Spacecraft Debris Odds Ratio
Spacecraft Debris Odds Ratio
[A chart is shown. Above the chart there is a heading, with a subheading below it:] Odds ratio for head injuries from falling spacecraft debris (Monte Carlo Simulation)
[The chart is rectangular with the X-axis labels above the chart with numbers from 1 to 5. These are places over vertical lines. The first at 1 is black, the other four are light gray. There are three smaller light gray ticks between each set of lines, and one on either side of the first and last. The distance between lines gets smaller and smaller towards the right, probably logarithmic.] X-axis: 1 2 3 4 5
[The Y-axis is not scaled; there are no ticks or lines. Instead it just gives five labels from top to bottom. Above those labels there is an arrow pointing to the top one with a label above explaning the axis.] Hours spent outdoors per day Y-axis: 0 (ref) 1 2-4 5-10 11+
[Aligned with each of these five divisions of the Y-axis there is a dot. The top one is placed on the solid line under 1 as a reference point. The other four dots all have long error bars, with the dots at the center of these. The second dot is a bit to the left of the solid line, with the error bar going almost to the left edge of the graph and halfway to the first light gray line to the right. The third dot is located halfway between the solid and the first light gray line with the error bar just crossing the solid line, and almost reaching the gray line. The fourth dot is about a third way between the first and second of the gray lines, with the error bar crossing both these lines. The fifth and last dot is just past the second gray line, with the error bar crossing both that, going more than half toward the first gray line, and also just past the third gray line. On the same height as the two bottom dots, there are asterisks just right of the edge of the graph.] * *
[Below the panel there is a caption:] Our new study suggests that spending more than 5 hours outside significantly increases your risk of head injury from spacecraft debris, so try to limit outdoor activities to 4 hours or less.

This comic is a misunderstanding of statistics very similar to that of 1252: Increased Risk . It explains that going outside for more than 5 hours per day significantly increases your risk of head injury from falling spacecraft, and advises to limit outside activity to avoid this risk.
However, since the odds of being hit in the head by (any part of) a falling spacecraft are astronomically low to begin with , quadrupling it or more still results in a negligible probability. The horizontal error bars for times greater than 4 hours are marked with asterisks to indicate they are significantly different from the reference value at 0 hours, as indeed those error bars don't overlap the vertical line for the 0-hours reference value.
Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement.
Presenting the data by hour brackets hides the data distribution inside each bracket. If the data were presented hour by hour, and not by groups of hours, they may show a different threshold of increased risk or no threshold (odds ratio could be linear).
The graph and error bars are based on a Monte Carlo simulation , a type of computational algorithm that uses repeated random sampling to obtain the likelihood of a range of results of occurring; see, for instance, this article about Monte Carlo simulations . Additionally, this may indicate that the entire study was conducted via a Monte Carlo simulation and that no real data was collected adding to the absurdity of the claim that more time spent outside could lead to an increased risk of head injuries due to falling space craft.  Indeed, it is so rare for humans to be struck by spacecraft debris that a simulation is probably the only way to study the risk; an absurdly large sample size, involving tens of millions of participants over several decades, would be necessary to obtain significant experimental data.
The specific reference to falling spacecraft is likely inspired by events happening around the time of this comics release (March 2022).  Around a month before this was posted, the head of the Russian space agency, Roscosmos , warned that sanctions against Russia (mostly those over the 2022 Russian invasion of Ukraine ) could result in the International Space Station crashing.  Since the Russian section of the space station is the one that provides propulsion (although it is built to rely on the power generated by the other sections), this was taken seriously and as of when this was posted, NASA was trying to come up with alternative stabilization strategies in case the situation worsened. There was also a recent report of some 600 kg space rocket debris found in Brazil.
The title text makes a similar joke. While the increase in chances of death by a bear attack are greater when going outside than the decrease in chances of death by cardiovascular disease, by getting out to exercise, it is incorrect to combine them in this way, since cardiovascular disease has a much higher starting chance of death, and reducing it by 30% has a much more significant effect on overall life expectancy than quadrupling the very very small chance of death by bear attack.  At least for the majority of us who don't live in or near wild bears' natural habitats.
The "280% increase" of the title text is also an error, though perhaps not for reasons that are obvious at first (for instance, the correct calculation is not "300% − 30% = 270%"). To "increase by 300%" means multiplying the probability by (1 + 3.0) = 4.0, while to "decrease by 30%" means multiplying by (1 − 0.3) = 0.7. Combining these means multiplying by both, for an overall change of 4.0 × 0.7 = 2.8, or 280%. However, this result means the risk has increased to 280% of its old value, not by 280%. And in any case, it is still not valid to simply combine two changes in wildly different risks like this.
The odds of an event is the probability that it happens divided by the probability that it doesn't happen. People often express odds as a ratio (e.g. the odds of rolling a 6 on a 6-sided dice might be expressed as 0.16777... : 0.83333..., or equivalently as 1:5), but it is important to note that such ratios are not odds ratios (it would be fitting to call this a "probability ratio", but this terminology is not standard).
An odds ratio is the odds of event O happening, given that some other event E has occurred, divided by the odds of O given that E has not occurred. O is sometimes called an "outcome" and E is sometimes called an "exposure", because people are often interested in comparing things like the odds of getting lung cancer (O) given that you smoke (E) to the odds of getting lung cancer given that you don't smoke, as a way of measuring the extent to which exposure to E influences outcome O. In the case of the comic, the outcome variable O is the event of getting a head injury from falling spacecraft debris, and the exposure variable E is the event of spending H hours per day outside, for various values of H. The comic appears to be saying that for each value of H, there are two options for E: either you spend H hours per day outside or you never go outside.
So for small values of H (e.g. 1 hour per day), the comic is saying that the event of being hit by spacecraft debris is more or less independent of the event of spending H hours per day outside, which is to say that the odds of being hit is more or less the same regardless of the choice you make between spending H hours per day outside and never going outside. Hence the dot on the 1-hour bar is close to 1, because the two odds are more or less equal (the dot appears to represent an average estimate of the odds ratio).
Note that when calculating the odds ratios for this comic, the odds in the denominators are always the same, as they are the odds of being hit given that you never go outside, which does not depend on H. So when the comic says that the odds ratio is above 3 for H={11+ hours per day}, it is effectively saying that the odds of being hit when you spend this much time outside is a bit more than 3 times the odds of being hit when you spend 1 hour per day outside.
Suppose the probability of being hit is: P when you spend 1 hour per day outside, and Q when you spend 11+ hours per day outside. The odds of being hit under these two exposures are P/(1-P) and Q/(1-Q) respectively, and because the odds ratios have equal denominators, the comic is saying that Q/(1-Q) = kP/(1-P), where k is a bit more than 3. If we rearrange this to get an expression for Q, we get:
As P is negligibly small, 1-P is very close to 1, and P+(1-P)/k is very close to 1/k. Thus Q is very close to kP (i.e. a bit more than 3 times P), meaning that the probability of being hit when you spend 11+ hours per day outside is still negligibly small. Thus, the comic's suggestion that we spend 4 hours or less outside based on the estimated odds ratios is extremely misguided.
[A chart is shown. Above the chart there is a heading, with a subheading below it:] Odds ratio for head injuries from falling spacecraft debris (Monte Carlo Simulation)
[The chart is rectangular with the X-axis labels above the chart with numbers from 1 to 5. These are places over vertical lines. The first at 1 is black, the other four are light gray. There are three smaller light gray ticks between each set of lines, and one on either side of the first and last. The distance between lines gets smaller and smaller towards the right, probably logarithmic.] X-axis: 1 2 3 4 5
[The Y-axis is not scaled; there are no ticks or lines. Instead it just gives five labels from top to bottom. Above those labels there is an arrow pointing to the top one with a label above explaning the axis.] Hours spent outdoors per day Y-axis: 0 (ref) 1 2-4 5-10 11+
[Aligned with each of these five divisions of the Y-axis there is a dot. The top one is placed on the solid line under 1 as a reference point. The other four dots all have long error bars, with the dots at the center of these. The second dot is a bit to the left of the solid line, with the error bar going almost to the left edge of the graph and halfway to the first light gray line to the right. The third dot is located halfway between the solid and the first light gray line with the error bar just crossing the solid line, and almost reaching the gray line. The fourth dot is about a third way between the first and second of the gray lines, with the error bar crossing both these lines. The fifth and last dot is just past the second gray line, with the error bar crossing both that, going more than half toward the first gray line, and also just past the third gray line. On the same height as the two bottom dots, there are asterisks just right of the edge of the graph.] * *
[Below the panel there is a caption:] Our new study suggests that spending more than 5 hours outside significantly increases your risk of head injury from spacecraft debris, so try to limit outdoor activities to 4 hours or less.
