into three sums of squares: one expressive of variations due to the type of film, 
one expressive of differences arising from variation of storage time, and the third 
representing the collective variability due to experimental errors. The first two 
components will be called ‘the beween-F sum of squares’ and ‘the between-t sum 
of squares’; the third will be referred to as ‘the residual’. Table 7 gives the analysis 
of variance of the data of Table 4. The component sums of squares (S.S.) are 
given in the first column opposite to the respective sources of variation, with the 
number of degrees of freedom (d.f.) in the second column; and the mean squares 
(= S.S./d.f.) in the third. 
The analysis may proceed as follows: We first put forward the hypothesis 
that Table 4 consists of a random sample from a set of measurements of a constant 
quantity. If this were true, all the mean squares in Table 7 would be consistent 
  
  
  
  
Table 7 
(Temperature 70° F) 
S.S. d.f. | M.S. 
Between-F 64.31 3 | 21.33 
Between-t 2.06 3 | .69 
Residual 35.57 9 | 3.99 
Total 101.94 15 | 
  
  
  
  
estimates of the same variance, and should not therefore differ from one another 
more than would be expected from random sampling. If, on the other hand, the 
length of storage time influences distortion, the between-t mean square would be 
larger than the residual. Similarly, if the films differ in their response to storage, 
the between-F mean square would be larger than the residual. 
It is obvious that there is no significant time effect, since the beween-t mean 
square is smaller than the residual (but of course it is not significantly smaller). 
We may therefore pool the Sums of Squares and degrees of freedom assignable to 
the 'between-£^ and 'residual', thereby obtaining (35.57 + 2.06)/(3 + 9) = 3.13 
as a new estimate of the ‘residual’ which has 12 degrees of freedom. The between-F 
mean square is approximately 7 times the residual. It had to be only 6 times the 
residual to be significant on the 1 per cent level. We may thus conclude that the 
70? F disclose significant variation of shrinkage with the type of film. Since, 
however the data do not reveal any time effect, we can therefore take the mean 
distortion over the four storage periods, and compare any particular pair of films 
which might be of interest to us by testing the significance of the differences 
between their respective means. It is clear from the Total column of Table 4 that 
the films group in two pairs of which the mean distortions differ by about 18/4 — 
— 4.5 units. This difference gives a value of t — 4.5/[3.13 (1/4 + */4)]^ — 3.6, with 
the 12 degrees of freedom of the residual. The odds against the chance appearance 
of a difference equal to or greater than the observed magnitude are greater than 
[00 to 1; and we therefore conclude that (at 70? F) the films AB-284 and N-045 
are equally good and better than the other pair. 
Proceeding similarly to analyse the data pertaining to storage at 90? F, we 
obtain the analysis of variance shown in Table 8: The time factor is again 
15