(only visible if either the Least Squares or Save Means...:
Only available if a means file has been opened (see "Open Means
File..." and "New Means File..." under the File Menu), if the current
statistics have not been saved, and if some statistics have been chosen. For
each active statistic (see below), you will be prompted for a three letter code
and a line of arbitrary length to be used in identifying the mean in the
future. Hitting "Cancel" will result in that particular statistic not being
saved; you will still be prompted for the other statistics that are active, and
any statistics saved in the same "Save Means" call by pressing OK (or hitting
enter) will be saved to the means file. The file is updated immediately; its
format is described in the "Data Formats" section below.
Brings up a dialog box for selecting the statistics to be
applied to the active equal area window (see dialog box below). Checking the
"Fisher" option produces a mean, kappa (), and using
Fisher statistics. As described in the Statistics section, directions
and statistics obtained with approximations produce a beep (up to 4 beeps for a
Least Squares Equal Area plot and 6 for the Locality Equal Area plot). The
Plot Error Ellipse option becomes active once the Fisher Stats option is
selected; when checked, the cone of confidence is plotted. The
"Hemisphere" option is identical to the "Fisher Stats" above except that points
in opposite hemispheres are inverted; this produces a Fisher mean of reversed
and normal polarities inverted through the origin so that they can be combined.
More details are in the Statistics section. When the "Elliptical statistics"
option is selected, either the Bingham or the Non-Parametric Statistic can be
used; one or the other will be checked. Bingham uses Bingham
statistics. Note that this uses a lookup table and approximations for the
construction of the estimates that are probably unreliable for data
distributed in a girdle (plane data). "Non-Parametric Stats" uses
non-parametric statistics suggested by Watson as presented in Fisher et al.
(1987) (thus the label "Watson" when the statistic is displayed). This
statistic becomes more accurate with larger numbers of directions; the
uncertainty ellipses are probably unreliable with under about 20 samples.
"Plot Girdle" plots the girdle to the confidence ellipse (the ellipse plus and
minus 90°ree;). This might be desired if you had a group of plane or circle
fits that all clustered near each other and you wished to plot the region where
the two magnetization components would lie.
One of the three options below is always checked when the "Elliptical stats"
option is active:
One of two options is available when either the Fisher or Fisher "Hemisphere"
statistics buttons is checked (the options will apply to both forms of Fisher
means if both are checked):
- Use as Lines: Assume all the plotted data represent line fits (i.e., are drawn
from a bipolar distribution). Thus apply bipolar forms of the elliptical
statistics to the data.
- Use as Planes: Assume all points represent plane or circle fits (i.e., drawn
from a girdle distribution). Thus apply the girdle forms of the elliptical
statistics (which produces the pole to the plane that best fits the data).
- Combine Lines plus Planes: Only available in the Least Squares Equal Area
plot. As described below in the Statistics section, combine line and plane
fits to get the best estimate of the desired magnetization component.
Conducts a reversal test on the points displayed in the active
window using the formulation described by McFadden and McElhinny (1990a).
Directions are tested in the current coordinate frame (geographic or
tilt-corrected). Directions are divided into two antipodal groups using the
algorithm described under "Hemisphere Fisher" in the Statistics section, below.
Concentration parameters (k's) are calculated for each group, and the two
populations are tested against the null hypothesis that they have identical
concentration parameters, provided at least 5 directions are in each group. If
the directions pass the "common concentration" test (that is, the null
hypothesis cannot be rejected at the 90% confidence level), then a common mean
between the two sets (one reversed through the origin) is tested using the
analytic equation in McFadden and McElhinny (1990a). If the "common
concentration" test is failed, or there are less than 5 directions in one or
both polarities, the bootstrap (sampling simulation) techniques of
McFadden and McElhinny (1990a) is used. This is time consuming, particularly if a large
number of directions are simulated. When either test is completed, its results
are presented in the dialog, indicating if the directions passed or failed the
reversal test or if the test was inconclusive. If the test is passed, the
classification of McFadden and McElhinny (1990a) is given (A, B, or C) along
with the critical angle at the 95% confidence level (the angle which, if
exceeded by the angular difference between the two means, indicates failure of
the test). In all instances the angular difference between the two means is
given. The user can either print the results or copy them to the clipboard.
For example, the dialog above indicates that the test was performed on
tilt-corrected directions, that these directions pass a common distribution
test. (The calculated F of the F test exceeds F0.80; thus the null hypothesis
would only be rejected at the 20% confidence level). The means differ by
12.7°ree;, much less than the 26.1°ree; critical angle, indicating that the data
pass the reversal test at the 95% confidence limit. But the high value of the
critical angle places this in the "indeterminate" classification of McFadden and McElhinny (1990a). The null hypothesis of a common mean would be rejected at or
below the 53% confidence level.
Note that this code is not derived from the code that McFadden and McElhinny
offer in their paper but was written from the algorithm described in the paper.
Also, tests of the bootstrap code on data with identical
concentration parameters yielded higher critical angles than those derived from
the analytic equation for populations with a common concentration parameter.
Thus the bootstrap test might pass data that should fail. The only test
suggested by McFadden and McElhinny (1990a) not implemented here is the test for a
single direction comprising one of the two groups.
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