Clifford Woody explains how he constructed his popular tests in Measurements of some achievements in Arithmetic (New York: Teachers College, 1916, p.25-26):
"In building the arithmetic scales there has been a definite attempt to approximate as closely as possible the accuracy and the constancy of a ruler or thermometer. The difficulty of each problem has been established and its position above a selected zero point determined. The problems have all been placed in their relative positions on a projected linear scale."
Woody used equated normal ogives - a "PROX"-type procedure - described in E. L. Thorndike's Mental and Social Measurements, 1912.
Woody's preliminary tests consisted of sheets of problems in addition, subtraction, multiplication and division. Test construction rules were to:
1) select problems of as great a variety as the fundamental processes would permit.
2) begin the series in each process with the easiest problem that could be found and then gradually to increase the difficulty of each succeeding problem until the last ones in the series would be correctly solved by only a small percentage of pupils in the highest grade.
3) set no time limit for the solution of problems. It was felt to be highly important, if the difficulty of each problem was to be firmly established, that each child should have a chance to solve each problem.
4) reduce the personal element in scoring to a minimum. An answer, to be marked correct, must be absolutely accurate and reduced to its lowest terms.
The preliminary lists of problems in addition, subtraction, multiplication and division were given to about 900 pupils. Based on their responses,
5) some problems were seen to be poorly constructed and were discarded.
6) when problems were ranked according to the total percentage of pupils solving them correctly, there were large gaps between problems in particular portions of the series. Wherever there tended to be too large a step between two consecutive problems in the original series an attempt was made to interpose two or three problems of intermediate difficulty.
7) only problems that were solved by a gradually increasing percentage of the pupils as one proceeded from the lower to higher grades were retained.
Woody's 1916 Rules for Test Construction, C Woody Rasch Measurement Transactions, 1992, 6:2 p. 211
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