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I measured weight of 5 participants, 5 times each, on 3 different scales accurate to 5 places after decimals.

In total, I took: [5 participants] x [5 times each] x [3 different scales] = 75 measurements.

EDIT 1: My null hypothesis is that the weight measured by the three weighing scales is the same. I'd like to be able to say with the help of a statistical test: 1) Whether or not any of the weighing scale is different, 2) If any of the three scales is indeed different, which one?

Since weight is a continuous response variable, if I wanted to use ANCOVA to test for differences between the scales, should I use participant ID (e.g. 1, 2, 3, 4, 5) as a covariate and run the ANCOVA?

Any pointers to the rights statistical test for such an analysis and the R functions I should look at would be greatly appreciated!

EDIT 2: For some additional context: the data has already been acquired as before and we cannot acquire new data. Looking at this data in retrospect, I first thought of ANOVA and then wondered if participant ID should be included as a covariate since measurements were repeated 5 times for each participant on all the scales.

Thanks to @whuber for teasing out the details and enriching the question.

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  • $\begingroup$ Just checking if anyone would be interested in answering! $\endgroup$
    – PAF
    Apr 14, 2020 at 10:39
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    $\begingroup$ The answer depends entirely on the purpose of performing this analysis. Unless the ID has some inherent, generalizable meaning, when you use participant ID as a covariate, you rule out all possibility of generalizing the results to anyone other than the participants. Are you really engaged in such a limited analysis? $\endgroup$
    – whuber
    Apr 18, 2020 at 14:44
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    $\begingroup$ Thanks a lot for your response @whuber, appreciate it. I just edited my post for additional context: "My null hypothesis is that the weight measured by the three weighing scales is the same." You raised an interesting question, no the end goal is not to come to a conclusion about the 5 participants, as you point out. Instead, I'd like to be able to say with the help of a statistical test: 1) Whether or not any of the weighing scale is different, 2) If any of the three scales is indeed different, which one? $\endgroup$
    – PAF
    Apr 18, 2020 at 15:36
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    $\begingroup$ That's interesting, because it suggests you study is not about "5 participants," but it's really about three scales. This seems like an elaborate and costly way to calibrate a set of scales! Is this really what your objective is? $\endgroup$
    – whuber
    Apr 18, 2020 at 15:42
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    $\begingroup$ @whuber, let's say that our experimenter has a lot of time and money at hand, not really constrained. Also let's say we are not at the liberty to acquire more data, these are the measurements we have, and now we just need to answer points 1) and 2) using the right statistical test (or as right as it can be in retrospect). I actually used ANOVA to do this, but then wondered if I'd get criticized if I did not include participant ID as a covariate, hence the question. Appreciate your interest in the problem! $\endgroup$
    – PAF
    Apr 18, 2020 at 15:47

1 Answer 1

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No, it is not advisable to use Participant ID as covariate, considering your hypothesis.

One of the assumptions of ANCOVA is that covarriate should be linearly related to the dependent variable. In this case, the Participant ID should be linearly related to the the weights which means when the participant ID is increasing the weight should be either increasing or decreasing. Moreover participant ID is a nominal variable and you cannot assume linear relationship with the nominal variable.

Even if you want use the participant ID as a covariate, you can use it with a dummy variable i.e., one of the participant IDs will be set as a reference and the output table will have all the categories of participant ID except the reference participant ID. You have to interpret the results accordingly.

It is better to stick to ANOVA, as your hypothesis is about the difference among weights measured by the three weighing scales only. You can take the descriptives of the measurements by the scales to check the differences among the means in each scales. Further, you can perform the post-hoc like Tukey or Duncan to find which pairs of means (among each pairs of scales) are making the significant difference. From this, you can find which scale is indeed different.

Edit:

Thank you @Carlos

You can include the participant ID into the ANOVA, so that you can find the fixed effect and the random effect which would add a little meaning to the model.

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    $\begingroup$ you are missing an important part: participant's id is a paramount blocking factor (one may prefer a random effect model, it would make little difference, as measurement error is expected to be extremely lower than sample variability) $\endgroup$
    – carlo
    Apr 24, 2020 at 18:49

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