An experiment was run to compare three groups. The sample sizes were 27, 31, and

Question

An experiment was run to compare three groups. The sample sizes were 27, 31, and 122, and the corresponding estimated standard deviations were 37, 28, and 46. (a) Is it reasonable to use the assumption of equal standard deviations when we analyze these data? Give a reason for your answer. (a) Based on the description of the experiment, what should the degrees of freedom be for this analysis? (b) Assuming that the degrees of freedom reported are correct, data from how many athletes were used in this analysis? (c) The researchers do not comment on the missing data in their report. List two reasons why these data may not have been used, and for each, explain how the omission could impact or bias the results.

Explanation / Answer

We have to compair three groups.The sample sizes of these groups are n1 = 27, n2 = 31 n3 = 122 with corresponding estimated standard deviations are s1 = 37, s2 = 28, s3 = 46

a) When we analyze the data the assumption of equal variance is not reasonable as the grop of athletes have differnt standard deviations.

b) Assuming that the degree of freedom reported are correct, the number of athlets used in the analysis are 27 + 31 + 122 = 180

c) The researchers do not comment on the missing data in their report because,

i) Missing data may be influence the prediction of the analysis.

ii) Variance increase due to missing data thats why the researchers do not comment on the missing data.

Due to omission of the data changes estimate of coefficets thats why bias should be increased.

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