances, coefficients of variation (CVs), treatment × environment interactions, or numbers of replications required to show treatment differences have been reported. This report describes the error variances and CVs from five soybean growth analysis studies (field and greenhouse) conducted in the southeastern USA. We use these data to develop calculations which aid in planning growth analysis experiments. For dry weight traits the average CV was 0.256 and ranged between 0.13 and 0.50. Based on the average CV value of the dry weight traits and assuming no treatment × environment interaction, an average of 3, 16, and 65 replications is required in order to detect 50, 20, and 10% treatment differences, respectively, for a single sampling date. The average error variance for percent N traits was 0.035 and ranged between 0.00636 and 0.366. Based on this average variance for percent N traits, an average of 2 and nine replications is necessary to show 0.4 and 0.2 unit differences, respectively, for a single sampling date. For multiple sampling dates and again assuming no treatment × environment interaction, the above values may be considered as the minimum value of replication number (per sampling date) × the number of sampling dates needed to show specified treatment differences. Treatment × environment interaction variances (5 to 10 % of error variance) were detected for some traits in the two experiments conducted over multiple environments. Although our data are limited, it appears that moderate treatment × environment interaction should be anticipated wben planning growth analysis experiments; i.e., one should expect to test in multiple environments for a reliable ranking of treatments. In that regard, the presence of treatment × environment interaction variance (10% of error variance) indicates that testing in at least two environments is necessary to detect 20 % treatment differences, and that testing in at least seven environments is necessary to detect 10% treatment differences. There is no unique combination of environment, replication, and sampling date which is required for detecting specified treatment differences, however. Charts and tables are presented as an aid in determining combinations of environments, replications, and sampling dates which should enable detection of treatment differences. From these combinations, a researcher can choose an allocation of resources which will fit a program budget and also give reasonable chances for detecting treatment differences. It is efficient to have the number of test environments as large as is practicable. Only two of the five experiments reported here had the precision needed to detect 20 % treatment differences when moderate treatment × environment interaction was present.