SummaryThe sampling distributions of the more important statistical derivates from the multivariate t·distribution are established.
SummaryThe relationship between the yield of wheat and seasonal rainfall in South Australia has been determined. The period chosen for examination was 1896-1941 and the analysis extends to practically the entire wheat belt of the State, all major soil groups and variants of climatic conditions within the area being represented. Yield was assessed using the hundred, which has an average area of approximately 118 square miles, as the basic territorial unit. Seasonal weather was represented by the rains in three subdivisions of the growing period of the crop, and these were taken as independent variates in an analysis by multiple regression. The regression of yield on rainfall, when considered as a,function of time, takes a mathematically simple parabolic form with a maximum in winter and zeros in autumn and spring or early summer, and the coefficients obtained provide a clear demonstration of the sub-optimal character of average seasonal rainfall over the greater part of the season and almost throughout the wheat belt. The conclusions drawn from the general survey are substantiated by analyses of a limited number of exact records.
SUMMARYA detailed analysis of the rainfall of Adelaide, South Australia, has shown that throughout the gj years 18391933 there has been a definite oscillation, with a period and amplitude of approximately 23 years and 30 days respectively in the incidence and duration of the winter rains. The amplitude, though small, is nevertheless about 2 0 per cent of the length of the rainfall season. The total quantity precipitated has shown no statistically significant changes. I STRODUCTORYThe general characteristics of the Australian rainfall with respect to geographicaI and seasonal distribution and reliability have been the subject of numerous investigations by different workers. In dealing with the broad mass of data, only the simpler statistics are normally made use of, but it was considered desirable t o ascertain how far recent methods developed by Professor R. A.Fisher ( I ) could be applied to the specific case of the rainfall record of Adelaide, particularly as a clearer knowledge of its characteristics is of some considerable value from the point of view of agricultural production. DATAOn January Ist, 1839, Sir George Kingston established a daily rainfall record in Adelaide on a site approximately 500 yards from the present position of the Observatory. This record was continued until November, 1879. From May, 1860, to the present day, the readings hate been taken a t the Observatory so that over 19 years the two sets of observations were concurrent. During this interval the average annual difference between the gauges was 0.26 inch (Kingston's being the higher), and considering the proximity of the sites it may be taken that the two series in combination give a continuous and practically uniform record of the Adelaide rainfall.No definite statement could be found as to the diameter of the gauge employed by Kingston, nor, in fact, the size of the gauge used in the early days of the existence of the Observatory. It is fairly certain, however, that no radical departure could have been made from the standard 8 in. gauge which has been in use since I 870. SECULAR VARIATION OF THE RAINFALL AT ADELAIDEIt is noteworthy that this record is probably unique, both with respect to its continuity and length, and constitutes valuable material for statistical analysis.At this juncture a word might be added on the character of the climate. The most prominent feature is the marked winter incidence of the rains. Approximately 7 & per cent of the annual precipitation, the average of which is in the neighbourhood of 2 1 in., occurs within the period April to October, the summer months being characterised by hot dry atmospheric conditions, low rainfall and high evaporation. ANALYSISThe method employed in this analysis was devised by R. A. Fisher (Zoc. cit.) and in brief consists of the following steps.The rainfall of each year was divided into 61 six-day totals and to these was fitted a series of orthogonal polynomial functions of the fifth degree in time, thus furnishing six constants with which to express the quantity and distribut...
SummaryThe history of the wheat industry in South Australia is reviewed to provide a background for discussion of the fomls of trend observed in yield. The period chosen for examination was , and the analysis extends to practically the entire wheat belt, the basic territorial unit used for assessing yield being the hundred, the mean area of which in South Australia is approximately 118 square miles. As a preliminary to the evaluation of the trends it was necessary to estimate and to eliminate the effects of variations in seasonal rainfall; the statistical technique used was that of partial regression, and reasons are given for the choice of rainfall variates.The major soil groups under cultivation are described and mapped. The elimination of phosphorus as a limiting factor in yield coincided with the beginning of the period under review, so that in classifying the forms of trend observed it was convenient to divide the hundreds into two groups, according to whether they were opened for cultivation before or after the advent of superphosphate.The nitrogen status of the major wl1eat soils is discussed, and after consideration of relevant literature, it is concluded that the nitrogen required by the crop has been drawn almost entirely from soil reserves under the exploitative systems of cropping generally employed. The wheat belt is broadly divisible into three parts:l. Sandy, stony, and mixed mallee soils and related types in which nitrogen becomes limiting after 20-40 years of cropping, and yields subsequently decline owing to exhaustion of the reserves. 2. Loamy mallee soils and red brown earths, where yields increase over the period , but at diminishing rates as nitrogen becomes limiting. 3. Sandy and loamy mallee and transitional mallee-solonetz soils, where yield increa;es linearly throughout, mainly because exploitative cropping has not been in progress long enough to make its influence apparent. These regions constitute only a small proportion of the total area.The economic restoration and maintenance of the nitrogen status of the wheat soils are discussed briefly.
SummaryA detailed analysis of the rainfall of Adelaide has established that periodic changes occur in the incidence and duration of the winter rains. These changes have a period and amplitude of approximately 23 years and 30 days respectively, and superimposed on them is a long-term trend which is manifested by protraction of the latter half of the season, spring rains now occurring about 3 weeks later than they did just over 100 years ago. The total quantity of rain precipitated has shown no statistically significant changes.
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