Statistics Notes
What is the procedure used to create the
Chisquare and Variance graphs, and how should they be interpretated?
The Chisquare figures show the cumulative
deviation of the second-by-second local deviations from expectation,
compounded across the N eggs (N=36 to 38 at this time).
That is, for each second, the Z's for all the N eggs
are added and normalized by sqrt(N), then the resulting Z is
squared to yield a Chisquare with 1 df, and finally the
Chisquares-1 (Chisq=1 is the expectation) are cumulatively
summed, to represent the departure from expectation.
More details are available
in exact descriptions of the GCP methods and
procedures and in the
extended analysis page.
The Variance figures show something similar, but instead of
the compounded Z across eggs, the variance (squared standard
deviation) is computed across the N eggs for each second.
The sequence of Variance-50 (Var=50 is the expectation) is then
cumulatively summed as before.
The Chisquare figure displays extreme departures, in either
direction, of the trial scores of the egg from what is
expected by chance. The Variance figure displays the degree
of variability among the trial scores for the eggs. Chisquare
addresses movement of the central value of the distribution,
Variance represents changes in the range or width of the distribution.
What is the difference in the the analyses by Roger Nelson and Dean
Radin?
The most important difference is in the treatment of the data at the
finest scale. Neither way is superior,
but there is a difference in what is expected or hypothesized about the
behavior of the eggs in the
presence of a possible influence. The two perspectives are
complementary, and though they are not fully
independent, using both contributes to our confidence that the apparent
effects are not accidents or
mistakes.
For each second, Roger calculates what is called a Stouffer Z across the
eggs as described above. This
means that in order to produce a large deviation, the eggs have to have
a positive correlation to be
doing the same thing. This composite Z is squared, so it does not matter
whether the average value is
shifted to the high or low direction, but there must be some excess
deviation and there must be a
tendency toward inter-egg consistency in the direction of deviation. The
result is a single squared
Z-score, which is Chi-square distributed, for each second.
Dean calculates a Z-score for each egg separately, and squares these
individual Z-scores. He then
sums the squared Z's across the eggs, producing a a single Chi-square
for each second. In this case,
the eggs are not expected to show a positive correlation, and a high
score requires only that there is a
tendency for excess deviation in either direction; no inter-egg
consistency in the direction of deviation is
predicted. Again, the result is a single squared Z-score, which is
Chi-square distributed, for each
second.
Dean's method of summing Z² is closely
related to Roger's variance analysis.
More
Many other analyses and graphs have been generated, and some show
certain details and perspectives that may interest you. The extended analysis page has most of the figures
shown here, but in the context of the developing analysis program over
the first few days following the tragedy. A question of particular
interest is whether distance makes a difference.
Dean Radin separated the results by
location of the eggs in a careful analysis.
Peter Bancel has been looking at the
interegg correlations and has
provided a draft report.
There is also an Interpretations page in the works, and one
that simply presents the flood of messages
from people all over the world who are involved in the GCP/EGG project.
For more details about the project itself, you can go to the GCP home page where you will
find links to all aspects.