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Forum index » Archive » Archive: The Haunted Apiary (Let Op!) » The Haunted Apiary (Let Op!): Puzzles

[PUZZLE] Axons: Statistics

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hamatoyoshi
Veteran

Joined: 02 Aug 2004
Posts: 127

[PUZZLE] Axons: Statistics

I'm starting this thread because I really don't want to deal with any speculation. I just want to figure out what calculations on the coordinates we have can tell us.

Honestly, there isn't much to work with from the data we have, so I'm going to toss out a few basic statistics to start. I'll toss out some explanations on the statistics as well.

Quote:

Mean Center and Standard Distance Deviation:
--------------------------------------------

Sample size ...........: 220
Measurement type ......: Direct
Unit ..................: Degrees

Variable ..............: X Y
Minimum ...............: -124.012600 26.043300
Maximum ...............: -70.279600 48.795000
Mean ..................: -99.334515 39.094994
Standard Deviation ....: 18.077369 5.130798
Geometric Mean ........: -97.674290 38.747400
Harmonic Mean .........: -96.020213 38.386334

Average Density .......: 0.000000 points per sq. m

Std Dist Dev ..........: 1648403.11 m, 5408146.68 ft, 1024.27021 mi

Circle Area Defined
by Std Dist Dev .......: 8536438757279.57 sq m
91885462061086.17 sq ft
3295937.43045 sq mi

The Mean Center is simply the average of the X (Longitude) and the average of the Y (Latitude) coordinates. The Geometric Mean and Harmonic Mean are both methods of eliminating extreme outlying values. I think both of these means can be eliminated due to precisely picked nature of the coordinate set. Nevertheless, (-99.334515, 39.094994) is the average of this coordinate set. I've not gone through the process to locate this on a map. It's probably unimportant at that.

Standard Distance Deviation is the measure of the standard deviation of the distance from each point to the Mean Center. This basically describes how far a typical point is from the Mean Center in miles (1024.27021 mi). As Standard Deviation measures uncertainty and precision of measurement in physical sciences, this may not relate to us at all.

Quote:

Median Center:
--------------

Sample size ...........: 220
Measurement type ......: Direct
Input units .... ......: Degrees

Median of X ...........: -93.71775
Median of Y ...........: 38.90590

The Median Center is the middle value of all the actual X values and the middle value of all the actual Y values. Also, I have not determined where (-93.71775, 38.90590) might lie.

Quote:

Center of minimum distance:
---------------------------

Sample size........: 220

Mean X.............: -99.334515
Mean Y.............: 39.094994
Solution did not converge after 50 iterations!
Tolerance..........: 0.000001
DeltaX.............: 0.000103
DeltaY.............: 0.000004
Median Center X....: -96.336850
Median Center Y....: 38.925690

The Center of Minimum Distance calculates the point where the distance to every point is the shortest. This cannot be done through a direct measurement and requires an iterative process. Unfortunately, the software I'm using gave up after 50 iterations and came up with (-99.334515, 39.094994).

Quote:

Nearest neighbor analysis:
--------------------------

Sample size........: 220
Measurement type...: Direct

Mean Nearest Neighbor Distance ..: 32422.51 m, 106373.08 ft, 20.14642 mi
Standard Dev of Nearest
Neighbor Distance ...............: 78805.06 m, 258546.80 ft, 48.96720 mi
Minimum Distance ................: 14.08 m, 46.20 ft, 0.00875 mi
Maximum Distance ................: 4427297.06 m, 14525252.84 ft, 2750.99486 mi

Based on Bounding Rectangle:
Area ............................: 11715425686385.26 sq m
126103792581870.89 sq ft
4523351.14576 sq mi
Mean Random Distance ............: 115381.90 m, 378549.55 ft, 71.69499 mi
Mean Dispersed Distance .........: 247962.63 m, 813525.70 ft, 154.07684 mi
Nearest Neighbor Index ..........: 0.2810
Standard Error ..................: 4066.26 m, 13340.76 ft, 2.52666 mi
Test Statistic (Z) ..............: -20.4019
p-value (one tail) ..............: 0.0001
p-value (two tail) ..............: 0.0001

Mean Nearest Neighbor Distance (m): 32422.5134
Expected Nearest Neighbor Distance (m): 115381.9038
Nearest Neighbor Index: 0.28100

Nearest Neighbor Index calculates the shortest distance between points as compared to what would be expected by chance. The number to compare this with is 1.0, which suggests that points are randomly distributed, but values less than 1.0 (like ours) suggest that our points are much closer than would be expected by chance.

So what does this all tell us? Pretty much a lot of what we already know. The points are much closer than chance would dictate (and we know they were specifically chosen). We have some central points that probably hold no significance. We also know that the average shortest distance between points is 32422.5134 meters, which is about 19.9570 miles.

I might do this with each column of coordinates to see what kind of significance we might be able to glean from the two and their differences. Also, I might map these points out in a number of fun ways if I feel like it.

Posted: Mon Aug 16, 2004 6:39 pm

Aelith
Decorated

Joined: 21 Jul 2004
Posts: 153
Location: Missouri

Re: [PUZZLE] Axons: Statistics

[quote="hamatoyoshi"]

Quote:

Median Center:
--------------

Sample size ...........: 220
Measurement type ......: Direct
Input units .... ......: Degrees

Median of X ...........: -93.71775
Median of Y ...........: 38.90590

The Median Center is the middle value of all the actual X values and the middle value of all the actual Y values. Also, I have not determined where (-93.71775, 38.90590) might lie.
/quote]

Those coords are for a Fayetville farm road half way between KC and Sedalia, MO.

This makes me think Sedalia was ment to be center of them all.

_________________
Looking forward

Posted: Mon Aug 16, 2004 7:39 pm

Extrasonic
Decorated

Joined: 03 Aug 2004
Posts: 233
Location: Suburban Chicago

Pairs?

Wow ... this is great data. I do have a question, though. The HTML of the coordinates table found at www.ilovebees.com/links.html is built using CSS absolute positioning, meaning that it will always show up as a two-column table, regardless of your screen resolution or browser window size. This leads me to believe that the two-column structure is important in some way. Is there anything statistically interesting when you analyze the individual rows? Or columns?

Posted: Mon Aug 16, 2004 9:19 pm

hamatoyoshi
Veteran

Joined: 02 Aug 2004
Posts: 127

Re: Pairs?

Extrasonic wrote:

I have the coordinate sets divided up. I haven't done any processing, but eyeballing the distributions on a map, I don't see that they differ significantly.

Also, I'm having difficulties compiling data and maps and such. I'm not in school any longer, so I don't have all the tools (ArcView/ArcGIS/SPSS) I used to have at my disposal, so I'm finding other free or commonly available utilities.

I've been using Microsoft Excel to format the coordinates how I want them in tables.

I've been using Map Maker Pro's (30 day trial and a free version) GPS data import utility to convert my Excel data to ArcView Shapefile format.

Then I've been using CrimeStat 2 to process the statistics so far. One can also save Crimestat results back to ArcView Shapefiles and import them back into Map Maker for analysis.

Right now I've been using simple state shapefile data from The National Atlas.

Posted: Mon Aug 16, 2004 9:39 pm

msekolpsu
Veteran

Joined: 03 Aug 2004
Posts: 119

If you get those coords and distances calc'd, could you post them please? Thanks!

Posted: Thu Aug 19, 2004 3:28 pm

hamatoyoshi
Veteran

Joined: 02 Aug 2004
Posts: 127

I'll recalculate all these stats for the latest set of coordinates if you come back late this evening (from an EST point of view).

Posted: Thu Aug 19, 2004 3:55 pm

hamatoyoshi
Veteran

Joined: 02 Aug 2004
Posts: 127

Here are the Stats for the latest coordinates.

Quote:

Mean Center and Standard Distance Deviation:

Sample size: 210
Measurement type: Direct
Unit: Degrees

Minimum: -124.012375 26.043309
Maximum: -70.289091 48.795015
Mean: -96.894099 38.926619
Standard Deviation: 18.378045 4.588931

Std Dist Dev: 1656092.20 m, 5433373.37 ft, 1029.04799 mi

Center of minimum distance:

Median Center X: -93.209127
Median Center Y: 38.703827

Median Center:

Median of X: -92.06881
Median of Y: 38.90082

Nearest neighbor analysis:

Mean Nearest Neighbor Distance: 35276.67 m, 115737.11 ft, 21.91991 mi
Standard Dev of Nearest
Neighbor Distance: 88076.94 m, 288966.35 ft, 54.72847 mi
Minimum Distance: 0.00 m, 0.00 ft, 0.00000 mi
Maximum Distance: 4435165.03 m, 14551066.37 ft, 2755.88378 mi

Based on Bounding Rectangle:
Area: 11741228656431.49 sq m
126381533439933.62 sq ft
4533313.72819 sq mi
Mean Random Distance: 118227.13 m, 387884.27 ft, 73.46293 mi
Mean Dispersed Distance: 254077.19 m, 833586.57 ft, 157.87624 mi
Nearest Neighbor Index: 0.2984
Standard Error: 4264.58 m, 13991.41 ft, 2.64989 mi
Test Statistic (Z): -19.451
p-value (one tail): 0.0001
p-value (two tail): 0.0001

Mean Nearest Neighbor Distance (m): 35276.6697
Expected Nearest Neighbor Distance (m): 118227.1253
Nearest Neighbor Index: 0.29838

Posted: Thu Aug 19, 2004 9:46 pm

hamatoyoshi
Veteran

Joined: 02 Aug 2004
Posts: 127

I'd post the statistics by left and right column, but I have to find a technique to divide them. Either that or somebody could divide them for me.

As a consolation prize in the mean time, I've posted waypoints and tracks.

Posted: Thu Aug 19, 2004 9:52 pm

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