Analysis of Factorial Arrangements when the Data are Proportions

The statistician is often confronted with data in which the measurement of interest is the proportion of units possessing a certain attribute. Such data can arise in factorial arrangements in either designed experiments or survey work. An example of the former is given by an experiment on a number of varieties of bulbs which have been infested with eelworm. Treatments of hot water at two temperatures are applied for two lengths of time, these treatments together with two sizes of bulb forming a 23 arrangement. The observations are the proportions of bulbs blooming in the different categories. A second example is taken from survey work. In a survey on virus diseases in potatoes the data may be recorded separately for each combination of a number of factors which may affect the data e.g. varieties, age of seed (new or old), and height of the field above sea level (above or below say 500 feet). Here the observations would be the proportion of diseased plants. In a factorial experiment on yield data, the main effects and interactions are estimated together with their standard errors. The estimates of the effects are given by linear functions of the observations. This paper is concerned with the corresponding analysis of factorial arrangements when the data are proportions.