Research Note:<br>Precision and accuracy of sward height distributions

Abstract

Double normal distributions can be used to resolve many sward height frequency distributions into two components representing the 'short' (patches) and 'tall' (non-patches)areas in the sward. The effect of sample size on the precision and accuracy of parameters of sward height distributions was examined by drawing sub-samples (n = 10) of increasing sample size (50 to 1 000) from simulated height data (n = 10 000) from three different, typical height distributions, viz. normal (ungrazed), bimodal (leniently grazed) and positively skewed (intensely grazed). The coefficient of variation of components of all three distributions decreased sharply with increasing sample size and CVs for all means were <15% with 200 height measures, and <10% for all means, with the exception of the 'tall' mean in the bimodal distribution, at a sample size of 100. At a given sample size, proportions in the two components were less-precisely measured than the means, especially when the components are equally represented in the population (i.e. bimodal), where 500 measurements are required for a precision of 15%. Accuracy also increased with sample size, and with 400 samples, deviations were within 10% of the true values for most parameters of the three distributions. A sample size of 200 is recommended for quantifying the mean height of 'short' and 'tall' components of the sward whereas 400–500 samples are required to precisely estimate their relative proportions.

Keywords: Double normal distribution, maximum likelihood estimation, patch grazing, sample size, sward structure

Keywords: Double normal distribution, maximum likelihood estimation, patch grazing, sample size, sward structure. African Journal of Range & Forage Science 16(l&2): 122–125