subscripts contain every letter in the corresponding source of variation, in addi- 
tion to o. 
The interaction between the effects of the type of film and the temperature 
of storage is highly significant; but the 7't interaction is insignificant, as we 
expected. The significance of the Ft interaction is rather interesting, since it will 
be shown later the common time effect is itself insignificant. Inspection of the data 
shows that the nitrate film can account for this interaction, because its distortion 
is consistently highest for the 9 month storage period. 
Let us consider next the between-7' mean square. This estimates a linear 
function of 00°, orri*, om?, Orr and oz?. We have seen that op? is not signific- 
antly different from zero, so that if the between-7T' mean square is significantly 
greater than the mean square corresponding to the 7 F interaction, this can only 
arise from a significant temperature variance, which would indicate a general 
temperature effect. The ratio of the two mean squares is 2.44, which falls below 
the 5 per cent point for 2 and 6 degrees of freedom. The data therefore do not 
reveal a common temperature effect. The next item is the between-£ mean square. 
Its components are o£, or?, or?, opp? and oy. Since we have already demonstrat- 
ed that or/'is in fact nil, we may test for a general time effect by dividing the between- 
t mean square by the Ft interaction. The ratio is in fact less than one. It follows 
that no common time effect is revealed by the data. This also agrees with the 
previous finding that time had no effect at any of the three levels of storage 
temperature. 
Let us now consider the between-F mean square. Here we are concerned as to 
whether or not there is a common behaviour shared by all films as regards the 
influence of time and temperature. The between-F mean square is a linear 
function of or^, opi?, or, opp? and o? of which both orr? and op? have estab- 
lished their significance. Testing the between-F mean square against the larger of 
these two interactions, we find that the ratio is not significantly greater than 1, 
and we therefore conclude that os” cannot be significant. It should however be 
noted that even if the ratio proved significantly greater than 1 we would not be 
able to attribute this to a significant oz^: it might have arisen from the demonstrat- 
ed significance of the other component or. 
The results of this analysis as regards the significance of the main effects are 
not incompatible with the previous conclusions which we obtained from analysis 
of each table separately, since, we were then interested in the effects as demonstrat- 
ed at the individual temperature levels. 
Let us now examine the experimenter's own conclusions in the light of the 
preceding analysis. His conclusions were “the safety film AB-244 is poorer than 
the nitrate N-045 at all temperatures but the safety AB-284 is as good as the 
nitrate 70° F and 90° F, and substantially better at 120° F”. 
We have seen that the AB-244 is indeed significantly poorer than the nitrate 
at the extreme temperatures, but it is about as good as the nitrate at 90° F. Our 
analysis bears up the conclusion of the equality of the AB-284 and the nitrate 
N-045 at 70° and 90° F. The superiority of the AB-284 at 120° F is self evident. 
As regards the film AP-311 (which the experimenter did not consider for other 
reasons), we have shown that it is significantly worse than AB-284 at 70° and 
about as good in the higher temperatures. In every case we have been able to 
attach the probability levels of significance, thereby gaining a clearer insight into 
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