Random Distributions

Abstract

For many of the experiments discussed in the preceding chapters there was an implied assumption: the experimenter could control the values of the independent variables. Often the assumption was that the independent variable x could be varied from x ₁ to x _n with a constant value of Δx = x _i+1 - x _i . For experiments with more than one independent variable it was usually assumed that the independent variable space could be spanned in a similar manner. For many experiments this is a reasonable assumption but there are innumerable experiments where this assumption is unrealistic. For example, experiments based upon the measurement of the effects of temperature upon some variable might or might not be controllable. If, for example, the temperature is the atmospheric temperature at the time the variable is measured then this temperature can only be observed. It cannot be controlled. Examples from the medical field are experiments related to the effects of cholesterol upon a variable that is a measure of heart function. The amount of cholesterol in a subject of the experiment is measured but not controlled. All that can be said for the subjects when taken as a group is that the amount of cholesterol in the blood of the subjects is distributed according to some known (or observed) distribution. If the experiment is designed properly, then the subjects taken as a group are representative of similar groups of subjects that are being modeled.