Analysis and interpretation of forest fertilizer experiments (1988)
AuthorsWoollons, R. C.show all
Sir Ronald Fisher's contributions to the design and analysis of field experiments have had a profound influence on the quality of forest fertilizer trials. Nevertheless, forestry experiments have unique features which are not always amenable to adoption of the routine analytical methods that are discussed and illustrated in many statistical texts. The aim of this thesis is to explore the nature and statistical standards appropriate for the analysis of forest fertilizer trials. The general linear model (GLM), embracing the techniques of analysis of variance, covariance, and regression analysis, represents a powerful tool with which to analyse forest nutrition experiments. An examination of pertinent literature reveals, however, that substantial numbers of forestry researchers have difficulty in applying GLM methodology to forest trial data. Indeed, there is clear evidence that some scientists are unaware of the utility of covariance as a means of removing the confounding effect of differences in initial plot growing stock; other researchers fail to extract all the data inherent in forest trial data, while a few advocate abandoning GLM methodology altogether, claiming it to be an insensitive tool for analysing forest fertilizer experiments. Re-analysis here shows how inappropriate some of these published results and claims are. A system of analysis is presented which is considered a reliable and sensitive procedure for examining later-age forest fertilizer trials. For non-factorial layouts, the method employs applications of regression analysis, allowing responses in each treatment to be represented by a unique intercept and regression slope. Tests of hypotheses are introduced to determine the need for disparate slopes and independent intercepts; alike parameters are pooled to achieve a minimum available residual error. Secondary covariates such as stand competition or plot fertility values are added to models whenever pertinent, to decrease experimental errors further, and to aid interpretation of trial results. Factorial experiments are analysed very similarly, but utilizing factorial linear models and (multiple) covariance. Appropriate manipulation of response variables and covariates is integral to the recommended system. The use of yield or growth as a response variable is demonstrated to give essentially equivalent results. Adoption of average yield per tree often achieves a more decisive analysis than with per hectare variables. Use of weighted least-squares can aid the interpretation of trial results when some plots have been partially damaged. The presented system is tested by examining data from eight later age (some long term) fertilizer trials established by N.Z.Forest Products Limited. Analysis and derived results completely vindicate the value of the proposed methodology; in particular, use of two covariates increases precision in some analyses by up to 76%. The analyses irrefutably confirm the potential of nitrogen fertilizer to boost yields in thinned Pinus radiata stands belonging to the Company. These responses are demonstrated to be associated frequently with significant, but small and transient changes in stand form-factor. Examination of the basal-area responses in each of the eight experiments highlights the fact that point estimation of fertilizer gain is inadequate for management planning and forecasting; yield tables of nutrient response are required, expressed as quantity of wood that can be realised in the future. The desired form can sometimes be achieved by modelling trial data to obtain a growth and yield model, then applying suitable realisation factors. Such a simulator has therefore been derived for the N.Z.Forest Products data, recognising variable inputs of fertilization, initial basal-area, initial stocking, and stand competition; experimental fertilizer response is estimated to be about 110 m³/ha by age 30 years. The suggested methodology has several implications for fertilizer trial experimental design as well as analysis; thus, it is now recommended that trials should be installed deliberately with a range of initial plot growing stock and to contain treatments which are distinctly different in their composition. Also, because multiple covariance is demonstrated to be a powerful technique to obtain good precision and additional information in later-age forest fertilizer trials, care must be taken to collect prior initial information about the trial material.