Someone who I don’t know writes:
If you decide to share this publicly, say in your blog, let me stay anonymous.
It’s funny how people want anonymity on these things!
Anyway, my correspondent continues:
I came across this 2016 PNAS article, “Seasonality in human cognitive brain responses.”
It has this interesting figure:
The same data are plotted twice, once in the left half of the figure, and again in the right half. The horizontal axis is repeated, so we are not looking at data fabrication. In the caption, the authors say “n=28”. (Two pairs of dots overlap, so you see only 26 dots in each half). They also describe this figure as a “double plot”. I did an internet search for “double plot” and, so far as I can tell, there is no such thing. The closest thing was a dual-axis plot, which is not what the authors have here. They’ve used “double plots” in other figures in the paper too.
Going by how the authors drew the x-axis and their disclosure that “n=28”, I assume that the authors did not mean to deceive the readers. But I still find it deceptive. I can hardly think of a situation where repeating a plot is a good idea. But if an author must do it, they should probably not just call it a “double plot” and leave it at that. They should describe what it is they have done and why.
Yeah, this is wack! The natural thing would be to just show one year and not duplicate any data—I guess then there’s a concern that you wouldn’t see the continuity between December and January. But, yeah, repeating the entire thing seems like a bit much.
Here’s what I’d recommend: Display one year, Winter/Spring/Summer/Fall, then append Fall on the left and Winter on the right (so now you’re displaying 18 months) but gray out the duplicate months, so then it’s clear that they’re not additional data, they’re just showing the continuity of the pattern.
Best of both worlds!
P.S. The duplicate graph reminds me of a hilarious lampshade I saw once that looked like a map of the world, but it actually was two maps: that is, it went around the world twice, so that from any horizontal angle you could see all 360 degrees. I tried to find an image online but no amount of googling took me to it.
The issue is that the “starting point” of the graph is arbitrary. The graph is actually a graph on a circle, but what makes us think the periodicity assumption is correct? They need 2 years of data or something.
It’s not ideal, but I do see what they’re trying to accomplish.
It looks like they missed the 8th grade lesson on polar plots. (Though, asking my just-finished-eighth-grader, they didn’t cover polar plots in his school.)
Raghu:
I don’t think a circular graph would be good. For this sort of time plot, I much prefer a linear graph. See Figures 12 and 13 here.
It gets better:
The 28 subjects are: 6 in winter, 4 in the spring, and 9 in the summer and fall, respectively.
Wouldn’t one expect one cohort to have been followed through the seasons?
Not only that but… uh, I kind of just skimmed the article so I might’ve misunderstood, but they report that they had (from fig. S2)
6 participants in winter
4 participants in spring
9 participants in summer
9 participants in fall
and then they did a chi squared test on those numbers, concluded that p is larger than 0.05 and so the distribution is basically uniform: “A χ2 analysis show a uniform distribution across seasons (χ2 = 2.57, df = 3, P = 0.46).”
I… hmm… that’s…. that’s… that’s… interesting! Yes, that’s the word: interesting!
Thank you for pointing that out! I would like to add that the meaning of this model goes against my intuition, which I think many people will share: People become more depressed as spring turns into summer and summer into fall? And become more euphoric in winter?
I know quite a few people who suffer from depression, and their verdict has always been that the dark, cold winter gives the depression an edge. The study measured ‘healthy’ people (quotation marks because healthy is a relative term); but I assume that the seasonal effect on depressed people does not have a different sign than the seasonal effect on ‘healthy’ people. At least I have no reason to think otherwise.
Unless the authors have a fundamentally different understanding of the seasons than I do, these findings are in strong opposition to my current belief system. However, if anyone has a deeper insight into the subject, I am happy to be corrected.
That means the data is consistent with both uniform and seasonal models. It does not mean you can conclude it is uniform.
To me it looks more constant except for the spring, more like a step function. The right thing to do is use bayes rule to compare the fits.
p(uniform|data) = p(uniform)*p(data|uniform)/p(total)
p(seasonal|data) = p(seasonal)*p(data|seasonal)/p(total)
p(spring|data) = p(spring)*p(data|spring)/p(total)
Where,
p(total) = p(uniform)*p(data|uniform) + p(seasonal)*p(data|seasonal) + p(spring)*p(data|spring)
If people want to come up with other relationships those can go in the denominator too.
NB: If you want to account for varying model flexibility/vagueness, you also need to expand each of those terms to include all the uniform models, all the seasonal models, and so on. Not just the parameters of each that give best post-hoc fits.
I think it’s worse than that, Anoneuoid.
What I think is happening is that someone was worried about the number of participants not being constant across the seasons, so what they decided to do was a chi squared test and use the result (p larger than 0.05) to conclude that actually… uh, their sample size WAS kind of in some strange statistical way constant across seasons and so they needn’t worry about the different N’s.
They make a same kind of chi squared test to conclude that there’s a “uniform distribution of males and females across seasons” (table S1).
Just to be clear… I don’t think that makes any sense at all.
I see now. I thought they were calling the distribution of “mood score” uniform.
The number of participants looks like it shows the same level of seasonality as those mood scores. So 21 year olds in belgium who sign up for “no access to daylight or external information such as internet access or cellular phones” are both more likely to show up, and be in a worse mood during the summer and fall.
Anyway, my earlier comment was not relevant to yours then.
Even that is too optimistic of an interpretation, Anoneuoid.
They say they had 36 participants of which 8 were excluded because they had incomplete data due to technical problems. They were left with 28 participants, which matches with the reported N across the seasons.
It seems that they were planning on having 9 participants per season (36/4 = 9, uniform, yay) but that plan was foiled due to the aforementioned technical difficulties, so they… did a chi squared test and concluded that their sample size was still, after exclusions, uniform because p-value. Or something like that.
Here’s a web version of a double globe:
https://www.jasondavies.com/maps/gilbert/
Oooh! I want the physical globe of this.
There is some prior art for “double plot”, for example
https://www.researchgate.net/figure/Double-plot-ie-the-annual-cycle-is-repeated-for-illustrative-purpose-of-the-variation_fig1_371278743
which says in the caption “Double plot (i.e. the annual cycle is repeated for illustrative purpose)”. They probably want two complete cycles (which could be two seasons on either side), but absolutely agree there should be a clear visual indication that there’s only 1 year of independent data.
Dan:
Yeah, I think it would work just fine if they were to gray out the duplicate parts.
And also don’t repeat the data points.
This is standard and recommended procedure in making phase dependent plots in astronomy. The x-axis is extended by at least 0.5, and sometimes by 1, to avoid making 0, 0.5, or 1 stand out as anything special. The eye is very good at picking up false positive edge effects!
You mention that they might be doing this to show “the continuity between December and January”.
My guess – too lazy to digitize the data and figure it out or read the paper ;) – is that they have IMPOSED this continuity. In other words, I’m guessing they fit their curve to the so-called “double plot” to begin with. In that case – this would be even more deceptive.
I work with nominally periodic data 100% of the time (I study human walking, which is cyclic). We often run into this issue about how/whether to enforce periodicity if we select a single cycle of data to examine. I would label the double-plot appproach pretty misleading, but maybe not on purpose (perhaps the authors didn’t think through the ramifications).
You could do a polar graph, of course…? Or is that gross?
This kind of thing is commonly done in astronomy when we plot light curves (time series) for objects exhibiting periodic variability. To find an example, I just had to do a Google image search for “pulsar light curves”; see, e.g., https://www.researchgate.net/publication/222695661_The_Crab_pulsar_seen_with_AquEYE_at_Asiago_Cima_Ekar_observatory/figures?lo=1. Often there is some visual cue used to focus attention on a single period, like the grayscale idea Andrew offered.