No. 603] MENDELIAN CLASS FREQUENCY 155 



The actual experimental value obtained was 30, which 

 is far below the lower quartile. From Table II we find, 

 remembering again that on a priori grounds the experi- 

 mental frequencies are reduced by the factor 0.582, that if 

 the two distributions were really samples of the same 

 population, obeying the same Mendelian laws, it would 

 be expected that the x class would show a frequency as 

 low as or lower than 30, only 18 times in 10,000 trials of 

 samples of 9017. Or, in other words, the odds against 

 so low a value as 30 are about 556 to 1. These are about 

 the same odds as those associated with the occurrence of 

 a deviation 4.63 times the probable error (cf. Pearl and 

 Miner^*). 



We may, therefore, conclude with great certainty that 

 the value of 30 is significantly smaller than would be ex- 

 pected to occur in the x class on the basis of chance (de- 

 viation due to random sampling) if the two distributions 

 were really samples of the same population. 



Let us now go back and approach the problem de novo 

 by the approximate method suggested in section 4. We 

 have 



<Z = mean — mode = 1.4281, 

 L4281 ^ ^^g^ 



■84.4281- .4760 = 83.9521 = median (approx.), 

 12.0207 X .67449=- 8.1078, 

 83.9521-8.1078 =75.8443 = Lower quartile, 

 83.9521 + 8.1078 = 92.0599 = Upper quartile. 



Comparing these values, in the obtaining of which all 

 the tremendously tedious and time-consuming arithmetic 

 involved in calculating Table II was avoided, with those 

 shown in (ix) makes it quite evident that for all practical 

 statistical purposes the approximate method would have 

 given sufficiently accurate results. 



"Pearl, R., and Miner, J. E., "A Table for Estimating the Probable 

 Significance of Statistical Constants," Me. Agr. Expt. Stat. Ann. Eept. for 

 1914, pp. 85-88. 



