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Single subject study test force with:

  • 2 Devices simultaneasly (A and B)
  • 5 differents positions (s1,s2,s3,s4 and s5).
  • 2 differents rooms (Y and Z)

Repeat each position 6 times consecutly. Different rooms test in different days.

Interested in:

  • With the same device, can we find significance differences between rooms?
  • In the same room and in the same device, can we find significance differences between positions?
  • For the six repeated measures for each position, which kind of reliability option can we report? Or maybe is repeatability?

From the point of view of the study, I understand that the variability of the repeated measurements for each position should be less than the difference between position 1 and 2 so that the change between 1 and 2 could be considered real.

My idea is to calculate, if possible, the standard error of the measurement for the pairs of positions (s1-s2...), and add it to the average of the 6 repeated measurements of each position, and check if ranges overlap. If there is no overlap, we could be saying that the change is real.

For example, we have an average for the repeated measurements of position 1 of 250, and an average for position s2 of 240. The standard error of the measurement for the two rows (s1 and s2) of 6 data (6 repeated measurements) de gives us 9. With this we would have that s1 could be between 241 and 259, and s2 between 249 and 231. Since the ranges overlap we could say that there is no real difference.

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  • $\begingroup$ I've tried to make the question clearer, please check I haven't got anything wrong. I don't think this is repeated measures anova. I don't quite understand your question: You have three categorical predictors, and one continuous outcome. You can therefore test 3 main effects (plus post-hoc analysis), three two-way interactions, and 1 three-way interaction. What do you want a confidence interval of? Finally,I"m not sure that anyone without substantive knowledge of the area can say whether the difference is relevant on a practical level. $\endgroup$ Commented Mar 14 at 16:26
  • $\begingroup$ On the one hand, I would like to report a value that characterizes the differences between the 6 test-retest measures for each of the 5 positions. Right now I have thought about the standard deviation, but I don't know if with this design I could opt for some other measure of reliability. Right now I have done a repeated measures anova in which I am only interested in the posthoc to compare the same position of the same method between different rooms. $\endgroup$
    – mdscience
    Commented Mar 14 at 18:07
  • $\begingroup$ But from another, more practical perspective, I would like to analyze the behavior of the 2 devices in rooms Y and Z. How? Going back to the beginning, I would like to know if the change between positions is real, that is, if this change is larger than the changes that are observed for records made with the same position. This is why I had thought about the SEM and the MDC. However, I don't know if it could actually fit this approach. $\endgroup$
    – mdscience
    Commented Mar 14 at 18:07
  • $\begingroup$ There are a lot of questions here, and a lot to unpack, so it's hard to write an answer. One thing to consider is that reliability and anova are very closely linked. Reliability is estimated using the ICC - the intra-class correlation, which is based on the sums of squares, anova is also based on the sums of squares. If your means are the same in the different conditions, your reliability (ICC) will be zero. $\endgroup$ Commented Mar 15 at 3:27
  • $\begingroup$ This is not a repeated measures anova. If it is repeated measures, your N is 1, and you cannot analyze anything. Remove that or no one can answer the question. $\endgroup$ Commented Mar 15 at 3:28

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