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).

(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

We fill the ANOVA table as given below :

a) There are 2 types of handedness. Hence degrees of freedom for handedness = A = 2 - 1 = 1 There are 2 types of Genders. Hence degrees of freedom for gender = B = 2 - 1 = 1 Degrees of Freedom for interaction = Degrees of Freedom (Handedness) x Degrees of Freedom(Gender) = C = 1 x 1 = 1 Total Degrees of Freedom = Sample Size - 1 = 949 - 1 = 948 Degrees of freedom for Within = Total Degrees of Freedom - (A+B+C) = 948 - (1+1+1) = 945 From the F- tables we find the p-value for each F-statistic (F-value, numerator df, denominator df) p-value for F-handedness = F(22.36, 1, 945) = 0.0000026 p-value for F-gender = F(37.44, 1, 945) = 0 p-value for F-interaction = F(2.1, 1, 945) = 0.1476

We fill the ANOVA table as given below :

We consider level of significance = 0.05 From the above results, we conclude that 1. Since p-value for handedness(0.0000026) < 0.05, there is a statistical significant relation between the handedness and the average age at death 2. Since p-value for gender(0) < 0.05, there is a statistical significant relation between the gender and the average age at death 3. Since p-value for interaction(0.1476) > 0.05, there is no statistical significant interaction between handedness and gender in relation to the average age at death b) We can see from the above conclusions, that there was a significant effect of handedness on age at death.   There was also a significant effect of gender on age at death But there was no significant interaction between handedness and gender in relation to age at death Thus, handedness and gender individually influence the age at death, but both considered together there is no significant effect on age at death Also since there is significant effect of handedness and gender, from the marginal mean ages, we can say that Left handed people (mean 66.03) live shorter than right handed people (mean 75) Females (mean 77.39) live longer than males (mean 71.32)

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