CAKI) TUAXSLATOli KXl'KlilMEXTS 397 



ing an oiToct (luitc diftVivnt from that of the six (hgit cards wlicn tho 

 four variables, Bins, Runs, Loads, and Position are allowcHl to \ary. 

 Sinee the ratio of the mean s(iuare of variables of lines !i, 10, I 1, and 12 

 of Table XII to mean scjuare for experimental erroi' is significantly large, 

 in the same way lines 13 and 14 show that the effect of Idler loads is not 

 independent of the Bins and Panis effects. Statistically then, we have 

 isolated many significant effects, but note that our experimental error, 

 (t\ for samples of four readings is 0.95 ms" and a is then 0.975 ms. 



If we compare two means Xi and x-> each based on N samples of four 

 observations each w(> will detect as significant, differences as small as 



= ^V^ 4-095 



\\'hen N is large we will, therefore detect as significant, differences which 

 may be of no interest engineering-wise. Thus not only is the significance 

 of the effects of interest but also the magnitude of the effect. 



When the component of variance attributable to each of the sig- 

 nificant effects is estimated only four are so large as to be of interest to 

 the engineer. The four variables are Idlers, Runs, interaction of Idlers 

 on Runs and Bins. The estimates of the components of variance, ^-effect , 

 are obtained by equating the linear combinations of the components of 

 variance shown in the right hand column of Table XII to the mean 

 squares which estimate them and solving. 



The component estimates are: 



0-2 



III. SOURCES AND MEASURES OF ERROR 



In any experiment a decision must be made as to the number of ex- 

 perimental units to be measured and the number of repeated measure- 

 ments to be made on each unit.^ It is important to note that measure- 

 ments made on the same unit and a measurement made on each of 

 several units give rise to two distinct sources of variation, and that both 

 of these should be estimated. Consider making n measurements on each 

 of /.• units, where the k units are a random sample of units belonging to a 

 normal universe with mean u and variance 0-5 . Further a set of measure- 

 ments on the i' unit is a random sample of measurements from a normal 

 universe of measurements with mean Ui and variance a^ . Clearly, if 



