34 



THKORV OV STATISTICAL KEDUCTIONS. 



IX. R. A. FiSHKK. "On the Mathematical Foundations of 



Theoretical Statistics/' Philosophical Transactions of 

 the Royal Society, 1922. Vol. CCXXII. pp. 309-368. 



The main desideratum in the statistical reduction of data is 

 that the statistics calculated shall include the whole of the informa- 

 tion supplied by the data. It has been possible to put this 

 requirement in a mathematical form, and so to lay down general 

 conditions for the complete exhaustion of the data ; in particular 

 it is possible to ascertain for any special statistical method pro- 

 posed, of what percentage of the total information available it 

 makes use. Many such tests are applied to current statistical 

 methods, and in particular to the estimation of the numbers of soil 

 protozoa by the dilution method. 



KAlNi-ALL IN BRITAIN. 



X. R. A. F'iSHEK and W. A. Mackenzie. "The Correlation 



of Weekly RainiaU." Quarterly Journal of the Royal 

 Meteorolog-ical Societv, 1922. Vol. XLVIII. pp. 

 234-242. 



To study the effects of weather on crop production by means of 

 simultaneous crop and weather records from different parts of the 

 country, and thereby to reduce the number of years required for 

 the accumulation of data comparable with the existing- Rothamsted 

 records, it is necessary to know the correlation between the 

 meteorolog-ical records of different stations. Such information is 

 also necessary in repairing- defective records from those of neigh- 

 bouring- stations, as also in estimating- weather conditions over 

 local areas, such as river basins. This paper is a study of records 

 from Aberdeen, York, and Rothamsted in respect of weekly 

 rainfall. Even Rothamsted and Aberdeen 375 miles apart show a 

 distinct positive correlation (average value .3717) in rainfall; the 

 intermediate station, York, 150 miles from Rothamsted, and 225 

 miles from Aberdeen, gives average correlations .5898 and .5275. 

 All three comparisons show well marked annual oscillations, the 

 rainfall being most uniform in winter and least so in the early 

 summer. Meteorologists suggest two possible causes for this 

 novel phenomenon : (i.) the summer prevalence of local thunder- 

 storms, (ii.) the more northern track of the summer cyclones. 

 Whatever its cause, it is apparent that simultaneous crop and 

 weather observations will throw light especially on the effects of 

 summer rain or drought. 



PREDICTION FORMUL.^. 



XI. R. A. Fisher. "The Goodness of Fit of Regression 



Formula and the Distribution of Regression Co-effi- 

 cients." Journal of the Roval Statistical Societv, 1922. 

 Vol. LXXXV. pp. 597-612. 



Statistical predictions are based upon regression formulae, and 

 their importance required that the correction established in Paper 

 No. VI IT. (see above) should be applied in detail to such cases. It 



