How to mathematically separate the wheat from the chaff

[Explorer]

1 hour ago, Mendoza said:

 

If I'm reading correctly, then you've determined that breaking down the human population density by county basically confirms comparisons in population density made on the state level (at least in the case of Washington and Florida).  This is more or less what I expect--that an analysis done on the county level is probably going to affirm, for the most part, what I've already done on the state level.  The degree of new information I would expect from a county-by-county analysis would be somewhere along the lines of finding that not all of Washington is Bigfoot territory (which I think is already quite obvious) and that maybe Bigfoot also has a presence in Florida (a definite possibility), as opposed to radically different findings that might suggest there's nothing in WA after all and FL turns out to be crawling with Bigfoot.

 

I do notice that the ratio of population density between the two states changed when you broke it down to the county level.  That does suggest to me that there is a lot of new information to be gained if I repeat my analysis at the county level.  This of course will take a while, because there are far more counties than states, which makes the county-level analysis more demanding in terms of raw number-crunching by a couple of orders of magnitude.

 

 

My conclusion was that the distribution of population density by county gave a totally different picture of the state (because it is highly skewed) and a totally different average than using a state average.

While I did not do the work, I would not be surprised if we find the same result for black bear population density by county and total population by county (i.e. skewed distributions).

Given that you are using few variables (BFRO reports, population, human population density, and bear population density), if all 4 variables are skewed (when distributed by counties) then it is likely that the correlations to BFRO reports (normalized) will change. 

Thus, I believe that pursuing the analysis with more granularity will provide more useful information and maybe different results.

 

Notwithstanding the averaging issue, I don't agree with your assumption that high correlation with bear density populations is indicative of mis-identification. Thus, I will have to respectfully disagree with the conclusions.

I consider BF and bear habitat to be the very similar, and a positive correlation is what I expect to find for all counties.

 

[Mendoza]

4 minutes ago, Explorer said:

 

Notwithstanding the averaging issue, I don't agree with your assumption that high correlation with bear density populations is indicative of mis-identification. Thus, I will have to respectfully disagree with the conclusions.

I consider BF and bear habitat to be the very similar, and a positive correlation is what I expect to find for all counties.

 

 

I actually have considered the possibility that my conclusions regarding Bigfoot sightings and black bears might need to be changed if a county-level analysis gives different results from the ones I obtained at the state level.

 

Unfortunately, I don't think consistent, nationwide, county-level black bear population data actually exists.  The state data may be the best we have to work with.

 

Unless--and I just thought of this--we can use some better-known variable as a proxy for black bear presence at the county level.  This would require some expertise on the ecology of black bears nationwide.

[hiflier]

I have to say this has been very interesting to follow. And I can understand your avenue of thought and also VERY much respect your being open and candid about accepting any reasonable changes. It shows a fine willingness to work thing through in a subject up to it's neck in variables. No easy task and I commend you for taking it on.

 

To meet the equation head on the way it is presented may work but be a bit premature. More data is needed as you say. I also think that in this case one needs a framework of behavior on the part of the creature itself to make the numbers work. It may be time to develop that framework with the goal of plugging it in to what you currently have. Not all patterns of behavior will fit however but eventually a pattern of perhaps creature lifestyle will bring everything into focus where the numbers will work. A reduction in variability is sorely needed and I would suggest looking at animal behavior patterns in general or specifically maybe the Great Apes. Stir in a higher intelligence, greater dexterity, and a handful of other criteria and things just may fall into place nicely.

 

Numbers are great, Mendoza, and you have shown a direction in which to run with them but right now they are sort of free floating and need a good framework to anchor them down to. I'm being somewhat, or entirely, obtuse as I do not wish to change the direction this thread is going. Nice work..

[gigantor]

Explorer pointed out in a different thread that higher resolution for stats are needed. Currently the SSR does not offer search criteria with enough resolution to study multiple counties, selected at will. It can only produce stats for one county at a time. This is a deficiency which I'm working to correct.

[BigTreeWalker]

5 hours ago, Mendoza said:

Explorer posted a link in one of the other threads. I found this map that shows which counties half the population reside in. 

 

 

To me it's interesting how small of areas the major population is concentrated in and how large of areas there are where the population is more dispersed. 

 

 

 

Sorry my Qoute function is messed up. It quotes my previous posts. 

[Mendoza]

Unable to find county-level black bear population data, I decided to get creative and try to model black bear population density in a roundabout way.

 

Going by images such as the ones I've attached at the end of this post, forest cover appears to be a fairly good proxy for black bear range.

 

Instead of dividing the black bear population by the total area of the state (which is equivalent to assuming that the black bear population is uniformly spread across the state), I recomputed a black bear population density by dividing the black bear population by the estimated area of timberland in the state.  This new method of deriving the black bear population density is equivalent to assuming that the black bear population is uniformly spread throughout the state's timberland.  This is still imperfect, but perhaps better than the previous method of derivation.

 

Recomputing the correlation between black bear population density and Bigfoot sighting frequency gives the following:

Group A:  0.7497

Group A':  0.2095

Group B:  0.1237

 

As before, we have the high correlation between black bear population density and Bigfoot in Group A, and little correlation in Groups A' and B.

 

Roughly an 88% overlap between Bigfoot and black bear ranges in Group A (or a significant component of black bear misidentification in the BFRO reports) could would be sufficient to account for the correlation observed in the Group A states.  An overlap of up to 61% in Group A' would not contradict the observed correlation in the Group A' states.  (I should caution that this is not sufficient evidence to conclude that there actually is a 61% overlap of Bigfoot and black bear ranges in the Group A' states--at correlations as low as the one observed here, the significance of the correlation is also low.)

 

We are still left with a big difference in this correlation when comparing Group A and Group A', so my prior reasoning still holds:  either there actually is a greater degree of overlap between Bigfoot's range and the black bear's range in Group A than there is in Group A', which virtually demands an ecological explanation, or else there truly is a significant contribution from black bear misidentification in Group A that does not exist in Group A'.

 

As I currently see no convincing ecological explanation for an actual difference in the degree of overlap between Bigfoot and black bear ranges in Groups A and A', I continue to lean towards the hypothesis that the heightened correlation in Group A is due to significant black bear misidentification in these states.

[norseman]

Where are the groups typographically speaking?

[Mendoza]

3 hours ago, norseman said:

Where are the groups typographically speaking?

 

Group A is Alaska, Yukon, British Columbia, Washington, Oregon, Northern California, Montana, Wyoming, and Manitoba.  In Alaska you find the Alaska Range and the Brooks Range; Yukon contains the Yukon Plateau, Mackenzie Mountains, and the Rockies; British Columbia includes the Coast Mountains and the Rockies; Washington contains the Cascade Range; Oregon contains the Cascades and the Columbia Plateau; California contains the Coast Ranges and Sierra Nevada; Montana has the Rockies in the west; Wyoming is in the middle of the Rockies; Manitoba is dominated by lowlands around Hudson Bay and Lake Winnipeg.

 

Aside from some coastal areas in Alaska, Washington, and Oregon; the valley in California; and Manitoba; Group A is dominated by highlands and rarely goes below 2,000 feet above sea level.

 

Group A' is Idaho, Alberta, Colorado, New Mexico, Texas, Utah, Ontario, Oklahoma, Arkansas, South Dakota, Saskatchewan, Missouri, and Arizona.  Idaho contains the Bitterroot Range spur of the Rockies; Alberta has the Rockies in the south and isolated mountains and Great Plains plateau in the rest of the province; Colorado contains the highest part of the Rockies; New Mexico includes the southern end of the Rockies; Texas is Great Plains and plateau in the west and lowlands around the Gulf of Mexico in the east; Utah is at the intersection of the Great Basin and the Colorado Plateau; Ontario is mostly lowlands but increasing in elevation as you move away from Hudson Bay; Oklahoma is plateau and Great Plains; Arkansas is Mississippi River lowland aside from the Ozark plateau; South Dakota is all Great Plains except for the Black Hills in the west; Saskatchewan is Great Plains; Missouri is more Mississippi River watershed lowlands except form the Ozarks; Arizona contains the Colorado Plateau and the Sonora Desert.

 

There's more variety in topography in Group A', ranging from the highest portion of the Rockies to plateau and Great Plains to coastal and river watershed lowland to desert.  The elevation drops below 2,000 feet more often in Group A' than in Group A, though there are also whole states that are almost entirely over 2,000 feet above sea level.

 

Which of the varied terrains Bigfoot actually lives in within these states will have to wait until a county-level analysis.

[bipedalist]

I am of the opinion that black bear residency is introducing a bias and there needs to be a correction factor somehow.  I for a fact know that black bear and sasquatch in NC do not mind overlapping. 

 

There are some huge gaps in black bear status/presence in intermountain west states that you could drive a western triple through as norseman alludes. 

 

Nice work, but there are some problems here.   There are coast ranges in Oregon and Washington too. 

Edited January 27, 2017 by bipedalist

[gigantor]

Mendoza, thank you for your analysis.

 

I'm having a hard time understanding what your findings mean. Can you please explain them in layman terms so a dummy like me can follow along?

 

Thanks again.

 

[Mendoza]

13 hours ago, gigantor said:

Mendoza, thank you for your analysis.

 

I'm having a hard time understanding what your findings mean. Can you please explain them in layman terms so a dummy like me can follow along?

 

Thanks again.

 

 

The method is based on the fact that, in order for a human to actually see an animal and report the sighting, both human and animal have to be in the right place at the right time.  On the other hand, in order for a human to produce a hoaxed report, the human only needs to exist and have a motive for doing it; there is no need for either human or animal to be in any particular place at any particular time.

 

If there is a significant amount of hoaxes in the database, you would expect to see more reports in states with more people.  (This assumption has been questioned.  See the post by MIB on this subject.)  We do see that relationship in the data.  The correlations in the paper are basically a measure of how consistently the number of reports lines up with the number of people in the state.  The high correlations found in the data show that hoaxing is a significant contributor to the database.

 

However, I found that the rates differ by geography.  Cluster analysis is a mathematical procedure that groups items of data based on their similarity, which is defined in various ways.  In my study, I assigned the states to groups based on their normalized report frequency, meaning the number of reports per resident per square mile, which is essentially averaged over the state at this level of analysis.  Three distinct groups emerge from the cluster analysis.  Yukon Territory, Alaska, British Columbia, Northern California, Montana, Washington, Oregon, Manitoba, and Wyoming, form Group A.  Idaho, Alberta, Colorado, New Mexico, Texas, Utah, Ontario, Oklahoma, Arkansas, South Dakota, Saskatchewan, Missouri, and Arizona, form Group A' (A-prime, derived from mathematical terminology).  Group B is the rest of the United States and Canada.

 

The rate of hoaxes per person appears to be higher in Group A, and roughly constant at a lower rate in the other two groups.  Possibly there is a stronger motive for hoaxing in those states, maybe related to media attention to the subject, or some assumption of greater potential for fooling people on the part of the hoaxer.

 

Now if there is a significant amount of animal sightings in the database, we expect that there will be more reports in states where the people are more concentrated, because they will be more likely to cross paths with the animal.  (This assumption has also been questioned.  See the post by JustCurious on this topic.)  We do find this relationship in the data as well.  So we can conclude that a significant portion of the database is the result of real sightings of some animal.

 

Again, it appears that the rate of animal sightings (reported as Bigfoot) per person per square mile is higher in Group A.  It is somewhat lower in Group A', and in Group B there appears to be no relationship at all.  This means that there are actual sightings of animals in the database in the Group A and A' states, but not in the Group B states.  The difference in rates between Group A and Group A' could be because the animal responsible is more concentrated in Group A than in Group A', or it could mean that multiple animal species are being reported as Bigfoot in Group A, and only one species in Group A'.  This second possibility could be a result of a combination of actual sightings of Bigfoot with misidentification of bears or other animals.

 

To study the effect of bear misidentification in the database, we can assume that there will be more reports in the database in states where bears are more concentrated, because the bears will be more likely to cross paths with a human.  We do find this relationship in the data for black bears in the Group A states, but not elsewhere, and not for brown bears anywhere.  I concluded that this means that many of the reports in the database from these states are really misidentified black bears.  Why this happens in Group A and not in Group A' may be because of media influences on the general public perception of Bigfoot's home range being in the Pacific Northwest.  (This has certainly been the most controversial conclusion of my paper.  An alternative hypothesis put forward has been that the relationship observed in the database should simply be interpreted as meaning that Bigfoot and black bears have coinciding ranges.  See the lengthy discussion in this thread.)

 

Putting it all together, I conclude that the reports from Group B states are hoaxes.  There are also hoaxes coming in at the same rate in Group A'.  In Group A, there is a heightened rate of hoaxing.  Many reports from the Group A and Group A' states are actual animal sightings.  In Group A', we can rule out bears, which essentially leaves us with nothing else that matches the description of Bigfoot other than an actual bipedal primate.  I regard this as the most exciting conclusion in my paper.  In Group A, actual Bigfoot sightings probably occur alongside many misidentifications of black bears.

 

A recommendation is that data miners attempting to glean accurate data (physical characteristics, behavior, etc.) from Bigfoot databases focus on the Group A' states.  These are the "purest" in the database--the Bigfoot are there, unlike in the Group B states, and there are fewer hoaxes and erroneous identifications than in the Group A states.

 

This study was restricted to the state level.  As was aptly pointed out by a number of contributors to this discussion, there are certainly going to be inaccuracies in the analysis and its conclusions at such a broad geographical level.  For example, it should be self-evident that Bigfoot is extremely unlikely to be living in downtown Seattle, even though a state-level analysis puts downtown Seattle in Group A.  My intention is to eventually follow this up with a county-level analysis that will provide a more detailed picture.  I expect to find that there are counties in Groups A and A' where Bigfoot doesn't live, and that Bigfoot does in fact have a presence in Group B in some counties.

 

Essentially, this work has been a preliminary towards closing in on the truth about Bigfoot's range.

[bipedalist]

On 1/9/2017 at 1:26 AM, gigantor said:

 

Dr Grover Krantz explained this a long time ago.

 

Black bears are diurnal. Bigfoot is thought to be nocturnal, so even though their ranges overlap, they operate at different times of the day, thus allowing them to share resources and coexist.

 

There are many other species who would normally compete for resources, but time-share instead.

 

I enjoyed reading your analysis. Thanks for posting it!

 

I do not believe Dr. Krantz's edict is as solid during many conditions as pronounced (there is disagreement), there is much more to the foraging behavior of black bear than strict diurnal presence.  Many see them as crepuscular but there are conditions where feeding preferences change, some involving other species of bear and some involving humans. 

 

See: http://www.web.uvic.ca/~reimlab/NOCTURNAL FORAGING-MORESBY0001.pdf

 

http://animaldiversity.org/accounts/Ursus_americanus/

 

This one tends to be in favor of diurnal for black bears

https://research.libraries.wsu.edu/xmlui/handle/2376/3011   and many others.

 

The second chapter evaluated whether grizzly bears and black bears were strictly nocturnal, diurnal, or crepuscular in the absence of human influence to switch. Although both species have shown flexibility in their activity profile in other areas black bears tend to be diurnal while grizzly bears are more often crepuscular. Although grizzly bears were seasonally nocturnal, black bears were strictly diurnal and did not temporally avoid the more socially dominant grizzly bear. The final chapter evaluated the separation of grizzly bears and black bears spatially in their habitat use and areas close to humans (e.g., trails, developments, and roads).

Edited February 18, 2017 by bipedalist

[BigTreeWalker]

If people have seen the trail cam pictures I posted in the research section from last September, that big black bear was mostly nocturnal. I only got a couple pictures of the big one and a smaller one coming in to feed during the day. The big one also showed up behind camp, about a mile from the feeding site, during the night. Of course in this part of the southern Cascades grizzlies are not an issue. 

[bipedalist]

^ Exactly, when I lost a back porch door to a huge male black bear it certainly wasn't during daylight, lol.  Nocturnal has been my experience with black bear.  In 30 years in a montane environment the only diurnal bears I saw were roadside park bears such as Cades Cove GSMNP.  Correction I saw one mother lead a malnourished cub up a driveway one day and I had a friend run into a female with cubs during daylight hours in one specific area I frequented for those 30 years.  I recall one small male launching himself off a logging road embankment late in the afternoon one day too, cutting me off and not even knowing of my presence until he looked up.   Very atypical to see diurnal bears even around dumpsters in daylight where I was hanging. 

Edited February 18, 2017 by bipedalist