Quantifying variation by the ratio of CSS to UCSS

Abstract

AbstractThe variance, the average of squared deviations of data values from their mean, is the most widely used criterion for measuring the variation. Small amounts of the variance indicate that the values tend to be close to the mean and its high amounts are indicative of more dispersion around the mean. However, when dealing with a single variable or variables with different measuring units, variance can not give us a proper understanding of the actual extent of variation. RCU, the ratio of corrected sum of squares (CSS) to the uncorrected sum of squares (UCSS) can quantify variation too. The values of RCU vary from zero, for a situation in which all values are the same, to 100 % when they are completely different or symmetric. To compare the efficiency of RCU and variance for measuring variation, data of seven variables with different units of measurement for 17 wheat cultivars including yield (g/plant), spikes (numbers), height (cm), earliness (days), viability (%), hectoliter (kg/hectoliter) and EC (micromohs/cm) were used. Variance of these variables respectively was 83.34, 72.01, 353.23, 81.48, 5.31, 69.52 and 7167.47. The highest and lowest RCU was obtained for spikes (9.38 %) and viability (0.05 %), respectively. The RCU for yield, height, earliness, hectoliter and EC was 8.97, 2.67, 0.29, 1.30 and 2.85 %, respectively. The RCUs were somewhat similar to coefficient of variation of the variables. Based on the RCU, the extent of variation was medium for spikes and viability and was low for the other variables. As a result RCU could be used as a simple criterion to quantify the actual extent of variation in the data.AbbreviationCSScorrected sum of squaresUCSSuncorrected sum of squaresRCUthe ratio of CSS to UCSSCVcoefficient of variationVARvariance