33 



However, in the event of any serious deficiency such as an in- 

 adequate nitrog^en supply, or a prolonged application of ammonium 

 salts only, the influence of the manurial treatment becomes the 

 most important factor and the flora undergoes modification of a 

 similar nature irrespective of the methods of cultivation. In such 

 cases a pereimial type of weed, as Equisetum arvense, Tussilago 

 farfara or Cirsium arvense, was invariably found to predominate. 



Comparisons are between with the weeds recorded in 1867 on 

 Broadbalk and Hoos fields and those found at the present day. 

 Considerable reduction in the number of species has taken place in 

 the former case, while changes in the individuals comprising the 

 flora have occurred on both fields. 



The distribution and relative abundance of species and 

 individuals are also described in the case of Broadbalk field. 



METHODS OF STATISTICAL EXAMINATION AND 

 RESULTS. 



STATISTICAL TREATMENT OF SMALL SAMPLES. 



VII. R. A. Fisher. "On the 'Probable Error' of a Co- 



efficient of Correlation deduced from a small Sample." 

 Metron, 1921. Vol. I., No. 4. pp. 1-32. 

 Agricultural experiments deal almost invariably with a number 

 of replicated plots, or parallel experiments, which is statistically 

 small ; approximate methods suitable for large samples are there- 

 fore liable to break down, and to lead to erroneous conclusions. 

 This paper gives the exact form of distribution for correlation co- 

 efficients obtained from small samples. By changing the scale 

 upon which the correlation is measured, correlations from small 

 samples may be treated with accuracy, and at the same time 

 corrected for the small bias which is introduced by the standard 

 methods of calculation. 



AGREEMENT OF THEORY AND OBSERVATION. 



VIII. R. A. Fisher. ''On the Interpretation of x", from 



Contingency Tables, and the Calculation of P." 

 Journal of the Royal Statistical Society, 1922. Vol. 

 LXXXV. pp. 87-94. 

 Statistical tests of the agreement of series of experimental 

 observations with any hypothesis, by which it is intended to inter- 

 pret them, may be carried out by calculating the statistic ^^^ which 

 measures the discrepancy. The distribution of -y^^, when the 

 hypothesis tested is in fact true, can be calculated, and in this 

 manner cases in which the discrepancy is excessive may be 

 detected. In this paper it is shown that when the data to be 

 tested have been used to construct the hypothetical expectation it 

 is necessary to adopt a more severe test of agreement than that 

 previously in use. This change of procedure, which particularly 

 affects tests of independence in contingency tables, and of the 

 goodness of fit of theoretical curves, may be simply and accurately 

 effected by taking account of the number of degrees of freedom in 

 which observations may differ from expectation, instead of merely 

 the number of frequency classes. 



C 



