Sensitivity of Tests of Significance: A Problem Posed

THIS paper contains a preliminary examination o f the effect o f using the dichotomy (o, i ) instead o f actual measurement in the study o f relation­ ship. First, the simplest case possible is dealt w i t h , i n the hope o f inspiring, or provoking, more thorough treatment by others. O f course, dichotomy or other ordinal treatment has to be used when measure­ ment is inconceivable, e.g. when the variable is sex or religion. I t is very familiar in dummy variable practice in regression, e.g. i n investigating relationship between time series when certain major events (e.g. a dock strike) are known a priori to have affected one or more o f the data. I t is thought that a comparison o f statistical functions pertaining to relationship, when cardinal values are possible, w i l l shed light on the meaning o f these functions when ordinal values only are available. Using t w o other examples we reconsider the customary x treatment o f 2 x 2 tables. W e end up w i t h a very general query bearing on stochastic decision­ making, arising out o f our simple examples, for consideration by our colleagues.