yielding ability of a new variety with that of a variety in common use, comparing the effect of fertilization versus no fertilization on yield, comparing the effect of a new diet on animal growth with growth on a standard feeding

In such experiments, two samples must be taken from the two populations involved. The difference between the sample means provides information about the difference between population means. Two samples are said to be independent if the observations in one are not in any way related to the observations in the other. For instance, animals of the same breed and of similar age are randomly assigned to two diet treatments, and gains are two independent samples. On the other hand, if two animals from each of several litters are randomly assigned to the two treatments, the resulting body weight gains of the two treatments are called paired (dependent) samples. Each observation in one sample is matched with one observation in another sample, both being from the same litter. The paired samples method is also frequently used in comparing observations made on the same experimental units before and after a treatment. The concept of comparing two sample means is illustrated in Figure 6-1.