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).

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Explanation / Answer

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

Solution:

For the given scenario, the degrees of freedom and approximate p-values are summarized as below:

Source

df

F Test statistic

P-value

Gender

2 – 1 = 1

37.44

0.0000

Handedness

2 – 1 = 1

22.36

0.0000

Interaction

1*1 = 1

2.1

0.1476

Error

948 – 1 – 1 – 1 = 945

Total

949 – 1 = 948

P-values are calculated by using the F-table or excel.

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

Solution:

From the above table, it is observed that the p-value for the gender is given as 0.00 which is less than the level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any significant difference in the average age at death due to gender. This means we concluded that there is a significant difference in the average age at death due to gender. Also, the p-value for the handedness is given as 0.00 which is less than the level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any significant difference in the average age at death due to handedness. This means we concluded that there is a significant difference in the average age at death due to handedness. The p-value for the interaction of the two variables gender and handedness is given as 0.1476 which is greater than alpha value 0.05, so we do not reject the null hypothesis that there is no any significant difference in the average age at death due to the interaction. This means we concluded that there is sufficient evidence that the interaction due to gender and handedness is not statistically significant.

Source

df

F Test statistic

P-value

Gender

2 – 1 = 1

37.44

0.0000

Handedness

2 – 1 = 1

22.36

0.0000

Interaction

1*1 = 1

2.1

0.1476

Error

948 – 1 – 1 – 1 = 945

Total

949 – 1 = 948

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