Summary In spite of the lack of a natural basis for ordering multivariate data, we encounter an extension of univariate order concepts such as medians, extremes and ranges to the higher dimensional situation. Also, much multivariate theory, and method, exploits order properties in the data or model. We examine the role of ordering in these descriptive and methodological aspects of multivariate analysis by means of a four‐fold classification of sub‐ordering principles.

No abstract

No abstract

No abstract

S U M M A R YYields from five of the plots on the Park Grass Continuous Hay experiment at Rothamsted, started in 1856, were examined to see if any long-term trends could be detected over the last 100 years. Three of the plots examined are unfertilized; two receive inorganic nutrients every year; all are harvested twice a year. In 1959 the harvesting procedure was changed: yields for the periods before and after this change were examined separately and together. On none of the three unfertilized plots was the slope of the regression of total yield (i.e. first and second cuts combined) on time significantly (P < 005) different from zero in either the 1891-1958 or 1960-1992 periods. On both the fertilized plots, there were significant declines in yield with time over the 1960-92 period, assuming that the effects of autocorrelation are sufficiently small to be ignored; there were no consistent changes between 1891 and 1958. There were some significant trends on the five plots when the two cuts were considered separately.A linear regression model was fitted to the data in an attempt to separate the effects of meteorological variables (rainfall and sunshine hours over selected parts of the year) on total yield from possible long-term effects brought about, for example, by the increasing concentration of CO 2 in the atmosphere. On four of the five plots this model accounted for between 12 and 21 % of the yield variance in the pre-1959 period and between 45 and 63 % after 1960. On the fifth plot, which received the highest level of N, the model accounted for 29 % of the variance in the first period but only for 16% in the second period. When a linear trend with time was included in the model, this was not significant on any of the plots over the entire 1891-1992 period, although some significant trends appeared when the two periods were considered separately. The model was also fitted with the atmospheric CO 2 concentration in place of the linear trend with time: again there were no consistent trends.Neither changes in the concentration of CO 2 in the atmosphere over the last century nor increasing inputs of combined N in rainfall or in dry deposition have had any detectable effects on yield in these plots.