1. Pretend that you are in a job situation and these questions are being asked b
ID: 3321018 • Letter: 1
Question
1. Pretend that you are in a job situation and these questions are being asked by nonstatisticians who read SAS printouts (it happens). Your comments will be evaluated based on what you know (technical content), and how well you enlighten the issue (conciseness, clarity). (a) In a study of mean differences between three groups (A, B and C), one-way Analysis of Variance does not declare a significant difference at the 5% level of significance. However, a t test between Group A and Group C is statistically significant at the 5% level of significance. Are the results contradictory? Is there a significant difference between Groups A and C or not? (b) In a blood pressure reduction study to compare two dose levels of drug (Groups 1 and 2) versus a control (Group 3), age is used as a covariate because blood pressure tends to increase with age. However, a comparison of the three groups shows that the age variable is evenly distributed throughout the three groups, which means that the age factor will not cause a bias in the comparison of treatment effects. True or false: inclusion of age as a covariate in the comparison of group means is unnecessary. Give a brief justification.Explanation / Answer
Answers
a) The t statistic is the ratio of mean difference and standard errors of the mean difference. We cannot apply t test by implementing multiple t tests on multiple pairs of means because the repetition of the multiple tests may repeatedly add multiple chances of error. For a comparison of more than two group means the one-way analysis of variance (ANOVA) is the appropriate method instead of the t test. Hence, there is no significant difference between groups A and C.
b)It is true that inclusion of age as covariate (also called explanatory variable, independent variable, or predictor) in comparison of group means is unnecessary because as it should be evenly distributed among 3 groups, it will not show bias in the comparison of treatment effects. Blood pressure may also correlate with other factors like BMI, body weight, gender and also health and fitness related variables like muscular strength, flexibility, heart rate.
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