Question

For studying the average pulse rates between three groups of people: smokers, ex-smokers, and non-smokers, three independent random samples of male subjects were selected from the three populations of same age, race, and income level. The data, sitting pulse rates per minute measured in the morning under a fix condition, is listed below. Smokers: 88, 82, 80, 75 Ex-smokers: 70, 72, 73, 72 Non-smokers: 68, 70, 70, 75 Which of the following is correct for multiple comparisons if using 5% for each pair comparison (i.e. non-family-wise level of significance)? (There are more than one correct answer. Please check all correct answers.) The following is the R Commander output for multiple comparisons: Simultaneous Tests for General Linear Hypotheses Multiple Comparisons of Means: Tukey Contrasts Fit: aov(formula = V1 ~ V2, data = Dataset3) Linear Hypotheses: Estimate Std. Error t value Pr(>|t|) 2 - 1 == 0 -9.500 2.563 -3.706 0.01202 * 3 - 1 == 0 -10.500 2.563 -4.097 0.00692 ** 3 - 2 == 0 -1.000 2.563 -0.390 0.92024 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Adjusted p values reported -- single-step method) Simultaneous Confidence Intervals Multiple Comparisons of Means: Tukey Contrasts Fit: aov(formula = V1 ~ V2, data = Dataset3) Quantile = 2.7959 95% family-wise confidence level Linear Hypotheses: Estimate lwr upr 2 - 1 == 0 -9.5000 -16.6661 -2.3339 3 - 1 == 0 -10.5000 -17.6661 -3.3339 3 - 2 == 0 -1.0000 -8.1661 6.1661 1 2 3 "b" "a" "a" Question 16 options: A) There is significant difference between Ex-smokers and Non-Smokers. B) There is significant difference between Ex-smokers and Smokers. C) There is no significant difference between Ex-smokers and Non-Smokers. D) There is significant difference between Smokers and Non-Smokers.

Answer 1

Assuming that the groups 1,2,3 represents Smokers, Ex-smokers and Non-smokers respectively,

Since the p values of the first two comparisions are significant, it may be infered that there is a significant difference between the groups compared. And as the last comparision does not yield any significant result, we do not find any evidence of a significant difference between the groups compared.

From the R output, we may draw the following inferences:

B) There is significant difference between Ex-smokers and Smokers. ( 2 - 1) C) There is no significant difference between Ex-smokers and Non-Smokers. (3 - 2) D) There is significant difference between Smokers and Non-Smokers. (3 - 1)