Biology Reference
In-Depth Information
Two-Sample t-Test and Cl: B, A
Two-sample T for B vs A
N
Mean
StDev
SE
Mean
B
10
2.840
0.317
0.10
A
10
2.440
0.403
0.13
Difference
¼
mu (B)
mu (A)
Estimate for difference: 0.400000
95% lower bound for difference: 0.117824
T-Test of difference
¼
0 (vs
>
):
T-Value
¼
2.466 P-Value
¼
0.012; DF
¼
17
The Z-test and t-test help us answer the first of the three questions we
posed at the beginning of this chapter; namely, how to find out whether
any observed group differences are statistically significant. In our
example, the Z-test and the t-test produce quite similar results because
of the fact that the empirical variances used for the t-test (calculated
above as 0.403 for type A corn and 0.317 for type B) are close to the
population variance assumed in the Z-test.
C. F-Test
The second question we posed was how to decide whether the
contribution of an underlying genetic factor is significant, relative to
environmental factors. To answer this question, we have to compare the
variance explained by the genotype to the entire variance observed in
the phenotype and decide whether the genotype explains a significant
portion of the entire variance. This brings us to one of the most
important markers evaluated in genetic studies—the metric called
heritability. Heritability is defined as the ratio of additive genetic
variance (V
A
) to the entire variance observed in the phenotype (V
P
),
and by tradition is denoted by h
2
Average
Parental
Stature
(X) [feet]
Child's
Stature
(Y) [feet]
V
P
. Numerous studies have
been designed to evaluate the heritability of various traits. For
example, the person's stature is a trait with relatively high
heritability, h
2
¼
V
A
=
Family
No.
1
5.60
5.70
0.65, while insulin resistance (a major factor in the
development of type 2 diabetes) has heritability h
2
¼
2
5.90
6.10
¼
0.31 (see Bergman
3
6.10
6.20
et al. [2003]).
4
5.30
5.60
In general, the methods used to estimate heritability include parent-
offspring regressions and analysis of variance (ANOVA) comparing
siblings to half-siblings, or identical to nonidentical twins. For the
purposes of this chapter, the important property of heritability is that it
is defined as the ratio of two variances. Therefore, we would expect that
in statistical problems heritability would have an F-distribution.
5
5.70
5.45
6
6.20
5.90
7
6.40
6.10
8
5.50
5.80
9
5.20
5.40
10
6.10
6.20
We shall illustrate the evaluation of heritability of stature via linear
regression. Consider the data in Table 4-4. To investigate the dependence
of the child's stature on the average parental stature, we choose
TABLE 4-4.
Example of parent-child stature data.
