From a scientific or statistical standpoint, it seems ridiculous to think one data point can teach us much. Even a study with ten data points is laughably small.
It’s also really common to see people over-react to a single experience they’ve had (e.g., “I know I don’t like Taiwanese food because I tried it once”) or to an anecdote (e.g., “I’m convinced this supplement will work because my friend took it and says it worked”).
And yet, in some contexts, one data point can teach us a LOT. Here are six ways that we can sometimes learn useful information from just one data point:
Providing Evidence
1. By Bayes Factors: suppose hypothesis “A” says a data point is nearly impossible, and hypothesis “B” says the data point is quite likely. Then the existence of that one data point (by Bayes’ rule) should move you substantially toward believing hypothesis B (relative to A).
Example: you have had a rash on your arm for ten years (with no variability). You buy some “rash cream” off of a shady website, and within two hours of applying it, the rash is gone. As long as your senses aren’t deceiving you, you can be confident the cream works because it’s otherwise highly unlikely for the rash to vanish.
2. By Providing the Mean When There is Very Low Variance: normally, a single data point doesn’t allow an accurate estimate of any statistics. But in situations of very low variability, a single data point can be an accurate approximation of the mean!
Example: there is very little variability in how long it takes to walk to the store from your home. Hence, walking that route just once allows you to estimate quite accurately how long it will take in the future (e.g., it takes about 40 minutes to walk to the store).
3. By Showing What’s Not THAT Unlikely: if we witness just one example of a thing, chances are its traits are not EXTREMELY unrepresentative of the class from which it comes. Of course, it’s possible they are, but the vast majority of the time, a single data point will not have extremely rare traits.
Example: you see an adult Spider Monkey for the first time (in the wild, let’s say). Chances are that this Spider Monkey is somewhere between the 1st percentile and 99th percentile for size. It’s unlikely that the only Spider Monkey you’ve ever seen is one of the very largest or smallest that exists. You can expect that most of the traits this particular Spider Monkey has are not incredibly rare.
Showing Possibilities
4. By Alerting Us to a New Possibility: sometimes, a single data point shows us that a possibility or phenomenon exists that we had never before seen or considered.
Example: Roentgen had a cathode tube covered in heavy black paper and was surprised when an incandescent green light escaped and projected onto a nearby fluorescent screen. He had discovered a new phenomenon. It eventually led to the discovery of x-rays!
5. By Causing Us to Think of a Hypothesis: if we see something work for a single example or see that things went a certain (surprising) way, it can give us a hypothesis or approach that may apply to other cases – especially if it coheres with other justified beliefs we have.
Example: suppose that, while bartering over a price at a food stand, you see a friend use a negotiation tactic you have never seen before. Upon seeing this tactic used, it immediately makes sense to you that the tactic works, yet the idea had simply never occurred to you before.
6. By Illustrating a Causal Mechanism: studying a single data point or example can allow us to see HOW a mechanism works, enabling us to build up a causal understanding or model. We can then apply this understanding to other examples.
Example: you take apart one mechanical clock and pay close attention to how it works. From this experience, you build up a causal model of how such clocks function. Later, when a different mechanical clock stops working, this causal model helps you quickly diagnose the problem.
An interesting aspect of learning from one data point is that, every once in a while, one data point unlocks the information from a whole bunch of other data points.
For instance, if someone is in an abusive relationship but is still convinced that their partner is a “good guy who means well,” a bunch of data points about the partner’s behavior may simply not make sense in the “he’s a good guy” frame. So those data points just sit around causing confusion and end up being dismissed or integrated in a contrived way (e.g., “It’s weird that he yells at his business partner on the phone so much, but I guess he’s just really passionate about his business. And it’s weird that he sometimes tells me I look terrible – but that’s just because he’s concerned that others will think badly of me, and he’s looking out for my best interests.”)
Then a single new data point can suddenly cause a reconsideration of the hypotheses that their partner is a good person and allow them to consider that maybe he’s actually a highly manipulative and selfish person (e.g., catching him cheating in a way that’s impossible to ignore). Once this new hypothesis becomes available, suddenly, all of those previously ignored data points make sense and can be integrated quickly. Hence, processing one data point can sometimes enable you to process a whole bunch of others.
A side point is that it’s not always clear what “one data point” means. From the point of view of health or social science or economics studies, a single data point can mean one person or one task completed or one school or the statistics for one country. In ordinary life, we’re experiencing lots of information all the time, though we can still sometimes think of “one data point” as being one example or one experience or one attempt, etc.
There are also times when “one data point” is exactly what we’re interested in. For instance, we want to know whether we like THAT dish or what’s true of that exact thing, not that type of dish or that sort of thing. In such cases, of course, it’s precisely that one data point that we need to learn from.
So, can we learn a lot from one data point?
Unfortunately, we humans often err on the side of OVER-reacting to a single data point. We take one example, anecdote or life experience, and generalize it inappropriately.
But, if we are very careful, there are (perhaps surprisingly) sometimes valid ways to learn a LOT from just one data point!
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