One of the goals of the Edinburgh Artery study was to investigate the risk facto

Question

One of the goals of the Edinburgh Artery study was to investigate the risk factors for peripheral arterial disease among persons 55 to 74 of age. You wish to compare mean LDL cholesterol levels, measured in mmol/liter, among four different populations of subjects: patients with intermittent claudication or interruptions in movement, with major asymptomatic disease, those with minor asymptomatic disease, and those with no evidence of disease at all. Samples are selected from each population; summary statistics are shown below. (a) Test the null hypothesis that the mean LDL cholesterol levels are the same for each of the four populations. What are the degrees of freedom associated with this test? (b) What do you conclude? (c) What assumptions about the data must be true for you to use the one-way analysis of variance technique? (d) Is it necessary to take an additional step in this analysis? If so, what is it? Explain.

Explanation / Answer

from above

a)

b) as p value is significantly low, we conlcude that there is at least two groups have diffierent means.

c) the assumptions made is that population follows norma;l distribution and have equal std deviation or variances

also they are independent.

d) Yes as we found test to be significant, we would like to see among which groups there exist a differnece among means

i ni Yi S;^2 ni*(Yi-mean)^2 (ni-1)Si^2 1 73 6.22 0.83 11.826 49.601 2 105 5.81 0.894 0.006 83.121 3 240 5.77 0.51 0.541 62.164 4 1080 5.47 0.741 130.417 592.458 mean 5.8175 142.791 787.344 Source of variation SS df MS F P value F crit Between groups 142.791 3 47.597 90.316 0.00000 2.610859 with in groups 787.344 1494 0.527 total 930.134 1497

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