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I have a repeated measures experiment where all participants completed several trials for each condition. My dependent variables are response time and accuracy. I am using the Interquartile Range as my outlier removal criteria. Before I ask my questions, here are a few details on the IQR:

The IQR represents the central 50 percent or the area between the 75th and 25th percentile of a distribution. Any point is an outlier if it is above the 75th percentile or below the 25th percentile by a factor of 1.5 times the IQR.

Here, we can describe our dataset with:

  1. Minimum (lowest) value of the data
  2. Quartile 1 = Q1 = first quartile = 25% of the data starting from the minimum value
  3. Quartile 2 = median = Q2 = midpoint of the dataset
  4. Quartile 3 = Q3 = 75% of the data starting from the minimum value
  5. Maximum value of the data set

The Interquartile Range = IQR = Q3 – Q1 = how the data are spread about the median. We then use the IQR to find the lower and upper bounds of our exclusion criteria:

  • lower: [Q1- (1.5)*IQR]
  • upper: [Q3+(1.5)*IQR]

Note: the 1.5 is a scale value. When you do the math, we can see that anything beyond 2.7 sigmas from the mean would be considered an outlier and this is closest to the Gaussian Distribution where an outlier is is any value beyond 3 sigmas of either side of the mean.

Here is a Wikipedia image (https://en.wikipedia.org/wiki/Interquartile_range):

enter image description here

My Questions:

Is it valid to remove trials as outliers using the IQR method? Is it more valid to (1) find the IQR of all subjects and then remove these trials or (2) to find the IQR of each subject and then remove each subject's respective outlier trials?

It seems more valid to remove trials rather than all of a single participants data because they may only have a few trials (of the many) that represent inattention (e.g., spaced out momentarily). And, these few trials might throw off their overall response time (or accuracy) measure.

Thanks for the input.

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    $\begingroup$ This amounts to removing outliers identified in a standard boxplot. Please, then, search our site for appropriate answers. The hit at stats.stackexchange.com/questions/259654 looks like a good place to start. $\endgroup$
    – whuber
    Oct 10, 2021 at 19:27
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    $\begingroup$ Why remove any points at all? The values you have are the values you measured, right? $\endgroup$
    – Dave
    Oct 10, 2021 at 19:37
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    $\begingroup$ I think it is OK to remove for highly-suspected 'inattention'. But your removal based on IQR has an automated feel that worries me. Important to bear in mind that even moderately large computer-generated normal samples often have a few outliers. Samples from moderately right-skewed distribution characteristically have high boxplot outliers. $\endgroup$
    – BruceET
    Oct 11, 2021 at 1:02
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    $\begingroup$ It would definitely be wrong to remove trials based on a lumped analysis of all participants. There are many options available, but providing good advice comes down to understanding what you really hope to accomplish by removing some of your data. $\endgroup$
    – whuber
    Oct 11, 2021 at 14:11
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    $\begingroup$ I am not suggesting anything like that, because--as others have commented here--such automatic methods are often inferior or even misleading. Better potential alternatives include using robust statistical procedures that do not require preliminary outlier identification and removal. What is best, or even reasonable, to do depends on what analyses you intend to perform. $\endgroup$
    – whuber
    Oct 11, 2021 at 15:27

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