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. This answer has not been graded yet. (b) Using the information given, write a short summary of the results of the study.

Answer 1

a)
Since there are two different groups in gender and two different groups in handedness, the degress of freedom for both handedness and gender will be 2-1 = 1.
The interaction degrees of freedom is (2-1)(2-1) = 1.
The within degrees of freedom is 949-1-1-1 = 946.

To find the p-value we need to refer to the F-table:
http://www.stat.purdue.edu/~jtroisi/STAT350Spring2015/tables/FTable.pdf

The p-value of handedness is less than 0.001
The p-value of gender is also less than 0.001
The p-value of interaction is greater than 0.1

We can conclude that both handedness and gender affect age but the relationship between handedness and gender does not affect age.

b)
The summary is that both handedness and gender have statistically significant effects on how long a person lives. However, the interactions between handedness and gender does not have a statistically significant effect on age.