Statistics menu

(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.

Which Statistics...:
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 (kappa), and alpha-95 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 alpha-95 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 alpha-95 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):

Reversal Test:
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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