Re: time series hypothesis test

Depending on what you mean by "differentiate the signal", this might be
just the same as taking the difference between the first and last values and
rescaling.

oops... talk about not seeing the forest for the trees. you're absolutely
right


But I have been told by a statistician that the assumption of
independence has been violated, because each value in a time series
is related... If we were to assume that each value is indeed still
related (even after my differentiation), then surely this still does
not break the assumption of independence for the rank sum test?
Because as I understand it, the 'assumptions of independence' concern
the independence between the sources of the observations - that is,
each trial must be fully independent of the others. This does not
(again, as I understand it) have anything to do with how one obtains
some final value that represents that single observation.


You might be right, but this would depend on what you mean by
"independence between the sources of the observation".

in my case I am using human participants, so this means that they must be
randomly selected and assigned to the experimental and control groups - as
you say below.


Notionally you want every value in a
given time series to be statistically independent of all values in every
other time-series. Statistical dependence might arise if some time-series
are recorded
over the same time-period and if there are common (randomly-varying)
factors that affect all series .... depending on context, such a factor
might be
temperature, economic conditions. So you need to think about all the
sources of variation that might affect val;ues in any given series
(fluctuation about the
trend), and think about whether the same source of variation may lead to
fluctutions in more than one series.

The problem would be most severe if all the series in one or both groups
had some dependence within the group.

Of course, if you have designed your experiment properly, you will have
protected yourself from the problem entirely if you have done a random
assignment of
the "control" or "experiment" tags to each of potential trials, as this
random assignment would induce all the statistical independence between
trial that you
require for the test.

David Jones

Thanks very much for your help - I believe it is clear to me now =)

J



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