This post contains slides I made to illustrate some points about phenomena, which will remain forever out of reach, if we continue the common practice of always averaging individual data. For another post on perils of averaging, check this out, and for an overview of idiographic research with resources, see here.
(Almost the same presentation with some narration is included in this thread, in case you want more explanation.)
Here’s one more illustration of why you need the right sampling frequency for whatever it is you study – and the less you know, the denser sampling you need initially. From a paper I’m drafting:
The figure illustrates a hypothetical percentage of a person’s maximum motivation (y-axis) measured on different days (x-axis). Panels:
A) measurement on three time points—representing conventional evaluation of baseline, post-intervention and a longer-term follow-up—shows a decreasing trend.
B) Measurement on slightly different days shows an opposite trend.
C) Measuring 40 time points instead of three would have accommodated both phenomena.
D) New linear regression line (dashed) as well as the LOESS regression line (solid), with potentially important processes taking place during the circled data points.
E) Having measured 400 time points instead, would have revealed a process of “deterministic chaos” instead. Not knowing the equation and the starting points, it would be impossible to predict accurately, but this doesn’t mean regression is helpful.
During the presentation, a question came up: How much do we need to know? Do we really care about the “real” dynamics? Personally, I mostly just want information to be useful, so I’d be happy just tinkering with trial and error. Thing is, tinkering may benefit from knowing what has already failed, and where fruitful avenues may lie. My curiosity ends, when we can help people change their behaviour in ways that fulfill the spirit of R.A. Fisher’s criterion for an empirically demonstrable phenomenon:
In relation to the test of significance, we may say that a phenomenon is experimentally demonstrable when we know how to conduct an experiment which will rarely fail to give us a statistically significant result. (Fisher 1935b/1947, p. 14; see Mayo 2018)
So, if I was a physiology researcher studying the effects of exercise, I would have changed fields (to e.g. PA promotion) when the negative effects of low activity became evident, whereas other people want to learn the exact metabolic pathways by which the thing happens. And I will quit intervention research when we figure out how to create interventions that fail to work <5% of the time.
Some people say we’re dealing with human phenomena that are so unpredictable and turbulent, that we cannot expect to do much better than we currently do. I disagree with this view, as all the methods I’ve seen used in our field so far are designed for ergodic, stable, linear systems. But there are other kinds of methods, which physicists started using when they left behind the ones that stuck with us, around maybe the 19th century. I’m very excited about learning more at the Complexity Methods for Behavioural Science summer school (here are some slides on what I presume will be among the topics).
Slide 4 of this presentation is what inspired me to do that illustration. Might be a bit difficult to understand without more context on the subject matter.
I don’t have examples on e.g. physical activity, because nobody’s done that yet, and lack of good longitudinal within-individual data is a severe historical hindrance. But some research groups are gathering longitudinal continuous data, and one that I know of, has very long time series of machine vision data on school yard physical activity (those are systems, too, just like individuals). Plenty has already been done in the public health sphere.
Hell do I know, this might turn out to be a dead-end, like most new developments tend to be.
But I’d be happy to be convinced that it is an inferior path to our current one 😉
[UPDATE: added distance correlation due to Vithor’s suggestion; see comments]
I’ve become increasingly anxious about properties of correlation I never knew existed. I collect resources and stuff on the topic in this post, so that have everything in one place. Some resources for beginners in the end of the post.
[C]ovariance doesn’t actually measure “Does y increase when x increases?” it only measures “Is y above average when x is above average (and by how much)?” And when covariance is broken [i.e. mean doesn’t coincide with median], our correlation function is broken.
So there may well be situations, where only 20% of people in the sample show dependence between two variables, and this shows up as a correlation of 37% at minimum. Or when a correlation of 0.5 carries ~4.5 times (and a correlation of 0.75 carries ~12.8 times) more information than a correlation of 0.25. As you may know, in psychology, it’s quite rare to see a correlation of 0.5. But even a correlation of 0.5 only gives 13% more information than random. This prompted the following conversation:
Real science maps nomological variables to primitive ontology. Far from correlation. E.G. in Newton's F = dp/dt, the nomological variable is momentum p. In quantum mechanics the nomological variable is the wave function. These are law-like constructs no correlations.
How can we interpret a result without in-depth knowledge of the field as well as the data in question? A partial remedy apparently is using mutual information instead. I know nothing about it, so like always, I just started playing around with things I don’t understand. Here’s what came out:
MIC and BCMI were new to me, but I thought they were easy to implement, which doesn’t of course mean they make sense. But see how they catch the dinosaur?
MIC is the Maximal Information Coefficient, from maximal information-based nonparametric exploration (documentation)
BCMI stands for Jackknife Bias Corrected MI estimates (documentation)
DCOR is distance correlation (see comments)
I’d be happy to hear thoughts and caveats regarding the use of entropy-based dependency measures in general, and these in particular, from people who actually know these methods. Here’s a related Twitter thread, or just email me!
ps. If this is your first brush with uncertainties related to correlations, and/or have little or no statistics background, you may not know how correlation can vary spectacularly in small samples. Taleb’s stuff (mini-moocs [1, 2]) can sometimes be difficult to grasp without math background, so perhaps get started with this visualisation, or these Excel sheets. A while ago I animated some elementary simulations of p-value distributions for statistical significance of correlations; selective reporting makes things a lot worse than what’s depicted there. If you’re a psychology student, also be sure to check out the p-hacker app. If you haven’t thought about distributions much lately, check this out for a fun read by a math student.
⊂This post has been a formal sacrifice to Rexthor.⊃
These are slides from my 2nd-ever teaching, which took place in a course on research methods for social scientists; topic was statistical testing. Some thoughts:
I tried to emphasise that this stuff is difficult, that people shouldn’t be afraid to say they don’t know, and that academics should try doing that more, too.
I tried to instill a deep memory that many uncertainties are involved in this endeavour, and that mistakes are ok as long as you report the choices you made transparently.
Added a small group discussion exercise at about 2/3 of the lecture: What was the most difficult part to understand so far? I think this worked quite well, although “Is this what an existential crisis feels like?” was not an uncommon response.
I really think statistics is mostly impossible to teach, and people learn when they get interested and start finding things out on their own. Not sure how successful this attempt was in doing that. Anyway, slides are available here.
TLDR: If you’re a seasoned researcher, see this. If you’re an aspiring one, start here or here, and read this.
For some years, I’ve been partly involved in the Let’s Move It intervention project, which targeted dysfunctional physical activity and sedentary behaviour patterns of older adolescents, by affecting their school environment as well as social and psychological factors.
I held a talk at the closing seminar; it was live streamed and is available here (on stage starting from about 1:57:00 in the recording). But if you were there, or are otherwise interested in the slides I promised, they are now here.
For a demonstration of non-stationary processes (which I didn’t talk about but which are mentioned in these slides), check out this video and an experimental mini-MOOC I made. Another blog post touching on some of the issues is found here.
The gist: to avoid getting fooled by them, we need to name our simplifying assumptions when modeling social scientific data. I’m experimenting with this visual approach to delivering information to those who think modeling is boring; feedback and improvement suggestions very welcome! [Similar presentation with between-individual longitudinal physical activity networks, presented at the Finnish Health Psychology conference: here]
I’m not as smooth as those talking heads on the interweb, so you may want just the slides. Download by clicking on the image below or watch at SlideShare.
Note: Jan Vanhove thinks we shouldn’t become paranoid with model assumptions; check his related blog post here!
These are the slides of my presentation at the annual conference of the European Health Psychology Society. It’s about presenting data visually, and taking publishing culture from the journals to our own hands. I hint to a utopia, where the journal publication is a side product of a comprehensively reported data set.
Please find a 14min video walkthrough of the slides (which can be found here) below. The site presented in the slides is here, and the tutorial by the most awesome Lisa DeBruine is here!
After the talk, I saw what was probably the best tweet about a presentation of mine ever. For a fleeting moment, I was happy to exist:
Matti Heino; Reijo Sund; Ari Haukkala; Keegan Knittle; Katja Borodulin; Antti Uutela; Vera Araújo-Soares, Falko Sniehotta, Tommi Vasankari; Nelli Hankonen
Background: Comprehensive reporting of results has traditionally been constrained by limited reporting space. In spite of calls for increased transparency, researchers have had to choose carefully what to report, and what to leave out; choices made based on subjective evaluations of importance. Open data remedies the situation, but privacy concerns and tradition hinder rapid progress. We present novel possibilities for comprehensive representation of data, making use of recent software developments.
Methods: We illustrate the opportunities using the Let’s Move It trial baseline data (n=1084). Descriptive statistics and group comparison results on psychosocial correlates of physical activity (PA) and accelerometry-assessed PA were reported in an easily accessible html-supplement, directly created from a combination of analysis code and data using existing tools within R.
Findings: Visualisations (e.g. network graphs, combined ridge and diamond plots) enabled presenting large amounts of information in an intelligible format. This bypasses the need to create narrative explanations for all data, or compress nuanced information into simple summary statistics. Providing all analysis code in a readily accessible format further contributed to transparency.
Discussion: We demonstrate how researchers can make their extensive analyses and descriptions openly available as website supplements, preferably with abundant visualisation to avoid overwhelming the reader with e.g. large numeric tables. Uptake of such practice could lead to a parallel form of literature, where highly technical and traditionally narrated documents coexist. While we may have to wait for fully open and documented data, comprehensive reporting of results is available to us now.
In this post, I present a property of averages I found surprising. Undoubtedly this is self-evident to statisticians and people who can think multi-variately, but personally I needed to see it to get a grasp of it. If you’re a researcher, make sure you do the single-item quiz before reading, to see how well your intuitions compare to those of others!
Ooo-oh! Don’t believe what they say is true
Ooo-oh! Their system doesn’t work for you
Ooo-oh! You can be what you want to be
Ooo-oh! You don’t have to join their f*king army
– Anti-Flag: Their System Doesn’t Work For You
In his book “The End of Average”, Todd Rose relates a curious story. In the late 1940s, the US Air Force saw a lot of planes crashing, and those crashes couldn’t be attributed to pilot error nor equipment malfunction. On one particularly bad day, 17 pilots crashed without an obvious reason. As everything from cockpits to helmets had been built to conform to the average pilot of the 1926, they brought in Lt. Gilbert Daniels to see if pilots had gotten bigger since then. Daniels measured 4063 pilots—who were preselected to not deviate from the average too much—on ten dimensions: height, chest circumference, arm length, thigh circumference, and so forth.
Before Daniels began, the general assumption was, that these pilots were mostly if not exclusively average, and Daniels’ task was to find the most accurate point estimate. But he had a more fundamental idea in mind. He defined “average” generously as person who falls within the 30% band around the middle, i.e. the median ±15%, and looked at whether each individual fulfills that criterion for all the ten bodily dimensions.
So, how big a proportion of pilots were found to be average by this metric?
This may be surprising, until you realise that each additional dimension brings with it a new “objective”, making it less likely that someone achieves all of them. But actually, only a fourth were average on a single dimension, and already less than ten percent were average on two dimensions.
As you saw in the quiz, I wanted to figure out how big a proportion of our intervention participants could be described as “average” by Daniels’ definition, on four outcome measures. The answer?
A lousy 1.98 percent.
I’m a bit slow, so I had to do a of simulation to get a better grasp of the phenomenon (code here). First, I simulated 700 intervention participants, who were hypothetically measured on four random, uncorrelated, normally distributed variables. What I found was that 0.86 % of this sample were “average” by the same definition as before. But what if we changed the definition?
Here’s what happens:
As you can see, you’ll describe more than half of the sample only when you extend the definition of “average” to about the middle 85% percent (i.e. median ±42.5%).
But what if the variables were highly correlated? I also simulated 700 independent participants with four variables, which were correlated almost perfectly (within-individual r = 0.99) with each other. Still, only 22.9 % percent of participants were described by defining average as the middle 30% around the median. For other definitions, see the plot below.
What have we learned? First of all: When you see averages, do not go assuming that they describe individuals. If you’re designing an intervention, you don’t just want to see which determinants correlate highly with the target behaviour on average, or seem changeable in the sense that the mean on those variables is not very high to begin with in your target group (see the CIBER approach, if you’re starting from scratch and want to get a preliminary handle on the data). This, because a single individual is unlikely to have the average standing on more than, say, two of the determinants, and individuals are who you’re generally looking to target. One thing you could do, is a cluster analysis where you’d look for the determinant profile, which is best associated with e.g. hospital visits (or, attitude/intention), and try to target the changeable determinants within that.
As a corollary: If you, your child, or your relationship doesn’t seem to conform to the dimensions of an average person in your city, or a particular age group, or whatever, this is completely normal! Whenever you see yourself falling behind the average, remember that there are plenty of dimensions where you land above it.
But wait, what happened to USAF’s problem of planes crashing? Well, the air force told the plane manufacturers to fix the problem of cockpits which don’t fit any individuals. The manufacturers said it was impossible and extremely costly. But when the air force said didn’t listen to excuses, cheap and easy solutions appeared quickly. Adjustable seats—now standard equipment in cars—are an example of the new design philosophy of individual fit, where we don’t try to fit the individual to the system, but the system to the individual.
Let us conclude with Daniels’ introduction section:
Three additional notes about the average:
Note 1: I’m taking it for granted, that we already know that the average is a useless statistic to begin with, unless you know the variation around the average, so I won’t pound on that further. But remember that variables generally aren’t perfectly normally distributed, as in the above simulations; my guess is that the situation would be even worse in those cases. Here’s a blog post you may want to check out: On Average, You’re Using the Wrong Average.
Note 2: There’s a curious tendency to think that deviations from the average represent “error” regardless of domain, whereas it’s self-evident that individuals can survive both if they’re e.g. big and bulky, or small and fast. With psychological measurement, is it not madness to think all participants have an attitude score, which comes from a normal distribution with a common mean for all participants? To inject reality in the situation, each participant may have their own mean, which changes over time. But that’s a story for another post.
Note 3: Did I already say, that you generally shouldn’t make individual-level conclusions based on between-individual data, unless ergodicity holds (which, in psychology, would be quite weird)?