Biostatistics

318 CHAPTER 8 ANALYSIS OF VARIANCE
It will be recalled that the original hypothesis we set out to test was
H 0 : m 1 ¼ m 2 ¼¼m k
Does rejection of the hypothesis about variances imply a rejection of the hypothesis of
equal population means? The answer is yes. A large value of V.R. resulted from the fact that
the among groups mean square was considerably larger than the within groups mean
square. Since the among groups mean square is based on the dispersion of the sample
means about their mean (called the grand mean), this quantity will be large when there is a
large discrepancy among the sizes of the sample means. Because of this, then, a significant
value of V.R. tells us to reject the null hypothesis that all population means are equal.
9. Conclusion. When we reject H 0 , we conclude that not all population means are
equal. When we fail to reject H 0 , we conclude that the population means are not
significantly different from each other.
10. Determination of p value.
EXAMPLE 8.2.1
Game meats, including those from white-tailed deer and eastern gray squirrels, are used as
food by families, hunters, and other individuals for health, cultural, or personal reasons. A
study by David Holben (A-1) assessed the selenium content of meat from free-roaming
white-tailed deer (venison) and gray squirrel (squirrel) obtained from a low selenium
region of the United States. These selenium content values were also compared to those of
beef produced within and outside the same region. We want to know if the selenium levels
are different among the four meat groups.
Solution:
1. Description of data. Selenium content of raw venison (VEN), squirrel
meat (SQU), region-raised beef (RRB), and nonregion-raised beef
(NRB), in mg=100 g of dry weight, are shown in Table 8.2.3. A graph
of the data in the form of a dotplot is shown in Figure 8.2.4. Such a graph
highlights the main features of the data and brings into clear focus
differences in selenium levels among the different meats.
TABLE 8.2.3
Selenium Content, in mg=100 g, of Four Different Meat Types
Meat Type
VEN SQU RRB NRB
26.72 14.86 37.42 37.57 11.23 15.82 44. 33
28.58 16.47 56.46 25.71 29.63 27.74 76.86
29.71 25.19 51.91 23.97 20.42 22.35 4.45
26.95 37.45 62.73 13.82 10.12 34.78 55.01
10.97 45.08 4.55 42.21 39.91 35.09 58.21
21.97 25.22 39.17 35.88 32.66 32.60 74.72
(Continued)