Intraclass Correlation Coefficient (ICC) the appropriate method?

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The discussion focuses on determining the reliability of a single instrument using test-retest reliability measures. The user is considering whether to use the intraclass correlation coefficient (ICC) computed in SPSS or to fit a random effects model for calculating ICC. They express confusion about specifying ICC for single measures with repeated observations and the implications of using ICC(3,10) versus ICC(3,1). Additionally, they raise concerns about potential interactions in a multilevel model affecting reliability assessment and confidence interval calculations. The user seeks guidance on the most appropriate method for their analysis.
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Homework Statement


I wish to determine whether a SINGLE instrument provides reliable measures (test-retest reliability). This single instrument is not random (it's the only one available), and I will take 10 measurements for each individual that is part of a control group (and then again for each individuals that is part of the treatment group).


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The Attempt at a Solution


I am reading a lot about intraclass correlation coefficient (ICC) but they all appear to require several different raters in packages such as SPSS. I am confused about whether I should use the ICC computed using SPSS or if I should fit a random effects model to directly calculate the ICC (or maybe they're the same thing?).

For the ICC, I was thinking of using ICC(3,10) by averaging the 10 observations. However, I am baffled as to how to specify ICC when I want to look at single measures - the documentation I've found for ICC(3,1) doesn't look like it allows for repeated measures for individuals.

For the random effects model, I would have 10 repeated measures for each individual, each as a linear combination of the group mean, the individual mean, plus an error that depends on the instrument. However, there may be interaction with the group, individual, and instrument so this may turn into a multilevel model. In that case, I'm not sure how reliability can be determined, and whether I can obtain confidence intervals for that.

Please advise on which method would be more appropriate. Thanks!
 
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Sorry for double-posting. The problem has been solved.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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