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I have a data set consisting of reaction time (RT) measurements. These will be used to calculate the duration of experimental trials in an MRI study. In each block (experimental condition) there are 10 trials. Now, due to various issues, there are some missing RTs. Due to the nature of MRI analysis, I need values for all 10 trials per block. Where more than 5 values are missing I will probably discard it from the analysis completely, but where only 1 or 2 are missing I plan on using the mean RT value for that condition in place of the missing value. However, I want to make sure that this is a principled decision to make, as the RT values in some conditions, by the same participant, can be quite variable.

How can I use the standard deviation or standard error of the mean to ensure that it is 'fair' to use the mean in place of the missing value? For example, see the data below.

Block 1 - Missing values: 2; Mean: 740; SD: 519; SEM: 196. Block 2 - Missing values: 1; Mean: 2245; SD: 292; SEM: 97.

I'm trying to figure out an honest, consistent way of deciding whether the decision to replace the missing value with the mean is sound. Where it is not, I would rather leave the block out of the analysis than skew the data.

Any advice? I hope this makes sense.

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  • $\begingroup$ A key to a good answer may lie in understanding how the "various issues" leading to missing RTs could influence the analysis. Could you then perhaps provide some information about the reasons for missingness? Also, what kind of "MRI anlaysis" do you have in mind (which requires values for all 10 trials)? Perhaps there's a substitute procedure that handles missing values in a more flexible way. $\endgroup$
    – whuber
    Jun 29, 2012 at 19:52
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    $\begingroup$ The RTs were behavioural observations using a video recorder. Sometimes the behaviour occurred slightly off-camera and therefore an RT value cannot be made. In terms of the MRI, the design is like this.. 10 seconds prep, 12 seconds 'action', 8 seconds rest. This is repeated 10 times in a block. The RT eats into the 12 seconds 'action' - thus lengthening the prep time and lessening the 'action' time. I want to do a comparison which represents this. So the analysis will be looking at functional data from the new 'prep+RT' and the new 'Action-RT' times. $\endgroup$
    – tony gabay
    Jun 29, 2012 at 20:16

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I don't think the standard error of the mean tells you anything that would aid imputation. If the sample size is large it will be small but it will not tell you what you want to know about subject to subject variability. Maybe there are factors that would explain long and short RTs relative to the mean. The variance from case to case is more relevant toward helping you decide on whether or not the mean time would be at all useful for imputation. If you have explanatory variables that through a rgeression you can show reduces this variability then the model might give oyu a better method for imputation.

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