A TAB'LE FOR ESTIMATING THE PROBABLE 

 SIGNTFIOANCE OF STATISTIOAL CONSTANTS.* 



By Raymond Pe;arl and John Rice Miner. 



The use of biometric methods in biology and related applied 

 sciences is beooming all the time more general. The increasing 

 Cise of this technique is not, 'hoiwever, entirely free from doubt- 

 ful features. Biometric methods and biometric conclusions per 

 se are not infallible. To use them safely and profitably de- 

 mandls a clear understaniding O'f this real meaning, so that a 

 speoious air of profundity and infallibility may not be given to 

 results which in reality lack these qualities. The present note 

 is offered as a slight numerical aid to sanity and conservatism 

 in statistical investigations. 



One of the most important O'f the contributions of biometry 

 is its insistence on the "probable error" as a test of the probable 

 validity of conclusions. This is an entirely commendable ten- 

 dency. But there has grown up a certain conventional way of 

 interpreting probable errors, which is accepted by many workers, 

 not all of whom are beginners, without any critical examination 

 of the real basis of the conventional usage. It 'has been prac- 

 tically a universal custom amongst biometric workers to say 

 that a difference (or a constant) which is smaller than twice its 

 probable error is probably not significant, whereas a difference 

 (or constant) which is three or more times its probable error is 

 either "certainly" or ait least "almost certainly" significant. 



Now such statements as these derive whatever meaning they 

 ■may possibly have from the following simple matliematical con- 

 siderations. Assuming ** that the errors of random sampling 

 are distributed strictly in accordance with the normal or 



* Papers from the Biological 'lyaboratory of the Maine Agricultural 

 Experiment Station, No. 63. 



** In the present connection we are in no way concerned with the gen- 

 eraHty or degree of validity of this assumption. It has been extensively 

 and adequately dealt with by Pearson and his students in many papers. 

 In most cases this assumption is sufficiently accurate for practical pur- 

 poses. 



