Biomedical Engineering Reference
In-Depth Information
2.2. Code and Sample
Data
We assume familiarity with data exploration in MATLAB. In each
section, where possible, we provide a 'snippet' of MATLAB code
that can be rapidly run on random data; this code is meant to give
a flavor of each analysis and should be used for exploratory anal-
ysis. The exact code and techniques we use for estimating inter-
actions often rely on toolboxes for MATLAB, and span several
hundred lines of code. For these reasons, the code included here
is relatively simple but demonstrates the principles that are rel-
evant in studying functional interactions; the exact code along
with a sample data of 11 motor cortex neurons is on our website:
http://spikelab.jbpierce.org/Resources/FunctionalInteractions.
3. Statistical
Significance of
Functional
Interactions
In any analysis of functional interactions, one must establish
clear criteria for statistical significance to determine if interactions
observed are due to chance. Although published formulas exist
for determining the significance of many statistical tests, we sug-
gest a statistical approach in which the empirical probability value
for any test statistic should be computed for each analysis of inter-
est. This approach has power because assumptions and data distri-
butions accounted for by published formulas may be violated by
particular data sets of interest. The best way to establish empirical
significance is to reapply the same statistical tests to the same data
in which the dimension of interest is randomly permuted. Most
commonly, this dimension is either in
time
or in
trials
(
Fig. 7.2
).
Using shuffling, one might test the significance of a functional
interaction by:
Fig. 7.2. Principles of shuffling can be used to assess empirical significance. (A) Time shuffling: In measures of cor-
relation between spike trains, statistical significance can be assessed by comparing data of interest to test statistics
generated from time-shuffled data in which spikes are shifted in time. This preserves basic statistics (i.e., firing rate),
while destroying temporal information. (B) Trial shuffling: In measures of correlation between neurons over trials, sta-
tistical significance can be assessed by comparing data of interest to test-statistics generated from trial-shuffled data
in which spikes from one trial are shifted to another trial. In a 'shift predictor', they are shifted by one trial; however, to
account for non-stationarities, it is best to simply scramble the trial order. This preserves basic statistics (i.e., peristimulus
time histograms, firing rate), while destroying trial-by-trial relationships with other neurons and with behavior.
