D 
- 0 MB PL. 
  
  
the roles of the sampling errors. We can also give the limits within which the true 
distortion of each film is expected to lie. A peculiar behaviour of the nitrate film 
has appeared from the analysis and was probably worth further study. We have 
also demonstrated that the storage time, within the examined range, had no generai 
effect on the distortion; and perhaps had no influence at all except on the 
nitrate film. 
The analysis which we have performed on the data, for what it is worth, 
was possible because the design of the experiment conformed to the so-called 
factorial scheme. 
The main features of the factorial design of experimental investigations are: 
(a) Several factors are experimented upon together; and 
(b) the variate under consideration (in this example the differential shrinkage) is 
measured at every combination of the experimental conditions of the experiment. 
There are many multi-factor schemes where this last condition is relaxed for 
economy at a minimum loss of information, but we shall not go into this here. 
The contrast between the classical ideal of experimental work and the tech- 
nique of factorial experimentation, which was developed by R. A. Fisher, will be 
demonstrated by means of an elaboration of a pictorial presentation due to 
Brownlee. 
Let us consider a hypothetical experiment in which the effects of three factor: 
P, Q and.R on a dependent variable are to be investigated; and let us suppose 
that it will be adequate to study these three factors at only two levels each, i.e. 
with each factor held at two levels or values. The level of a factor will be indi- 
cated by a subscript, e.g. P,, P.. 
In the classical way we would do an experimental control with values Pi, 
Q,, R,, giving a value of x which may be denoted by (P1Q1 R3). 
To obtain the effect on x of changing P from P, to P,, which will be sym- 
bolized by (P, — P.), we do an experiment with values P,, Q,, R,, thus obtaining 
a value of x which will be denoted by (P.Q, R;). 
Thus, (D,—P)-2 (PQ RK)— (P.Q R1) 
Similarly, experiments at P,, Q,, R, and P,,Q,, R, give 
(Q —Q:) = (PQ R)— (P,QR:). 
and (R, = R.) = (P, Q, R4) = (P, Qı Ra). 
Now, it is very important to note that each of these experiments would have 
to be repeated at least once; otherwise it would be impossible to make any estimate 
of the experimental error. Without such an estimate it becomes impossible to say 
whether any apparent difference between (P,Q, R,) and (P,Q» R;) is indicative 
of a real effect of the level of P or has arisen as a chance sampling effect, or if it 
was nothing more than a mistake in the recording. We therefore require our four 
measurements to be repeated once, making eight observations in all. The obser- 
vations which we make according to this scheme may be located at four corners 
of a cube, as in Figure 1. 
The effect of a change in the level of a factor will be deduced by comparing 
the mean of two observations with the mean of two observations. The experiment 
gives no information whatever as to any possible interaction between the factors. 
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