A Empirical Investigation of the Problem of Disproportionate Frequencies in Analysis of Covariance as Applied to a Methods Experiment

Abstract

THE EXPERIMENT to be described en countered difficulties familiar to many who un dertake research the classroom. They arise from the fact that it is seldom possible, prac tice, to attain an experimental structure exactly conforming to the requirements of statistical theory. In England, the yearly entry of 100 or more into a secondary school is often divided to strearns'' of different intellectual ability, and there, for instance, it is not likely that a ''random sample for experimental purposes will be found in situ the classes of any giv en age. Rearrangement randomised groups as envisaged by Lindquist (1) could so disrupt school organisation that the co-operation of those authority would not be readily forthcoming even though they were favorably disposed towards experimental work. If the differences are almost certain to be due to unequal average mental capacity of the indi viduals the various classes, or some other measurable quantity, they may be overcome by using the method of analysis of covariance i n cases where the normal methods would be t h e analysis of variance. A second difficulty, not disposed of so easily, is that many designs re quire rather rigid restrictions on the number of cases the experimental units. If, again, the convenience of the schools is studied, and the classes are not altered numbers, appr?ciat if the fact that existing methods based on exact theory lead to prohibitively laborious calcula tions, evidence on the nature of the error likely to be committed using numbers only slightly departing from the ideal theoretical condition would be valuable. Both matters are considered a statistical handling of the data of the exper iment. It was desired to compare the relative effects of each of three methods of presenting diagrams, otherwise similar lessons, to children of first year secondary school age. In order that prev ious training should not affect the results, the lesson chosen was on a topic not likely to have been met previously by the children, and involved illustration. topic chosen was The Construction of a Hand Sewn Slipper and all groups were given the same lesson by Mr. Parkin. lesson could be conveniently illustrated by means of three line diagrams. first showed the shape and names of the parts which are sewn together to make the upper of a simple slipper, the sec ond was an exploded' ' line diagram showing the upper on a last and the various components which have to be attached to complete the slip per, and the third was a perspective line sketch of the finished slipper with the toe cut away to show section the relative positions and mode of attachment of the various components. lesson, which took about fifteen minutes, follow ed the order of practical procedure of slipper construction and a short recapitulation was made when explaining the third diagram. So far as was experimentally possible the only difference between the lessons lay the method of presenting the diagrams. In one case they were built up freehand one at a time on the black board, the second case they were presented the form of projected images from three film | slides, and the third case they were present ed the form of three prepared wall charts. Both wall chart and filmslide diagrams consisted of white lines on a black background so as to con form with the blackboard diagrams, and the size of the illustration presented all cases was kept as uniform as possible. experimenter took care to build up the board diagram the manner which he would normally illustrate a lesson. He considers that he is competent, but not exceptionally gifted, blackboard work. In England, allocation of children into various types of secondary school takes place at the age of eleven, approximately, mainly on the basis of a selection examination which the district con cerned consists substantially of tests of intelli gence and attainment Arithmetic and English. Roughly, their order the examination places them into Grammar, Technical or Modern Schools, though parents occasionally suggest that they wish a child to go into a Technical School instead of a Grammer School even though his performance entitles him to a place the latter. Since the education offered the s e types of school is different, the results of the experiment might be affected by this fact, and