Question

Do left-handed people live shorter lives than right-handed people? A study of this question examined a sample of 949 death records and contacted next of kin to determine handedness. Note that there are many possible definitions of "left-handed." The researchers examined the effects of different definitions on the results of their analysis and found that their conclusions were not sensitive to the exact definition used. For the results presented here, people were defined to be right-handed if they wrote, drew, and threw a ball with the right hand. All others were defined to be left-handed. People were classified by sex (female or male) and handedness (left or right), and a 2 ✕ 2 ANOVA was run with the age at death as the response variable. The F statistics were 22.36 (handedness), 37.44 (sex),and 2.10 (interaction). The following marginal mean ages at death (in years) were reported: 77.39 (females), 71.32 (males), 75.00 (right-handed), and 66.03 (left-handed).

(a)

For each of the F statistics given, find the degrees of freedom and an approximate P-value. Summarize the results of these tests.

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(b)

Using the information given, write a short summary of the results of the study.

Answer 1

a: Degree of freedom:

Degree of freedom for Sex: 1 (As there are two categories, 2-1=1)

Degree of freedom for handedness: 1 (As there are two categories, 2-1=1)

Degree of freedom of interaction= 1*1 = 1

Total degree of freedom = 948 (Tota subjects = 949)

Degree of freedom of error = 948 - 1 - 1 - 1 = 945

We shall use Rto get p-value. pF(q, n1, n2)

F-handedness = F(1,945), P-value = 2.604464e-06

F-sex = F(1,945), P-value = 1.37921e-09

F-interaction= F(1,945), P-value: 0.1476309

b: Seeing this information, we reach to the conclusion that

1. There is enough evidence to say that there is no interaction effect of sex and handedness on life span.
2. There is enough evidence suggesting that females live longer than males. As p-value is very small, we reject the null hypothesis is the favor of alternative that females live longer than male
3. There is also enough evidence to conclude that the right handed and left handed have different mean age. BUT as the data suggests that mean age of right handed is higher than mean age of left handed, our conclusion must be that right handed people live longer than left handed