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RAP Statistics
The following statistics can be displayed/printed at present for each stimulus point within any
data set. This is done using the "PRINT STAT" or "PLOT STAT" commands.
NUMSPK
SPKRAT
PKRATE
SSRATE
PK/SSR
SYNC
PHASE
RYCOFF
FSREP
FSLAT
SDLAT
PKLAT
ISMEAN
ISDEV
ISKEW
ISKURT
ISCV
SDRAT
: No. of spikes within analysis window
: Spike rate within analysis window
: Peak spike rate using a 100 microsec window
: Steady state spike rate, using last x% of analysis. window
: Peak rate divided by steady state rate
: Sync. coeff. computed using "HI BF ..."
: Phase computed for "HI BF .." (fraction of cycle)
: Rayleigh coeff. computed from SYNC and NUMSPK
: No. of repetitions with at least one spike
: Mean first spike latency in millisecs
: Standard Dev. of first spike latency (msecs)
: Latency computed using x% to PST peak
: Mean interspike interval from ISI histogram (msecs)
: Std. Dev. from ISI histogram (msecs)
: Skewness of ISI histogram
: Kurtosis of ISI histogram
: ISDEV/ISMEAN for ISI histograms
: Std. Dev. of spike rate for different repetitions
(1) NUMSPK: This is simply the total number of spikes, counted over the specified analysis
window, and over all repetitions at the particular stimulus point. The default analysis window
is the stimulus duration time, and by default all repetitions (trials) are included, but these can
be modified by the "AW ..." and "TR ..." commands.
(2) SPKRAT: Very similar to NUMSPK, except here we convert the spike count to a "spike
rate", expressed as "Number of Spikes per second", by dividing the count by the analysis
window in secs (multiplied by the number of reps). The default analysis window is the stimulus
duration time, and by default all repetitions (trials) are included, but these can be modified by
the "AW ..." and "TR ..." commands.
(3) PKRATE: The "peak spike rate" is computed by computing the spike rate over a fixed time
window (100 microsecs), and sliding this window over the entire "peak window". The largest
spike rate during this window is reported as PKRATE in units of spikes/sec.
The default peak window is the first half of the stimulus duration time, or the first half of the
analysis window, whichever is less. By default all repetitions (trials) are included, but these can
be modified by the "SET PST PKW ..." and "TR ..." commands.
The following commands have a direct impact on the computation of PKRATE:
SET PST PKW #1 #2
AW #1 #2
(Peak window in millisecs)
(Analysis window in millisecs)
(4) SSRATE: The "steady-state spike rate" is computed by computing the mean spike rate over
a time window (the "steady-state window"), which is defined by the “SET PST SSW …”
command.
The default steady-state window is the second half of the stimulus duration time, or the second
half of the analysis window, whichever is less. By default all repetitions (trials) are included,
but these can be modified by the "SET PST SSW ..." and "TR ..." commands.
The following commands have a direct impact on the computation of SSRATE:
SET PST SSW #1 #2
AW #1 #2
(Steady-state window in millisecs)
(Analysis window in millisecs)
(5) PKSSR: The "Peak Spike Rate" is divided by the "Steady-state Rate" to obtain this
statistic. The computation method for the individual statistics is described above.
(6) SYNC: The “sync” or “synchronization coefficient” is sometimes also referred to as the
“vector strength”. It is a dimensionless number that varies between 0 and 1, and provides an
indication of how “phase locked” the unit response is to the stimulus waveform.. It is computed
as follows:
1
sync 
(  cos  i ) 2  (  sin  i ) 2
N
i
i
mod( t i , T )
where
 i  2
T
and ti is the time of occurrence of the i’th spike, T is the time period of one cycle of the
binning frequency, and N is the total number of spikes.
The default binning frequency is the frequency of the stimulus waveform. For some cases
(such as when the stimulus is a noise waveform, e.g.) the binning frequency cannot be
determined by default. In such cases it must be specified first with a “HI BF …” command.
The following commands have a direct impact on the calculation of “sync”:
HI BF ….
AW ….
TR ….
(set binning frequency)
(analysis window in millisecs)
(trial number range)
The default analysis window is the stimulus duration time, and all trials are included by
default.
A graphical way to visualize the “sync coefficient” is to bin a “cycle histogram”. A low sync.
coeff. would be the case where the all the bins have a roughly uniform height, and a high sync.
coeff. would be where there is a single large peak. In the limit, if all bins had exactly the same
height, then the sync. coeff. is exactly zero, and if all the bins are zero except for one, the the
sync. coeff. is exactly 1.0.
(7) PHASE: The Phase is computed as follows:
  sin  i

phase  tan  i
  cos  i
 i
1





mod( t i , T )
T
and ti is the time of occurrence of the i’th spike, and T is the time period of one cycle of the
binning frequency.
where
 i  2
The Phase is converted to units of “fraction of a cycle” before being reported, i.e. it can range
from 0 to 1.0.
The following commands have a direct impact on the calculation of “sync”:
HI BF ….
AW ….
TR ….
(set binning frequency)
(analysis window in millisecs)
(trial number range)
The default analysis window is the stimulus duration time, and all trials are included by
default.
(8) RYCOFF: The “Rayleigh Coefficient” is a measure of the confidence that one may place
in the “sync” and “phase” values described above. A description of it’s calculation is beyond
the scope of this chapter. Some details can be found in “A test for the significance of the mean
direction and the concentration parameter of a circular distribution” by W.S.Rhode (1976),
which can be found at http://www.neurophys.wisc.edu/comp/docs/not011/not011.html
For purposes of this discussion, it should be noted that the smaller the value of RYCOFF, the
more confidence one can place in the values of phase and sync. The RYCOFF is derived from
sync. and numspk (total number of spikes). It is independent of phase. For example, if the
RYCOFF is equal to 0.02 at a particular stimulus point, then there is only a 2 percent chance
that sync. value is non-significant. If RYCOFF is 0.05 then there is a 5 percent chance, and so
on.
(9) FSREP: This is simply a count of the number of stimulus repetitions (at a particular
stimulus point) with at least one spike event. It can range between 0 and the NREP (the number
of stimulus reps actually presented). Only spikes within the analysis window are considered,
thus the “AW ….” And “TR ….” commands have an impact on the result.
(10) FSLAT: This is the mean first spike latency in millisecs. The time of occurrence of the
first spike is averaged for all repetitions at the current stimulus point. The “AW ….” And “TR
…” commands impact the result. It is computed as follows:
1 N
 t (1) i
N i 1
where t(1)i is the time of occurrence of the first spike in trial number “i”. Note that “N” is the
number of trials (repetitions) that actually had at least one spike; trials with no spikes are not
counted in N.
LM 
(11) SDLAT: This is the standard deviation of the first spike latency, in millisecs. The first
spike latency is the time at which the first spike occurs at each repetition. The standard
deviation is computed as follows:
N
SDL 
 t (1)
i 1
N
2
i
  LM 
2
where t(1)i is the time of occurrence of the first spike in trial number “i”, and LM is the mean
first spike latency, computed as explained above. Note that “N” is the number of trials
(repetitions) that actually had at least one spike; trials with no spikes are not counted in N.
(12) PKLAT: This is the “peak latency”, i.e. the latency to the “peak” of the PST histogram,
expressed in millisecs. It is computed as follows:
(a) A PST histogram is binned, with a bin-width of 100 microsecs.
(b) The mean bin height within the steady-state window (“SET PST SSW ….”) is computed.
Call this RS.
(c) The histogram is smoothed using #-point smoothing (“SM PKL #”)
(d) The height of the largest bin within the window set by “SET PST PKW …” is determined.
Call this RM.
(e) The difference of these two is computed:
Diff=RM-RS
(f) A Target bin height is computed as follows:
Targ=RS+(Diff*(Per/100))
where Per is a “percent to peak” defined by the command “PER PKL #” command.
(g) The “Peak Latency” is then computed by looking for the first bin (starting with the second
bin) that is equal to greater than the value of Targ.
(13) ISMEAN: This is the “mean inter-spike interval”, computed from the Inter-spike interval
histogram. The ISI histogram is computed using only the second half of the analysis window,
i.e. spikes in the first half of the analysis window are excluded from the computation. The
units of ISMEAN are millisecs. The default analysis window for the ISI is the stimulus
duration time, and the default number of bins is 100. These can be modified by the “AW ….”
and “NB ….” commands.
(14)
ISDEV: This is the “Standard deviation of the inter-spike interval”, computed from the
Inter-spike Interval histogram. The ISI histogram is computed using only the second half of the
analysis window, i.e. spikes in the first half of the analysis window are excluded from the
computation. The units of ISDEV are millisecs. The default analysis window for the ISI is the
stimulus duration time, and the default number of bins is 100. These can be modified by the
“AW ….” and “NB ….” commands.
(15) ISKEW: This is the “skewness of the inter-spike interval histogram”. The skewness is the
third moment about the mean. If the ISKEW is negative, it suggests that the histogram is
“skewed” to the left, if it is positive then the histogram is skewed to the right. A histogram that
is perfectly symmetric about it’s mean will have a skewness of zero. As for ISDEV and
ISMEAN, the ISI histogram is binned only on the last half of the analysis window. It is
computed as follows:
1 M
 H i ti
N i 1
1 M
2
U 2   H i t i 
N i 1
1 M
3
U 3   H i t i 
N i 1
U1 
UM 2  U 2  U 1 
2
UM 3  U 3  (3U1U 2 )  (2U1 )
UM 3
Skew 
3
UM 2 2
where M is the number of bins, and N is the total number of spikes in the histogram.
Hi is the height of the i’th bin, and ti is the time of the i’th bin.
3
(16) ISKURT: This is the “kurtosis” of the Interspike-interval histogram. The ISI histogram
is computed as described above, using the spikes from the second half of the analysis
window. Then:
U4 
1
N
M
 H t 
i 1
i
i
4
UM 4  U 4  ( 4U 1U 3 )  (6U 12U 2 )  (3U 14 )
U4
U 2 2
where U1, U2, U3 are as computed above for the case of Skewness.
The Kurtosis is a measure of the “peakedness” of the histogram. A more sharply peaked
histogram will have a larger kurtosis than one which is more flat.
Kurt 
(17)ISCV: The Coefficient of variation of the Interspike histogram is computed by dividing
the ISMEAN by the ISDEV, each of those being computed as described above.
(18) SDRAT: This is the standard deviation of the spike rate for different repetitions at the
current stimulus point.