In a previous post, I plotted Sweep Width (ESW) vs. Average Maximum Detection Range (AMDR), using the data from the sweep width experiments in Koester et al. 2004. Based on those 16 data points, it seemed there was a good correlation, with Sweep Width being about 1.5 * AMDR.
Since then, a few more sweep width experiments have been conducted, yielding another 9 points, and for the NASAR 2009 conference I updated the plots. The new data comes from Pennsylvania experiments (6 points, thanks to Ken Chiacchia for the data) and the Berkshires experiment (3 points which I should really have incorporated long ago).
As you can see above, the correlation is still quite good (r^2 is 0.8). Also, the best-fit line is still quite close to the fixed line ESW = 1.5 * AMDR, and the suggested bounding lines of 1*AMDR and 2*AMDR (light tan) still pretty much bound the points.
The tan lines were suggested in the 2004 report. The experimenters felt that things divided into about 2*AMDR for good conditions and about 1*AMDR for bad conditions. I made the first scatterplot partly to say, "Maybe, but it looks like one line around 1.5 to me."
For the most part, that's still how the points look, but there is a role for expertise here. For example, Ken Chiacchia noted that ALL the low-vis targets (green camouflage) fall below the 1.5 line. This makes sense. So he considered whether we get a better fit by taking each target type separately. The correlations generally improved, but the result was not statistically significant. Just for illustration, below I break the data into just two groups: low-vis and else. (The low-vis group has r^2 of 0.6, and the rest have 0.8.)
Ken is going to redo his statistical tests to include the Berkshires points, and after filling in some missing fields, I might consider computing message lengths for a couple of variants. I expect the story to be: the data alone do not yet justify a split, but expertise does. Bayesians should be comfortable with that -- it's all about conditional knowledge.
"Good" conditions are probably high-vis targets in good weather, with alert experienced searchers. "Bad" is probably low-vis targets etc. Consider that one of the high-vis points (34, 36) falls near the 1.0 line. According to Bob Koester the AMDR for this point was collected in good weather, but the sweep width experiment was done in the rain. That lowered sweep width at least three ways: some reduced visibility/contrast, dampened enthusiasm, and hats and hoods.
Until we can establish those categories, or some correction factors, Koester and Frost recommend using 1*AMDR as a conservative estimate. Operationally, we would rather underestimate sweep width (hence POD) than overestimate.
We would also love to have some more Sweep Width data. So if you want to run one, ping someone who has.
Theory?
No progress on why this correlation should be what it is, other than the key points:- AMDR and ESW are both affected by target, searcher, and environment.
- Although it is for an alerted searcher, AMDR is not the maximum detection range. It's an average of several samples. By definition, that has to be less than the maximum.
Credits
Thanks to Ken and Bob, and of course, all the experiment participants and organizers. Bob and I presented this material at NASAR 2009. Thanks to all those who attended.Update: And thanks to Dwight Yochim of Coquitlam SAR, for getting me back into this. Ken has since run some stats suggesting we can probably say the medium vis clues don't have a slope of 2.
- Ken's Blog -- Don't say I didn't warn you about the name.
- The Sweep Width Report (Koester et al. 2004) -- Contains full instructions for running your own, though I recommend asking someone who has run one before to assist.