An experiment to ascertain the effect of two randomly selected brands of soil fertilizer on wheat yield. In the upper figure two brands of fertilizer (1 and 2) are randomly chosen from a population of potential choices. The mean yields produced by the population of fertilizers \(E(Y|A_i)\) are normally distributed. That is, it is possible to select a factor level that will result in very small average yields, or one that will result in large average yields, but it is more likely that a chosen factor level will produce some intermediate average effect. We proceed with the experiment by assigning two experimental units (two wheat fields) to each fertilizer. We assume that the yield of fields is normally distributed for each fertilizer, and furthermore that the factor levels are homoscedastic. We weigh our evidence against the H\(_0\) of a non-zero population variance by estimating the variability among factor levels. The more that yield varies with respect to nutrient treatments the more evidence we will have against H\(_0\).
see.rEffect.tck()Ken Aho