USE OF BIOMETRICAL ANALYSIS 719 



were not in general use in wildlife research. As the work progressed every effort was made to 

 subject each problem to the most thorough and critical analysis possible. At the same time 

 methods were being developed wherebv the significance of biological data could be judged 

 more precisely. As applicable techniques of this kind became available the Investigation has 

 used them. 



The results have added weight to the conclusions drawn. Substantiation has been given to 

 many relationships already recognized while new ones have been disclosed and some, appar- 

 ently valid by inspection, but found not to be statistically significant, have been discarded. 



The wildlife biologist, of necessity, must often work with samples of unknown quantities, 

 whether they be grouse populations, cover composition, food availability or weather. A fun- 

 damental characteristic of such samples is variability, i. e. repeated measurements of the same 

 thing seldom yield the same value. The greater the variability, the greater the number of 

 measurements that must be taken before a summation of the information will not be unduly 

 affected by an additional measurement that might, by chance, be either very low or very high. 

 Statistical methods have afforded a means of taking this aspect of the data into account in 

 analysing the records of the Investigation. 



Of paramount importance has been the fact that biomelrical analysis provides objective 

 criteria for evaluating the significance of relationships in terms of probability. In other words, 

 they make it possible to determine the degree to which a correlation may have occurred by 

 chance rather than from cause and effect. 



Significance 



To denote the degree to which chance may be involved three terms are used, namely, not 

 significant, significant, and highlv significant. These terms define three limits of probability. 

 Not significant indicates that the relationshi|i would be expected to occur more frequently than 

 once out of 20 times by chance alone: significant that it would occur not more than once out 

 of 20 times by chance; highlv significant that it would occur by chance not more than once 

 out of 100 times. 



The mathematical basis of statistics is not important li> the average field worker, but may be 

 found in standard text books'"' "*• "°. However, a brief discussion of the methods used in 

 analysing the data of the Investigation seems worthwhile. 



Chi-Square 



The chi-square test is designed to compare observed with expected or hypothetical values 

 and to determine the significance of departures therefrom. With sex ratios*, for example, 

 an expected ratio of 50 males to 50 females was assumed and the magnitude and consistency 

 of the recorded deviations from this ratio controlled the degree to which such differences 

 might be considered real. Chi-square was also used in evaluating cover type use. Here, 

 however, the determination of the "expected" values from which departures could be measured 

 constituted a preliminary problem'^. 



Analysis of Variance 



When data are taken in such a manner that the variability of a single factor can be segre- 

 gated into component ])arts. each traceable to an independent source, then the technique known 

 as analysis of variance may be used to test the significance of each. In preparing this re- 



* See Chapter VHI. 



A See discussion of Dclcrniining Sliellfi Relatioii^liips. p. Till, 



