Random Experiments

Random Description

Consider a population of classes, say the counties of Wisconsin, with an arbitrary class in this population labeled by u. This class represents a sub-population of elements, say the population of farms in county u. If this class is selected for the experiment, an independently selected random sample of its elements (farms) would be selected for measurement, for instance of annual milk production per farm. The key questions concern estimating the average response across the population (state) and understanding the sources of variation in this measurement. Note that a different way to run the experiment would be to take a random sample of all elements (all farms in the state), without regard to which class (county) they come from. This latter design structure is completely randomized, while the former has two stages of randomization. Substantial variation among classes (counties) would be confounded with element-to-element variation (among farms) in the latter design.

Rantwo Description

Consider a population of seed packets and a population of fields in Dane County. The experiment consists of taking a random sample of seed packets and a random sample of fields, then placing several seeds from each seed packet in each field. Individual plants grown from seed are measured for yield at the end of the growing season.

Data & Setup

randat.s

random generation of data

rantwo.dat

seed farm yield

rantwo.s

two-factor anova

ran2est.dat

fixed model estimates and random model predictions

seed farm estim seest blup seblup

SAS Data Analysis

rantwo.sas

read data, analyze

rantwo.prt

Book Figures

random.s

G

ran2.s

G