Hi,

I have some general questions about statistical analysis for a research
dataset and a request for advice on using R and associated packages for a
valid analysis of this data.  I can only pose the problem as how to run
multiple ANOVA tests on time series data, with reasonable controls of the
family-wise error rate.  If we run analysis at many small sections of a long
time-series, the Type-I family-wise error rate is a concern.  Is it
important to consider the temporal dependence in the time-series data?
There are papers on ramdomization tests for the sort of time-series data we
have (eg, Blair and Karnisky, 1993), but these papers often report only
t-test comparisons, not F-tests with 2+ factors.

BACKGROUND:

We have a dataset from a human neuroimaging experiment.  Subjects view a
screen, with a fixation point at the center.  A cue arrow appears, directing
their attention to the lower left or right visual field (cue left or cue
right, this is one factor in our analysis).  After 1 sec, a stimulus (S)
appears in the lower left or right visual quadrant and subjects have to
respond to it only if it appeared in the cued location.  This sequence of
events repeated hundreds of times.  Each trial comprised a cue followed 1
sec later by a stimulus (cue - S), with a longer gap in between these trials
(about 2 sec).

The brain activity was measured with magnetoencephalography (MEG), with a
very high sample rate (1200 Hz).  The activity from 275 MEG sensors was
segmented precisely in relation to the onset of the cue.  Each of these
segments is known as an 'event-related field' or ERF and the segments for
every cue left or cue right trial were averaged across trials (to improve
signal-to-noise of the event-related activity).  We have data that are
averaged ERFs over several hundred trials.  These averaged ERF for cue left
or cue right was used to estimate the brain source activity (the details are
not relevant here).

A small example dataset and R scripts are available via
ftp://ftp.mrsc.ucsf.edu/pub/dweber/cortical_timeSeries.tar

These example data are from one brain region of interest (roi), called the
middle frontal gyrus (MFG).  We have estimated activity in this brain region
for the left and right cerebral hemisphere (this is one factor in the
analysis).  These data are for a short period prior to the cue (-300 ms) and
a longer period after the cue (1400 ms; the S appeared at 1000 ms).  There
are 8 subjects in this dataset.  Each subject has an ERF

ANALYSIS to DATE:

For each time bin of about 20 ms duration, from -300 to 1400 ms, we need to
evaluate the ANOVA model,

MFGactivity = CUE + HEMI + error

where the CUE (left, right) and HEMI (left, right) interactions are
important.  These two factors are within-subjects factors (ie, repeated
measures for each subject).  In classical terms, this is a split-plot
design.  The data frame and aov model are specified in the R scripts of the
download.

Given time-bins of about 20ms and a time-series of -300 to 1400 ms at small
increments of 1-2 ms, we have a lot of analyses in just one brain region.
How can we do this analysis and minimize family-wise error rates?  Is it
possible to run permutation analysis for an ANOVA model?

R scripts in the download:

source("Rscript_HiN_cortical_roi_analysis_aov_specifics.R")

This will run ANOVA on several time-bins of the data.  The time-bins are
defined in Rscript_HiN_cortical_roi_analysis_setup.R, which is sourced by
the script above.

Reference
Blair RC, Karniski W. 1993. An alternative method for significance testing
of waveform difference potentials. Psychophysiology 30:518--524.

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