The Relation Between Coefficients of Correlation and Difficulty Factors

Abstract

The purpose of the following inquiry was to test the view, put forward by Ferguson and others, that unequal dichotomization of items tends to produce spurious difficulty factors. Subtests of three levels of difficulty were compiled for each of the three factors, and applied to nearly 500 students. The correlations were calculated by the phi, cosine‐pi, and full tetrachoric formulae, and four factors extracted. The results obtained do not support Ferguson's hypothesis.

A Study on Testers’ Learning Curve in Crowdsourced Software Testing

“…We combine the number of people participating in the project with the number of people finding test function points to calculate how easy the project is. Use the item difficulty factor [23] to cancel the impact of difficulty on the tester's score.…”

Chapter IV: Research Tools: Statistical Methods

“…Additional References: Other references of general interest, which are worthy of reading particularly by those interested in empirical examples or by those who are only beginning their study of factor analysis, include the contributions of Bernyer (1957) ; Borgatta (1958-59); Dingman (1958) ; DuBois and Manning (1959) ;French (1959) ; Garside (1958) ; Kline (1959) ; Michael (1958) ; and Royce (1958). Somewhat more mathe matically oriented articles are those of Baggaley (1960) ;Bernyer (1958); Demaree (1957) ; Hamilton (1958) ; .…”

Stochastic Models and Factor Analysis

“…Most strongly associated with the latent structure model and most important for the purposes of the present paper is the concept of item trace lines (Lazarsfeld, 1950;Fischer, 1968). Using the notation given below its meaning can be explicated as follows.…”

“…These issues become particularly salient when the manifest variables are dichotomous. Which correlation coefficients should be used and how the extracted factors should be interpreted are at present still problems without unequivocal answers (Ferguson, 1941 ;Wherry & Gaylord, 1944;Carroll, 1945Carroll, , 1961Gourlay, 1951 ;Dingman, 1958;Borgatta, 1965;Henrysson & Thunberg, 1965). I n the case of qualitative manifest variables it seems to be more appropriate to formulate a stochastic model of test behaviour within a factor analytic framework by borrowing terms from the latent structure model (Lazarsfeld, 1950;McDonald, 1962;Meredith, 1965).…”