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

Part a

For the given 2X2 two way ANOVA, we have

Number of factors for gender = a = 2 (Male or female)

Degrees of freedom for variable gender = a – 1 = 2 – 1 = 1

Number of factor for handedness = b = 2 (Left or right)

Degrees of freedom for variable handedness = b – 1 = 2 – 1 = 1

Degrees of freedom for interaction = (a – 1)*(b – 1) = 1*1 = 1

Total number of observations = N = 949

Total degrees of freedom = N – 1 = 949 – 1 = 948

Within degrees of freedom = 948 – 3 = 945

For F statistic = 37.44 for main effect A (gender), degrees of freedom = (1, 945)

Corresponding p-value = 0.00

For F statistic = 22.36 for main effect B (handedness), degrees of freedom = (1, 945)

Corresponding p-value = 0.00

For F statistic = 2.10 for interaction effect AB, degrees of freedom = (1, 945)

Corresponding p-value = 0.1476

Part b

For the factor A (gender), we get the p-value as 0.00 which is less than the alpha value 0.05, so we reject the null hypothesis that the factor A or variable gender is not statistically significant. This means we conclude that there is sufficient evidence that the variable gender is statistically significant. The p-value for the variable handedness is given as 0.00 which is less than alpha value of 0.05, so we reject the null hypothesis that the variable handedness is not statistically significant or we conclude that there is sufficient evidence that the variable handedness is statistically significant. The p-value for interaction is given as 0.1476 which is greater than the level of significance or alpha value 0.05, so we do not reject the null hypothesis that the interaction is not statistically significant. There is no sufficient evidence that the interaction is statistically significant.

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