694 ' TRANSACTIONS Of SECTION L. 
but need not abdicate in favour of medicine. Education may use the results 
of both Psychology and Physiology without in any way surrendering its claims 
to be an independent science. We must not, of course, make too much of the 
distinctions among the sciences. Nothing but error can result from seeking to 
make each of them rigidly self-contained. So far as Education is concerned, 
what we have to seek is that objective standard that we have conceded to be 
essential to the recognition of a study as a possible science, and this without 
falling back on the standards of either pure Psychology or pure Physiology. 
We may learn something from what we have found out about the results of 
the individual examination system. The general tendency of quantitative 
methods is to eliminate the subjective element. Even in the case of marking 
examination papers experience shows that the use of numerical marks tends to 
objectify results, and to get rid of some at least of the difficulty involved in the 
personal equation of the examiners. Marking by general impression of a whole 
paper is much less free from subjective variation. Every individual number set 
down as a mark implies a fresh exercise of the critical power, and when there 
are many questions there is a compensating principle at work, inasmuch as each 
impression is recorded as it is made and the addition of the marks produces a 
balancing in which the latest impression has not the determining influence it 
too frequently has when a paper is marked as a whole. If an examination in- 
cludes many subjects, many examiners, and a great body of examinees, the 
subjective element in the marking is, to a large extent, eliminated, and we can 
deal with the results in accordance with what is practically an objective stan- 
dard. We must not, of course, neglect the fact that after all the whole basis of 
the results is the judgment of the individual examiner on the material submitted 
to him. This corresponds to the application to real life of any of the physical 
sciences. Here, as in many of the other sciences, we have a surd of subjectivity 
that can never be got rid of entirely. But its disturbing influence can be mini- 
mised by the counteracting influences of other forces in the quantitative manipu- 
lation of the data. 
Of late the quantitative method of dealing with educational problems has 
been greatly developed. Karl Pearson’s product-moment formula has enabled 
us to make an accurate arithmetical statement of the amount of correlation that 
exists between series of quantitative data. By the application of this formula, 
and the simpler formule of Professor Spearman, it is now possible to correlate 
a great many facts that were formerly treated as having only a problematic 
connection with each other. If these formule produce really reliable results, 
we have at our command a means of answering definitely and definitively a 
. great number of questions that have hitherto been regarded as the more or less 
legitimate matter for the professional controversialist. The vexed question of 
‘formal training,’ for example, may be set at rest once and for all by a sufficiently 
extended series of correlations of the results of pupils’ progress in certain 
subjects. The peculiarity of this method of dealing with correlations is that 
once we have handed over our facts to the formule, the process passes out of 
our hands altogether. We have only to work out our equations and the resalts 
make their appearance. Here we certainly seem to have reached an objective 
standard. 
Such results, however, are not unnaturally regarded with some suspicion. 
Once the formule have been established by mathematical proof they must, of 
course, be accepted as irrefutable on that side; but their application to educa- 
tional problems is so mechanical and indeed inhuman that many are unwilling to 
accept and use them. Some people are doubtful whether, in dealing with human 
beings, it is desirable, even if it were possible, to have an objective standard that 
eliminates humanity from all human problems. It has to be pointed out to such 
critics that all human problems must begin with the individual and end with the 
individual. All the intermediate process may be carried on in the pure objec- 
tivity of quantity, without dehumanising the application of its results. This 
will be kept in view when we deal with the average. 
Apart from this danger of dehumanising our subject, there are two real possi- 
bilities of error in the application of the formule. First, there is the danger that 
the investigator may be satisfied with an application to an insufficient number 
of cases. The second danger is that the subjective element may cause error in 
