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Static versus Dynamic Z-Scores

The following drawing from a forthcoming book is posted by popular demand.  It illustrates the basic concepts of static versus dynamic z-scores.  Note that z-scores based on the static distribution will be larger, but in the same direction, as z-scores based on the dynamic distribution.  Both BrainAvatar/BrainDX and NeuroGuide Deluxe use the static distribution for z-scores.  The ANI Z DLL uses the dynamic distribution for z-scores.  Therefore, “BrainAvatar/BrainDX live maps should (and do) look like NeuroGuide Deluxe maps.”

Whether you use FFT or JTFA is an issue of how you average the data over time.  FFT uses a fixed “epoch,” say 1 or 2 seconds, to compute each block of data.  JTFA computes the output continuously, on each datapoint.  Both of them are Fourier-based methods, and both of them would produce identical data, if the input signal was a steady sinewave.  They would “converge” over time to the correct amplitude value, although their time response would look different.
The second issue is whether or not you consider the short-term variations.  A “static” norm is based on a long term average, say a minute.  You can get that data either from an FFT or JTFA, it does not matter, and you would get the same 1-minute average (or very close) by either method.  A static norm is built up of taking a lot of 1- or 2-minute averages from a lot of people, and seeing how the values distribute.  This is the static norm.  it is the range of the individual averages, over many individuals.  It does not reflect the momentary variations in the signal during the minute, it ignores them.
A dynamic norm is obtained when you take the momentary variation in the data during that minute, and add it into the analysis.  This produces more variance in the data, so there is more spread.  The dynamic norm has a larger standard deviation.  For example, although it is very rare for someone’s average alpha to be 18 microvolts, it is not at all unusual for it to reach that value momentarily.  So while 18 microvolts of alpha may be 3 standard deviations high as a static norm, it would only be more like 2 standard deviations high as a dynamic norm.  How you got the 18 microvolts does not matter, it could be from a momentary FFT, or from a spot on a JTFA curve.
In real-time, most everyone uses JTFA (or digital filters, which are mathematically equivalent), or an FFT (which no one uses, because the epoch delay is too long), you still have the choice of comparing to either a static norm or a dynamic norm.  When we started using the ANI Z DLL, people were dismayed to see the smaller z-scores than they saw in the maps, until we explained this important difference.  There is nothing wrong with using the dynamic norm for live z-scores, but there is also nothing wrong with simply using the static norms either.  As the chart I point to shows, the mean values (targets) are by definition identical.  They have to have the same mean value, and the only difference is the standard deviations.  Therefore, the statement that “only an instantaneous norm can be used to compute a valid instantaneous Z score is not correct.”
Because we chose to use a static reference, you see now that the BrainDX live surface maps look essentially identical to the NeuroGuide Deluxe static maps of the same data segment.  When running live, the map changes in real-time, but when you average out by applying a damping factor, the maps converge, just as they should.
People using the BrainDX live Z DLL in BrainAvatar are now becoming accustomed to seeing z scores more in line with the static maps, which is fine.  It is not a problem.  No one has “complained” about the z-scores being too high.  Most are relieved to now see live z-scores that match their NeuroGuide maps, which is completely reasonable, and is in fact what was expected years ago, so now we are able to provide data in that scaling format.

 

 

 

The following  illustration from Collura et al. (2009) and produced by Dr. Thatcher shows that the only difference between the static and dynamic z-scores is the denominator, which accounts for the difference in variance.  By this analysis, it is clear that the target values (means) for both types of z-scores must be identical:

 

 

 

Collura, T.F., Thatcher, R.W., Smith, M.L., Lambos, W.A., and C.R. Stark (2009) EEG Biofeedback training using Z-scores and a normative database, in: (Evans, W., Budzynski, T., Budzynski, H., and A. Arbanal, eds) Introduction to QEEG and Neurofeedback : Advanced Theory and Applications, Second Edition. New York: Elsevier.

Available at:

 

http://www.brainm.com/software/pubs/budz%20collura%20z-score.pdf

 

Conclusion: It has been shown that the relationships between three types of norms are as follows:

population dynamic data show the largest distribution, hence will produce the lowest z-scores.

population static data will produce higher z-scores, but will have the same target (mean) values as the population dynamic references

individual dynamic data will have a different mean for each individual, and a distribution that is smaller than the population dynamic data.  Z-scores based on this referencew will reflect how the client compares with the individual from whom the reference data were gathered.

 

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