The Estimation of Response-Time Distribution III Truncation and Survival

A general survey of the problems involved in the estimation of response-time distributions was given in the first paper of this series (Sampford, 1952a). Many of these problems arise as consequences of failure to observe the desired response in all subjects. The courses to be followed when this failure results from the operation of a stimulus other than that under investigation-when, for example, animals die from an infection, as well as from the application of a poison-have been discussed in a second paper (Sampford, 1952b). However, incomplete data may also occur as a result of truncation, when the experimenter fails, intentionally or accidentally, to observe the response on some individuals, or of survival, a convenient term adopted from the particular case in which the response is death, and indicating a failure on the part of some individuals to show the response, either because they are immune to the treatment or because they recover from its effects. These two problems are discussed in this paper. In future references the two papers cited above will be denoted simply by (I) and (II). A detailed list of conventions, definitions, and symbols used consistently throughout the series was given in (II). Throughout this paper the word 'time' will be used indifferently for true time and for a transformed time-metameter; the meaning in any instance should be clear from the context, or from the symbols used, r denoting a measurement in 'true time', t some function of r, normally distributed when the stimulus under investigation operates without interference. (Usually t = r, log r, or 1/r).