Statistical Analysis
Regarding the printer's measure used by compositors X and Y, we can say
with some confidence that they were different and by how much. For each
exemplar, we can think of the twelve readings for compositor X as a
sample from a wider body of measurements that we could not take (because
he set prose on only twelve pages) and this wider body of measurements
would have a mean value that we do not know. We may treat compositor Y
likewise, although we have a larger sample, twenty-four readings,
from the wider body of measurements with an unknown mean. We are
interested in the difference between the two unknown means, and can use
the statistic called 'the difference in the sample means' to comment
upon it. In Appendix One, the numerical means of the sample for each
exemplar are given: this is simply the sum of the readings divided by
the number of readings, twelve for compositor X and twenty-four
for compositor Y. An expression of how widely or narrowly the readings
are spread around the mean is called the 'standard deviation' (here SD).
This is calculated by squaring each reading's difference from the mean,
summing these squares and then dividing that sum by the number of
readings, and finally taking the square root of this quotient.
Once we have the standard deviations for the sample readings, these can
be used to calculate a pair of numbers, a lower limit and an upper
limit, for which we can say to an arbitrary level of confidence that the
mean of the unknown distribution readings (that is, the actual width of
compositor X or compositor Y's composing stick) falls within those
limits. The lower the confidence level, the narrower the span between
the lower and upper limits, and a typically useful value for the
confidence level is 95%. The formulas giving the lower and upper limits
for a confidence level of 95% are:
Lower limit = Ymean – Xmean – (1.96 × √ (Comp X's SD2/n + Comp Y's SD2/n))
Lower limit =
Ymean – Xmean + (1.96 × √ (Comp X's SD2/n + Comp Y's SD2/n))
where Xmean is the average of the compositor X readings,
Ymean is the average of the compositor Y
readings and n is the number of readings in each man's sample.11 This calculation is done for each exemplar
separately. This statistic is included in Appendix One to demonstrate
that to a reasonable level of confidence the differences in the readings
are statistically significant rather than 'noise'. From it we can
confidently say that compositor Y set his pages somewhere between half a
millimetre and one millimetre wider than compositor X, with the
likeliest difference being around three-quarters of the
millimetre.
Although each exemplar has a different storage and handling history that
might affect its absolute readings (which cannot therefore be combined
across exemplars), these histories ought not to affect one compositor's
pages more than the other's within each exemplar. The raw data vary
around the means because each sheet of hand-made paper would have
absorbed a different amount of water when wetted for printing, would
have shrunk by a different amount when dried (and during storage over
the ensuing centuries in different locations), and because the depth of
ink applied before each pull would vary, as would the pressure exerted
by each pull and hence the depth that the type bit into the paper. Also,
there is human error in measuring by eye. The readings were taken by
placing a measuring rule on the page to press it flat and recording the
full distance from the first sign of ink in the first letter of the line
to the last sign of ink in the last letter on the line, ignoring where
necessary letters with kerns extending beyond the body of the type.
Where different lines on a page produced different readings, the
readings for the page were averaged. The Huntington exemplar's values
for both compositors are consistently higher (by about half a
millimetre) than the others, which might reflect a permanent expansion
upon washing (and subsequent pressing); it is the only exemplar whose
leaves have been inlaid, which operation is not infrequently accompanied
by washing.
