Question

5. A study was conducted to investigate the risk factors for peripheral arterial disease among persons 55-74 years of age. Data were collected pertaining to LDL cholesterol levels (mmol/liter) from four different subgroups of subjects:

Group	Sample Size	Sample Mean
(intermittent) Patients with intermittent claudication	25	6.28
(major) Major asymptomatic disease cases	35	5.70
(minor) Minor asymptomatic disease cases	27	5.04
(no) Those with no disease	30	5.16

It is assumed that LDL values are approximately normally distributed in each of the groups and that the variances of the LDL values are approximately the same in the four groups. The data were analyzed in R and the following output was produced.

Analysis of Variance Table   

Response: LDL

   Df Sum Sq    Mean Sq F value Pr(>F)  

group       3 25.685 8.562    4.2051 0.007343 **

Residuals 113 230.070 2.036                   

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The p-values for the pairwise tests are provided below:

        Pairwise comparisons using t tests with pooled SD

data: LDL and group

intermittent major minor

major 0.1214 -    -    

minor    0.0022 0.0751 -    

no    0.0044       0.1312    0.7582

Carry out the 7 steps of the ANOVA test corresponding to the output shown above using a 5% significance level. Use a p-value decision rule to decide if you should reject or not reject the null hypothesis. If you reject the null hypothesis in the ANOVA test, go on to describe which pair-wise differences are significantly different from 0 using an overall significance level of 5% and using a Bonferroni correction. If you find any pair-wise differences, be sure explain which group has the larger/smaller mean LDL. You do not have to do any calculations, just use the output to complete the hypothesis test.

Answer 1

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