Do left-handed people live shorter lives than right-handed people? A study of th

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 gender (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 (gender), 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).

Please answer both paragraphs in sentences.

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


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

Explanation / Answer

Total degree of freedom=949-1=948

Degree of freedom of handedness=2-1=1

Degree of freedom of gender=2-1=1

Degree of freedom of interaction =(2-1)*(2-1)=1

Error degree of freedom =948-1-1-1=945

Part-a

Handedness:

F-statistics =22.36

Degree of freedom=(1, 945)

p-value=P(F(1,945)>22.36)= 0.0000026 using excel function = FDIST(22.36,1,945)

Gender:

F-statistics =37.44

Degree of freedom=(1, 945)

p-value=P(F(1,945)>37.44)= 0.000000001 using excel function = FDIST(37.44,1,945)

Interaction:

F-statistics =2.10

Degree of freedom=(1, 945)

p-value=P(F(1,945)>2.10)= 0.1476 using excel function = FDIST(2.10,1,945)

We conclude that there is no interaction effect as p-value(interaction)=0.1476>0.05.

However there are significant main effect of handedness (p<0.05) and gender(p<0.05).

Part-b

We found that the females have significantly higher average age at death as compared to males. Also right handed people have significantly higher age at death than left handed people.

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