Comparing Means of More than Two Samples
In Chapter 12 we took two approaches to comparing the means of two samples. The first approach involved using each sample separately to estimate the mean of the population that the sample came from. We then attached error ranges for several confidence levels to these estimates and drew a picture of the whole thing with a bullet graph (Fig. 12). This approach is easily extended to the comparison of any number of samples. In this chapter we will use another fictitious example consisting of 127 Archaic projectile points from the Cottonwood River valley. After considering possible sources of bias we decide to work with these as a random sample from the large and vaguely defined population of Archaic projectile points from the Cottonwood River valley. We are interested in whether, during the Archaic period, there was much change in hunting of large and small animals in the Cottonwood River valley. We reason that large projectile points are more involved in hunting large animals and small projectile points are more involved in hunting small animals. We can divide the 127 projectile points into three groups: Early, Middle, and Late Archaic, and we decide to compare the weights of projectile points in these three periods. One way to organize these data for this sample is shown in Table 13.1. Here two observations are recorded for each of the 127 projectile points: the weight (in grams) and the period (Early, Middle, or Late Archaic). Our two variables, weight and period, are of different kinds. Weight, of course, is a measurement, and period is a set of three categories.