The joys of Z-scores

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    Ajay Halai

    Hi everyone,

    There might be a very simple answer to this question, but I am yet to come across one. So I hope you can help me, or steer me towards the right answer.

    I am working on some neuroimaging data, that have been collected using different acquisition methods. Essentially, this means that each method has a slightly difference sensitivity to certain aspects we are interested in. I have done the ‘usual’ analysis using a fairly standardised analysis toolbox (SPM,

    As each method has different characteristics, which is largely seen as differences in mean and variance, I decided to convert the group average into z-scores.

    I have two questions:

    1). I think this is doing fundamentally different things, but when I calculate a z-score of the group brain map, I get results that fit the output at group level (i.e if the output shows regions of activiation, then the z-scores are reflected in this). However, I thought to obtain variance to do stats on whether there was a difference between methods, I calculated a z-score for each subject then averaged and conducted within subjects ANOVAs on these. This two values, the z-score at the overall group level and at the subject level where different, and I think it is because they are calculating different things. But I can’t quite get my head around it.

    2). If when I calculate a group z-score, I get say a higher score for one method in comparison to another. Is there a way I can check if they are statistically different, given that z-scores are measures of variance. The problem is that it is only comparing one value to another.

    3). Another way I thought of doing this was to compare the t-values, as I think this value would take into account differences of each method.

    I am not sure if that makes sense. Please feel free to comment, or ask for more details.

    Best wishs


    Rafael Garcia


    What sort of multiple methods are you using?

    Ajay Halai


    I am using different fMRI acquisition methods. I am using two Gradient-echoes (GE) at short and long echo times and Spin-echo (SE).

    I was thinking in terms of comparing group z-score values. I have read that using sampling distributions can allow you to compare z-scores. By taking the z-score and adding/subtracting the standard error to give you boundaries for the distribution.

    For example, if I wanted to compare an overall z-score of 2.6 and 1.6 for 14 subjects. The standard error would be S.D / sqrt(N) –> SD = 1 (as it is z-score) and N = 14 therefore Standard error = 0.267. Then the boundaries for 2.6 would be 2.066, 2.333, 2.6, 2.867, 3.134. As 1.6 is lower than 2.066 (2 SE away from the mean), than we can suggest that 2.6 is significantly higher than 1.6 at 0.05 alpha, based on 14 subjects.

    Could anyone comment on that, please?

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