Unbelievably, it has been 3.5 years since I last addressed the readership. Life gets in the way, indeed. Well, not entirely. I have been semi-actively analyzing athletics at my other blog. Also, I was preoccupied, in no particular order, amassing insurmountable debt for a graduate degree, leveling friendships, making unsound financial choices, learning that ≥25.21% of the American adults I’ve never met are ignobly myopic, forsaking my practiced skills, discarding possessions, falling for unavailable women, leaving projects unfinished, and reconfiguring my perspective.

Readers who have interacted with me in the physical world, or IRL, know that I stubbornly oppose any attribution to the paranormal. They know I quickly brandish alternative—material—explanations or at least hypotheses at any mention of purported phenomena such as hauntings and sorcery. Every day, humans impose undue burdens onto each other and onto sentient actors of other species. So, I needn’t cite any examples of human behavior when I casually pose that I am more afraid of human behaviors than I am of their ghosts and incantations.

One of those paranormal concepts that particularly irks me is attributions of purpose in events. By ‘purpose’ I mean, references to destiny or preordainment as if an outcome or series of events was somehow special, “meant to be”, or “supposed to happen”. Without question, fortuitous, unexpected, and coincidental outcomes occur every day. But, by all indications to the present, we exist in a dull state of otherwise meaningless outcomes.

Humans though, you and I, it seems, are programmed to endow meaning to outcomes and events, often arbitrarily. And we do so prolifically. We are the creators of meaning, the ascribers of valence; we are the quantum measurement problem. Unsurprisingly then, persistent are notions about the influence of astrology, the occurrence purpose, and so on. Some folks, paranormal researchers, even resort to examining these phenomena—dare I say, systematically—and have been for well over a century.

I personally believe that we create the meaningfulness in the moments of our lives through our interactions with others, through our engagement in activities, and in our responses to events in the environment, and that’s good enough for me. The materiality of life and the experience of living itself are, perhaps, insufficient for some. Allow me to interrupt my reductionist ramblings but, just wait ‘til I someday tell you a love story.

Let us imagine that I have long-believed that red is an omen. A significant event will come without notice. One day, Imaginary me notices the situation in the parking lot of an apartment building I previously took residence in, as shown in Figure 1. The preponderance of red automobiles is undeviatingly an omen. It might be great or it could be painful, Imaginary me has no way of knowing. Imaginary me experiences cognitive dissonance because he has been taught to consider alternative explanations before reaching for conclusions. But…but, it’s red. So. Much. Red. It must be an omen.

Imaginary me elects to leave it to chance so I flip a coin and dispute the outcome. 37 rolls of unbiased dice and I’m still unconvinced. It is an omen. Having had cursory training in statistical analysis, Imaginary me reckons that this is a matter of counts and proportions. Specifically, that the proportion of red automobiles in the parking lot is greater than we would expect based on the proportion of red exteriors within all automobiles in the USA (in the analysis its North America) and therefore, it is an omen. Imaginary me prepares a table identical to Table 1 on a kitchen napkin, while dripping anxious sweat. Table 1 contains the observed counts and proportions for exterior colors of the 14 automobiles in the parking lot contiguous the building. Table 1 also contains the counts and proportions of colors we would expect to find in that parking lot based on that of all automobiles currently in use. (Real me’s methods for deriving expected proportions are outlined at the close of the post, after the fox graphic.)

	Observed		Expected
Color	count	%	count	%
Silver	1	0.071	2.50	0.179
White (solid+pearl)	2	0.143	2.69	0.192
Black (solid+effect)	2	0.143	2.04	0.145
Blue	0	0.000	1.41	0.100
Gray	0	0.000	1.54	0.110
Red	6	0.429	1.54	0.110
Brown/beige	0	0.000	0.89	0.064
Green	2	0.143	0.57	0.040
Gold/yellow	0	0.000	0.30	0.022
Other	1	0.071	0.52	0.037

Imaginary me really wants to ‘prove’ it is an omen and to assure himself, he consults an old statistics textbook. Table 1 lends itself to a Chi-square (goodness-of-fit) test that was outlined in Imaginary me’s textbook.  Our null hypothesis is that the proportions of automobile exterior colors in Figure 1 are no different than that of all automobiles currently in use. Our alternative hypothesis is that the proportions of colors in Figure 1 differ from that of the population of automobiles. To uphold the integrity of empiricism, Imaginary me takes the textbook authors’ advices and explicitly specifies that only a Chi-square value with a p-value < 0.05 will be considered compelling evidence of different proportions; or, in more sensational language: PROOF IT IS AN OMEN.

A Chi-square test indicates that the proportions of exterior colors in Figure 1 are significantly different than that of all automobiles in use, χ2 = 22.308, df = 9, p = 0.008. Imaginary me interprets this to mean that because it is statistically significant, the omen is very real. Real me says shut the fuck up and directs our gaze to the farground of Figure 1, beyond the parking lot. Real me pushes Imaginary me away from R and creates a new vector that also includes the 4 white, 1 black, and 1 grey automobiles that are identifiable beyond the parking lot. Imaginary me futilely argues that only automobiles located in the parking lot are relevant. With the 6 other automobiles, the result is no longer significant at the 0.05-level, χ2 = 15.927, df = 9, p = 0.068. Imaginary me is so flummoxed he dematerializes just in time for this paragraph to end.

Indeed, there is the lack of established material mechanisms by which paranormal phenomena are actualized. However, the belabored antidote exemplifies my concerns with the statistically significant results reported in a slew of systematic examinations of paranormal phenomena. There was not a good theory indicating why this sample of exterior automobile colors would be expected to differ from all automobiles. That is, there was no grounds for comparing this sample to the population.

Chi-square tests can be used to, say, test whether there is a lower proportion of twin-births by vegan mothers compared to that by omnivorous and vegetarian mothers. The test would be warranted because studies of biochemistry and nutrition provide good theory for why vegans’ twinning proportions would differ from other mothers.  Besides proximity to my then-apartment, however, the hypothesis offered by Imaginary me contained no concrete rationale for distinguishing our sample of automobiles from the population. I suppose we could have performed the analysis if, for whatever reason, we wanted to test whether the distribution of exterior colors of automobiles owned by residents of that building at the time the image was captured differed from the distribution for all automobiles.

Regarding paranormal research, it is a bit more involved than our example. People for millennia have reported experiencing paranormal phenomena. A host of individuals from the late-1800s through present have examined related phenomena. Like our example above, there is no theory for why or how these phenomena occur, simply subjective reports that the phenomena were experienced. And I agree, researchers should systematically examine subjective accounts of experience.

However, aside from being marred by outright fraud^a,b and selective reporting of data,c  as well as repeated failures to replicate,^d,e,f an accumulated paucity of evidence over ~140 years bespeaks discontinuing the research program. Thus, Imaginary me’s interpretation of statistical significance found in the first Chi-square test from our example is common in the paranormal research literature. Paranormal researchers hail statistical significance as proof of phenomena. Fine. Great. Whatever. Absent a theoretical foundation and controllable variables, really, it’s just algebraically torturing numerical values yielded by whatever method of data collection was used.  Err to parsimony and control your variance or GTFOH.

Let me conclude my somnolescent and overwrought return by emphasizing two points. One, assuming honest data and that there were not ~140 years of distortion, paranormal research findings would be anomalous and intriguing, indeed. However, in the ~20 manuscripts published from 1930-2012 that I have read, there is never any attempt to manipulate the laboratory procedures to alter the findings. By that I mean, paranormal researchers never implement additional variables or constraints to experimentally alter the intensity or frequency of the paranormal phenomena they examine. Two, aside from loose allusions to developments in physics, there is never any attempt to examine the phenomena within the parameters of the currently measurable world. By that I mean, paranormal researchers will hypothesize, say, causal mechanisms hidden beyond the firmament of unresolved topics in quantum physics. However, they never design experiments where good theory indicates that manipulating some established physical or cognitive variable(s) would be expected to produce outcomes reminiscent of a given paranormal phenomenon. That is, outcomes that could be misinterpreted by reasonable observers as the occurrence of a given paranormal phenomenon. As I alluded earlier, while good enough for me, material explanations are perhaps insufficient for others.

 

The derivation of expected proportions. I obtained median age of all highway vehicles registered in the USA, 2000-2014. For each year, 2000-14, I computed the year in which vehicles of the median age would have been new. I obtained quantities of all highway vehicles registered in the USA, 1960-2014,  and new highway vehicles registered in the USA, 1960-2014. I computed the proportion of registered vehicles that were new, 2000-14. Then I obtained the proportions of new automobile exterior colors for each year 2000-14. I used these values to estimate the proportion of automobile exterior colors in 2014 that were from new vehicles in each year from 2000-14.  I used these values to estimate the proportions of exterior colors for all automobiles in 2014. Each year-color proportion was multiplied by 1/quanity of year-color combinations for all years <= 2014. Then all the year-color combinations from 2000-14 were summed, producing the 2014 estimates. Essentially, I generated an estimate for each year prior to 2014 such that the proportion of year-color combinations were assigned the most weight at the median year and progressively less weight as the years departed from the median.