One of the subjects I find difficult to convey is the rather unintuitive idea that objectively bad (or otherwise flawed) data is useful. Surprisingly, erroneous data does not invalidate it, nor obligate us to throw it away.

To illustrate this, I like to use an example from signal and data processing, the analog-to-digital conversion. Say you have a 10-bit A-to-D converter. If you don’t know what this is, it is a device that takes in some electrical signal on an input and outputs an integer value between 0 and 1023. With only a calculator, one can then scale that digital value in various ways to “cook” the value into something useful (like a discrete temperature or humidity value).

Now imagine that your signal is further afflicted by 60 Hz line noise bleeding over from your power source, adding additional error to the resulting A/D conversion. Each individual data reading is objectively worse. Due to the noisy error, a value that should be, say, 512 might fluctuate between 510, 511, 512, 513, and so forth.

This creates a lot of uncertainty and you might think it makes the data useless. But, if you take a  whole bunch of different readings over time and average the results together, something rather remarkable happens. You an increase your effective resolution—the precision—from 10-bits to 11-, 12-, or even 13-bits. Now, if a real value was 512.3, you can more closely represent that than the closest integers (512 or 513). Even with just two points, the average of 512 and 513 is 512.5, which is closer to the real value of 512.3. It gets even better the more data points you have.

This is called oversampling.

The point is that error itself, despite being bad, inadvertently conveys useful information.

Now, consider this claim by a Muslim on Twitter:

Having just read about the engineering example, can you find the flaw in this Muslim’s thinking?

If you said, “this is just like oversampling,” then you are correct. The addition of so many bad variants with numerous errors quite often makes the end product much, much more accurate. In fact in a number of seemingly paradoxical cases, we are more confident of the accuracy of the Bible because of the transmission errors.

I admit that this is highly non-intuitive, but so much about mathematics (and statistics in particular) is not intuitive. But what about the comment that inspired this article?

The problem is, of course, mostly with people. Data is quite often poorly interpreted by people who have perverse incentives to misinterpret and mislead, by people who are incompetent, and by people who are poor and dishonest witnesses. In a not insignificant number of cases, people are fabricating the data entirely.

The key then is recognizes the potential sources of error and, wherever possible, accounting for them. Consider what I wrote on the “Origin of Covid” back in January of 2021. I examined a February, 2020 paper (and its various revisions) by T. Koyama, D. Platt & L. Parida: “Variant analysis of COVID-19 genomes.”

In the process, I saw exactly the kind of manipulation that Charlton warns about: “perverse incentives relating to research.” I even contacted one of the paper’s authors and got the kind of answer I would expect from someone who was being paid to come to a particular conclusion and therefore unwilling to do anything to jeopardize that. Yet, the data itself was incredibly useful. Damning in fact.

It is astounding to me that, back in February of 2020, there was a paper that that debunked many of the later narratives surrounding the origin, spread, and even the identity of SARS-COV-2 and the incorrectly named disease COVID-19. Before most Americans had even heard of a ‘wet market’ or a ‘zoonotic crossover’—well before any lockdowns, interventions, or panic—those theories had already been discredited. And, more importantly, we knew why, despite all the erroneous information.

I could say much more and provide many different examples (e.g. here), but I think I have made my point well enough. Data may be subject to numerous problems, but it remains useful. Even completely fabricated data has a story to tell (albeit not the one you expected).