702 Journal oj Agricultural Research voi. 62, no. » 



The purpose of this investigatioa, however, was to develop an 

 equation with which, if the actual mean number of spores per field 

 is obtained with sufficient accuracy, the theoretical number of spores 

 per field may be estimated, thereby giving the data necessary for 

 estimating the number of spores per cubic centimeter in an unknown 

 sample of honey. The regression equation or the theoretical mean 

 number of spores per field can be used for this piirpose, and was found 

 to be Z=1.1228F+0.2034. Substituting for Y in this equation, the 

 various values of the actual mean number of spores per field, as 

 obtained in table 1, gave the most probable estimated values for the 

 theoretical mean number of spores per field that should be obtained 

 from the actual counts for each honey-spore sample (table 3). By 

 this method of estimation these- values were found to agree closely 

 with the original calculated values for the theoretical mean number 

 of spores per field for each honey-spore sample (table 2). 



DETERMINATION OF PERMISSIBLE LIMITS OF ERROR 



The analysis of the data so far indicates the accuracy of the method 

 outUned above for determining the most probable actual mean spore 

 count per field from the mean of 60 fields counted. Variations in the 

 counts may occur in individual samples, however, owing to the failure 

 to recover all the spores, as stated previously. 



The permissible limits of error in the statistical analysis of such 

 cases are customarily determined by use of the standard error of 

 estimate. This, for the most probable estimated actual means 

 derived from the theoretical means, was found to be small, ±0.1298 

 spore, and indicates the closeness with which new estimated values 

 may be expected to approximate the true but unknown values. Since 

 two of the five actual means fall within ±0.1298 spore of the esti- 

 mated actual means while the other three are only from 0.11 to 0.26 

 percent outside this zone, within which approximately two- thirds 

 of the observations may be expected to fall in relation to the most 

 probable values, a sufficient accuracy for the method is indicated. 



The standard error of estimate for the most probable theoretical 

 means derived from the actual means (which were found to agree 

 closely with the estimated actual means) was found to be ±0.1458 

 spore. As is to be expected in this case, again two of the original 

 theoretical means fall within the zone of ±0.1458 spore while the 

 other three are only from 0.11 to 0.25 percent outside this zone. 

 However, since ± 3 times the standard error of estimate, which should 

 include 99.7 percent of all observations, is used customarily in delin- 

 eating the largest error to which statistical analyses of this type are 

 subject, it is found that all the theoretical means fall well within this 

 zone, or within ± 0.4374 spore. This indicates the probable accuracy 

 of estimating the number of spores per cubic centimeter in an unknown 

 sample by calculating the most probable theoretical number of spores 

 per field from the actual mean number counted. 



PRACTICAL APPLICATION OF THE METHOD 



In a previous paper ^^ it was shown that during observations cover- 

 ing 5 years no cases of American foulbrood developed in 19 colonies 

 of bees fed less than approximately 50,000,000 spores of BaciUus 



" Stuktbtant, a. p. See table 1 of reterence In footnote 3. 



