"t 
et S 
  
  
  
samples, we can assess the significance of all the interactions, and in the meanwhile 
obtain further information about the main effects, by analysing all the data 
together. We thus have three main effects, F, T' and t, and the interactions FT, 
Tt and tF, and a residual. This analysis of variance is in Table 10. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Table 10 
| SS. | d.f. M.S. | 
A = 3s a a Le 
 Between-t ir anos [ned = 3. 12.43 PE DZ | o 
TF Interaction 50140 (ny—1) (np—1) - 6 835702 (opp?| |o mo 
inion 1598 (000) = 9 87 0 oo 
MT Interaction | 37.89 |(n—1) (ny—1) =" 6.32) 0,2 ump” Or, 
Residual ~~ | 7212 m—005—0 (=) = 15) 4010? [ener 
Total | 1817.67 npnn—1 = 47 mr 
  
To ease the interpretation of this analysis, the components of variance are 
given on the right hand side of the Table: The variances or^, or? and 0°? measure 
the fluctuations of shrinkage due to the three factors covered by the experiment, 
namely the type of film, the temperature at which it is stored and the period of 
storage. There are also the terms orr^, or? and oi? expressing the interactions of 
these three factors. The practical asset of the method of analysis resides in the 
fact that the significance of any of the variances and interaction terms can be 
assessed, on any probability level, by comparing suitably chosen mean squares. 
The component variance or” describes the temperature changes which are 
common to all types of film, and all periods of storage. Similarly or^ describes 
the variation of shrinkage from one type of film to the other which can be 
distinguished at every storage temperature and period under consideration. The 
common effect of storage time is similarly represented by the component variance 
61”, It may happen that the effect of temperature, for instance, changes from film 
to film; orr? represents this effect, the time factor being held constant. The same 
term describes the change of shrinkage variation among films due to changing 
the temperature. The order of the subscripts is therefore immaterial. This applies 
to all the interaction terms. The terms oz? and o; are similarly introduced to 
measure the extent to which the storage period influences the temperature effect 
and is influenced by the type of film, respectively. Finally, the interaction term 
opp? estimates the effect of the choice of one factor on the interaction of the 
other two; and o? is the variance of the experimental error. Since we do not 
know 00°, and in the absence of the original data, we have no means of assessing 
the second order interaction orri”. 
The routine of partitioning the total sum of the squares of the deviations 
from the general mean into component sums of squares is explained in any text- 
book on statistical analysis, and need not detain us here. In general each mean 
square estimates a linear function of the variances and interaction terms whose 
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