-up to my earlier article: The Risks of Misleading Knowledge–Complicated Charts and Deceptive Headlines. My first article centered on how visualizations can be utilized to mislead, diving right into a type of information presentation extensively utilized in public issues.
On this article, I’m going a bit deeper, taking a look at how a misunderstanding of statistical concepts is breeding floor for being deceived by information. Particularly, I’ll stroll via how correlation, base proportions, abstract statistics, and misinterpretation of uncertainty can lead individuals astray.
Let’s get proper into it.
Correlation ≠ Causation
Let’s begin with a traditional to get in the best way of thinking for some extra complicated concepts. From the earliest statistics lessons in grade college, we’re all advised that correlation just isn’t equal to causation.
When you do a little bit of Googling or studying, yow will discover “statistics” that present a excessive correlation between cigarette consumption and common life expectancy [1]. Fascinating. Nicely, does that imply we should always all begin smoking to stay longer?
After all not. We’re lacking a confounding issue: shopping for cigarettes requires cash, and international locations with greater wealth understandably have greater life expectations. There is no such thing as a causal hyperlink between cigarettes and age. I like this instance as a result of it’s so blatantly deceptive and highlights the purpose properly. On the whole, it’s essential to be cautious of any information that solely exhibits a correlational hyperlink.
From a scientific standpoint, a correlation will be recognized by way of statement, however the one solution to declare causation is to really conduct a randomized trial controlling for potential confounding components—a reasonably concerned course of.
I selected to begin right here as a result of whereas being introductory, this idea additionally highlights a key concept that underpins understanding information successfully: The information solely exhibits what it exhibits, and nothing else.
Hold that in thoughts as we transfer ahead.
Bear in mind Base Proportions
In 1978, Dr. Stephen Casscells and his staff famously requested a bunch of 60 physicians, residents, and college students at Harvard Medical College the next questions:
“If a take a look at to detect a illness whose prevalence is 1 in 1,000 has a false optimistic charge of 5%, what’s the probability that an individual discovered to have a optimistic outcome really has the illness, assuming nothing concerning the particular person’s signs or indicators?”
Although offered in medical phrases, this query is admittedly about statistics. Accordingly, it additionally has connections to information science. Take a second to consider your individual reply to this query earlier than studying additional.
The reply is (roughly) 2%. Now, in case you regarded via this rapidly (and aren’t up to the mark along with your statistics), you could have guessed considerably greater.
This was definitely the case with the medical college of us. Solely 11/60 individuals appropriately answered the query, with 27/60 going as excessive as 95% of their response (presumably simply subtracting the false optimistic charge from 100).
It’s simple to imagine that the precise worth must be excessive as a result of optimistic relaxation outcome, however this assumption comprises an important reasoning error: It fails to account for the extraordinarily low prevalence of the illness within the inhabitants.
Stated one other means, if only one in each 1,000 individuals has the illness, this must be taken under consideration when calculating the likelihood of a random particular person having the illness. The likelihood doesn’t rely solely on the optimistic take a look at outcome. As quickly because the take a look at accuracy falls beneath 100%, the affect of the bottom charge comes into play fairly considerably.
Formally, this reasoning error is called the base charge fallacy.
To see this extra clearly, think about that only one in each 1,000,000 individuals had the illness, however the take a look at nonetheless has a false optimistic charge of 5%. Would you continue to assume {that a} optimistic take a look at outcome instantly signifies a 95% probability of getting the illness? What if it was 1 in a billion?
Base charges are extraordinarily essential. Keep in mind that.
Statistical Measures Are NOT Equal to the Knowledge
Let’s check out the next quantitative information units (13 of them, to be exact), all of that are visualized as a scatter plot. One is even within the form of a dinosaur.
Do you see something attention-grabbing about these information units?
I’ll level you in the best path. Here’s a set of abstract statistics for the information:
| X-Imply | 54.26 |
| Y-Imply | 47.83 |
| X-SD (Normal Deviation) | 16.76 |
| Y-SD | 26.93 |
| Correlation | -0.06 |
When you’re questioning why there is just one set of statistics, it’s as a result of they’re all the identical. Each single one of many 13 Charts above has the identical imply, customary deviation, and correlation between variables.
This well-known set of 13 information units is called the Datasaurus Dozen [5], and was revealed some years in the past as a stark instance of why abstract statistics can’t all the time be trusted. It additionally highlights the worth of visualization as a device for information exploration. Within the phrases of famend statistician John Tukey,
“The best worth of an image is when it forces us to note what we by no means anticipated to see.“
Understanding Uncertainty
To conclude, I need to discuss a slight variation of misleading information, however one that’s equally essential: mistrusting information that’s really appropriate. In different phrases, false deception.
The next chart is taken from a examine analyzing the feelings of headlines taken from left-leaning, right-leaning, and centrist information shops [6]:
There’s fairly a bit occurring within the chart above, however there may be one explicit facet I need to draw your consideration to: the vertical traces extending from every plotted level. You will have seen these earlier than. Formally, these are known as error bars, and they’re a method that scientists usually depict uncertainty within the information.
Let me say that once more. In statistics and Knowledge Science, “error” is synonymous with “uncertainty.” Crucially, it doesn’t imply one thing is unsuitable or incorrect about what’s being proven. When a chart depicts uncertainty, it depicts a fastidiously calculated measure of the vary of a price and the extent of confidence at varied factors inside that vary. Sadly, many individuals simply take it to imply that whoever made the chart is actually guessing.
It is a severe error in reasoning, for the harm is twofold: Not solely does the information at hand get misinterpreted, however the presence of this false impression additionally contributes to the damaging societal perception that science is to not be trusted. Being upfront concerning the limitations of data ought to really enhance our confidence in a declare’s reliability, however mistaking that limitation as admission of foul play results in the alternative impact.
Studying learn how to interpret uncertainty is difficult however extremely essential. On the minimal, a superb place to begin is realizing what the so-called “error” is definitely making an attempt to convey.
Recap and Remaining Ideas
Right here’s a cheat sheet for being cautious of misleading information:
- Correlation ≠ causation. Search for the confounding issue.
- Bear in mind base proportions. The likelihood of a phenomenon is extremely influenced by its prevalence within the inhabitants, regardless of how correct your take a look at is (aside from 100% accuracy, which is uncommon).
- Beware abstract Statistics. Means and medians will solely take you to this point; it’s essential to discover your information.
- Don’t misunderstand uncertainty. It isn’t an error; it’s a fastidiously thought of description of confidence ranges.
Bear in mind these, and also you’ll be properly positioned to sort out the subsequent information science drawback that makes its solution to you.
Till subsequent time.
References
[1] How Charts Lie, Alberto Cairo
[2] https://pmc.ncbi.nlm.nih.gov/articles/PMC4955674
[4] https://visualizing.jp/the-datasaurus-dozen
[6] https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0276367