Driving Science · Statistics literacy · Guide 38

The study that went looking for cannabis and found the seat belt

Two economists set out to measure something topical and frightening: whether the spread of legal marijuana was showing up in America's road-death figures. To do it properly they built a serious dataset, every US state plus Washington DC, seven years of data, road deaths measured against the miles actually driven. Then they did something most studies skip. Instead of picking one tidy model and reporting it, they stress-tested every variable against a vast number of reasonable model set-ups and asked a blunt question of each: does this finding hold up whatever sensible assumptions you make, or does it only appear when the analyst arranges the numbers just so? One variable, and only one, passed that test under every assumption they tried. It was not marijuana. It was not speed or alcohol or the mobile phone. It was the plain seat belt. This guide is about why that happened, what it teaches you about reading any scary statistic, and why the least glamorous habit in the car turns out to be the one you can be most certain about.

Foil study: Fowles & Loeb (2021), Journal of Transport & Health 51 jurisdictions, 357 state-years 📅 July 2026

Section 1

What the study did, in plain language

Before any headline earns your trust, you need to know what was measured, on whom, and how hard the finding was pushed. This study is unusually honest on the third point, and that honesty is the whole reason it is worth your time.

In 2021, two economists, Richard Fowles and Peter Loeb, published a paper in the Journal of Transport & Health with a straightforward title: the association between marijuana and motor vehicle crashes. Their raw material was a balanced panel of the 50 US states plus Washington DC across the years 2010 to 2016, which works out to 357 state-years of data. The thing they were trying to explain was each state's road-death rate, expressed the sensible way: fatalities per 100 million vehicle-miles travelled, so a big state with more driving is not automatically counted as more dangerous. Against that they lined up the usual suspects, alcohol consumption, posted speed limits, seat belt use, mobile phones, the age of the car fleet, unemployment, and their headline variable, marijuana use.

Here is the first thing to hold on to, because it shapes everything after. Their marijuana measure was not impaired drivers at the wheel. It was the percentage of adults in each state who said they had used cannabis at all in the past year, taken from a national health survey. That is an ecological measure: a population-level figure that says nothing about whether the person who used cannabis in March was the person who crashed in November, or whether they were even the same kind of person. Ecological data can hint at patterns, but it cannot pin a crash on an individual. The same caution, in a milder form, applies to their mobile-phone variable, which was really phone subscriptions per head, a proxy the authors admit may just be standing in for distraction in general. Keep that in your pocket. It matters later.

🧪 The clever part: stress-testing every finding with "s-values"

Most studies pick one model, run it, and print the result. The trouble, as the statistician Edward Leamer spent a career pointing out, is that the analyst chooses which control variables to include, and different reasonable choices can flip a result from significant to nothing. Fowles and Loeb used Leamer's Bayesian "sturdy values", or s-values, to sidestep that. In plain terms, the method re-runs the analysis across a huge number of reasonable model set-ups, every sensible combination of the factors the study considered, and reports how the finding behaves across all of them. If a variable's effect stays the same sign and stays strong no matter how you slice it, they call it sturdy, or non-fragile: an s-value above 1 in absolute terms under a given assumption. If it only appears under favourable assumptions and vanishes under others, it is fragile, which is a polite way of saying the finding might be, in Leamer's phrase, "cooked up by the analyst".

They ran that stress test under three different attitudes, which the paper calls priors and which you can read as three moods. The wide prior is the most demanding, an agnostic "show me". The pessimistic prior assumes the variables probably do not explain much, so a finding has to fight to survive. The optimistic prior assumes the variables do matter and lets the data speak more freely, so findings survive more easily under it. A finding that only holds up under the optimistic mood is real but conditional; a finding that holds up under all three is about as solid as this kind of data gets. That single distinction is the spine of the whole story.

⚠️ This is a statistics guide, not a cannabis guide

The paper is about marijuana, and the authors draw firm conclusions about it. We are deliberately not relitigating those here. Cannabis and impaired driving, including where Irish drug-driving law sits, is a separate subject we will cover in its own guide. In this article marijuana plays one role only: it is the frightening headline that turned out fragile, which is exactly what throws the sturdiness of the boring seat belt into relief. Read on for the statistics lesson, not for a verdict on cannabis.

Section 2

The robustness ladder

Rank the study's variables not by how big or how scary they are, but by how many of the three moods they survive. Do that and a very clear pecking order appears, with an unglamorous winner at the top.

This is the heart of it. The paper's own Table 3 reports, for each variable, whether it stayed sturdy under the wide, pessimistic and optimistic priors. Line them up by that count and you get a ladder. At the top sits the one variable in perfect conformity, the same sign and a strong result every single way you look at it. At the bottom sits the recreational-legalisation law, which held up nowhere. In between, tellingly, the frightening headline variables cluster on the bottom rung of "only under the friendliest assumptions".

357state-years of data: 50 states plus DC, 2010 to 2016
1variable sturdy under all three priors: seat belt use, and nothing else
s=-13.5the seat belt's s-value under the optimistic prior, far beyond the sturdiness line of 1
t=-6.06the belt's classical t-statistic, comfortably past the significance line of 2
VariableSturdy under how many priorss-values (wide / pessimistic / optimistic)What it means
Seat belt use (actual observed wearing rate) All three. The only variable in full conformity -2.04 / -2.38 / -13.50  (t = -6.06) Higher observed belt-wearing goes with fewer deaths, and that link never wobbles whatever assumptions you make. The star of the table.
Speed (higher urban-interstate limits) Two: pessimistic and optimistic 0.82 / 1.02 / 4.14  (t = 1.82) Higher posted limits go with more deaths, and the link is more Bayesian-robust than marijuana. Its t just misses the classical bar of 2.
Marijuana use (past-year, population) One: optimistic only 0.16 / 0.06 / 1.08 Only sturdy under the friendliest mood. Loosen the assumptions to the wide prior and its bounds run from below zero to above it, so the sign itself is not pinned down.
Alcohol consumption One: optimistic only 0.34 / 0.32 / 1.70 Positively associated with deaths and significant on a t-test, but Bayesian-fragile once you stop assuming the variables matter.
Mobile phones (subscriptions per head) One: optimistic only 0.23 / 0.25 / 1.05 Strongly and positively associated with deaths, but the sturdiness is conditional on the optimistic prior, and the measure is only a proxy for distraction.
Recreational-legalisation dummy (the law itself) None. Fragile under every prior 0.17 / 0.23 / 0.81  (t = -0.27) The legal change on its own showed no detectable effect on the death rate in this data, sturdy under nothing.

Read the ladder as a whole and the shape of it is the lesson. The variable with the most alarming press, the one the study was built around, sits on the weakest rung it can occupy while still counting at all. The variable nobody writes a headline about, the seat belt, sits alone at the top, sturdy under the demanding wide prior, the sceptical pessimistic prior and the generous optimistic prior alike. And the specific legal change that generates the most heat, whether a state has legalised recreational cannabis, does nothing detectable to the death rate on its own. A study designed to measure the frightening thing ended up handing its cleanest result to the boring thing.

Every variable in that study was tested against the same gauntlet of models. The scary headline variable survived only when the assumptions were kind to it. The plain seat belt survived every single version.
Reading of Fowles & Loeb (2021), Journal of Transport & Health 21:101043, Table 3

Section 3

Why the belt won, and what "sturdy" really means

This is the stats-literacy core of the guide. The belt did not win because seat belts are magic. It won because of what "sturdy" measures, and there are three traps in reading a study like this that the belt quietly steps over and the marijuana finding falls into.

First, the single most important distinction in the whole piece: sturdy is not the same as proven, and association is not the same as cause. When we say the seat belt was the sturdiest variable, we mean something narrow and specific. We mean that in this one panel of US data, the statistical link between higher belt-wearing and fewer deaths held its sign and its strength across every reasonable model the authors tried. That is a strong statement about the robustness of an association. It is not, on its own, proof that belts save lives. This study did not, and could not, prove that. What makes us confident that belts genuinely save lives is a different and stronger body of evidence, built from individual crash records rather than state averages, which we come to in the next section. Hold both thoughts at once: the panel study shows the belt as the most stubbornly reliable association in the data, and separate, better-designed research supplies the causal proof. The article rests on the second, and uses the first only to make its point about certainty.

⚠️ The sign-flip trap: the number that looks like it exonerates cannabis, and does not

Here is a genuine trap the paper itself flags, and it is the sharpest teaching moment in the study. If you take the raw, uncontrolled figures and simply correlate state cannabis-use rates with state death rates, the correlation comes out negative, about r = -0.371: on the face of it, more cannabis use, fewer deaths. A careless reader could wave that number around as proof cannabis makes roads safer. It is nothing of the kind. It is a textbook example of why a raw correlation is a feature of the data and not a finding. States differ in a hundred ways that travel with cannabis-use rates, wealth, urban density, age profile, enforcement, and once you control for the other factors the simple negative link does not survive as a clean result at all. We show you this number only as the trap, never as a claim. If a single before-controls correlation can point the opposite way to the controlled analysis, that is your cue to distrust any statistic quoted without its controls, in either direction.

Second trap: fragility hides inside a confident-sounding sentence. The marijuana finding is the case study. Under the optimistic prior it is sturdy, with an s-value of 1.08, just over the line, and the paper leans on that to make firm claims. But loosen the mood one notch to the wide prior and the picture changes: the estimated effect runs from below zero to above zero. In plain terms, the assumptions you bring decide whether the effect even points the way you expected. A finding that depends that heavily on the analyst's starting mood is not worthless, but it is conditional, and it deserves a hedged sentence, not a headline. The belt needs no such hedge, because it never crossed zero under any mood.

🔬 Why a proxy weakens a finding, and why the belt had none of that problem

Third trap: some variables in any study are measured cleanly and some are measured through a proxy, and proxies carry noise. The mobile-phone variable here was phone subscriptions per head, not observed phone use at the wheel; the authors themselves concede it may just be standing in for distraction in general. Marijuana was a population survey answer, not a roadside test. The belt was different in kind. It used actual observed wearing rates, the share of people seen buckled in roadside observation, not a yes-or-no flag for whether the state had a belt law. Better-measured variables tend to give steadier results, and that is part of why the belt behaved so well. When you read a study, ask not just what was found but how well each thing was measured. A sturdy result built on a clean measure is worth more than a fragile one built on a proxy.

Put the three together and the belt's victory stops being a surprise. It was the best-measured variable, it never flipped sign, and it survived the harshest assumptions. That combination is what statistical certainty actually looks like, and it is why the unglamorous fundamental beat the frightening headline. The frightening thing was not disproven. It was simply shown to be a less certain finding than the boring thing sitting quietly next to it in the same table.

💡

The reader's rule, in one line: when a statistic frightens you, ask whether it survives being pushed. The findings that stay put under every reasonable assumption are usually the dull, well-measured basics, and those are the ones worth acting on, ahead of whichever variable happens to be in this week's news.

Section 4

The causal backbone: why belts really do save lives

The panel study shows the belt as the sturdiest association in its data. That is not why you should wear one. The reason to wear one comes from a different, stronger body of evidence built on individual crashes, and it is worth stating clearly so the whole argument rests on solid ground rather than on one clever panel study.

If we stopped at Fowles and Loeb, a fair critic could say: interesting, but a sturdy association across US state averages is still just an association. Quite right. So here is the causal backbone, from the kind of research designed to establish cause, individual occupants in real crashes, matched and compared. It is settled, and it is not close.

The primary figure comes from the US National Highway Traffic Safety Administration. Analysing decades of real crash records, NHTSA's technical work reconfirmed that a standard three-point lap-and-shoulder belt reduces the risk of a fatal injury to a front-seat car occupant by about 45%, and by about 60% for occupants of light trucks and vans. For serious but non-fatal harm the same belt roughly halves the risk of moderate-to-critical injury in a car, and cuts it by around 65% in an SUV, van or pickup. These are individual-level, causal-grade numbers, and they are the ones NHTSA still relies on.

Seating positionFatality-risk reduction from a three-point beltSource
Front seat, passenger carAbout 45% (moderate-to-critical injury roughly halved)NHTSA (Kahane 2000)
Front seat, light truck or vanAbout 60% (moderate-to-critical injury cut ~65%)NHTSA (Kahane 2000)
Centre rear seat, passenger carAbout 58% (95% confidence bounds 41% to 69%)NHTSA (Kahane 2017)
Centre rear seat, light truck or vanAbout 75% (95% confidence bounds 63% to 84%)NHTSA (Kahane 2017)
Vehicle occupants, global summaryUp to about 50% (45 to 50% for front-seat occupants)WHO road-safety figures

The World Health Organisation puts the same message in round global terms: wearing a seat belt can cut an occupant's risk of death by up to half, with the standard differentiated figure being a 45 to 50% reduction for drivers and front-seat occupants and roughly a quarter for rear-seat occupants. Different bodies, different datasets, the same direction and roughly the same magnitude. That convergence is what a genuinely causal, well-established finding looks like, and it is the opposite of a fragile one.

🔬 The part people forget: an unbelted rear passenger is a danger to the people in front

Belting up is not only self-protection. In a crash, an unbelted body keeps moving at the car's speed until something stops it, and in the back seat that something is often the person in front. Peer-reviewed crash research bears this out: MacLennan and colleagues (2004) found that being exposed to unbelted occupants raised the injury-or-death risk to other people in the car by roughly 40%, and Bose, Arregui-Dalmases and colleagues (2013) found that an unbelted rear passenger sitting behind a belted driver increased that driver's own risk of dying by about 137% compared with a belted rear passenger. The classic corroborating study, Ichikawa and colleagues in the Lancet (2002), found front occupants had roughly double the death risk when the person directly behind them was unbelted. The physics is not in dispute. "Everyone belts up" is not nagging; it is the front-seat occupants' protection too.

This is the ground the article actually stands on. The panel study is a lens, a way of seeing that even a dataset built to chase a frightening variable kept pointing back at the belt. The reason to wear one, and to insist your passengers do, is the causal evidence above: individual crash records, consistent across agencies and decades, showing that this one cheap habit removes something on the order of half of your risk of dying. No fragile headline comes anywhere near that combination of size and certainty.

Section 5

The Irish translation: the boring-basics trio

The US panel and the NHTSA figures are not Irish. But the lesson translates cleanly, because the three variables that came out sturdiest or best-established in that literature, belt, speed and phone, are exactly the three the Irish system polices hardest and the three most within your own control. Here are the current Irish facts, verified, not guessed.

Start with the law, because it is simple and it is stricter than many drivers assume. Where seat belts are fitted, they must be worn by the driver and every passenger, front and rear. Children under 150cm or under 36kg must use a suitable child restraint, and a rear-facing seat must never go in front of an active airbag. Responsibility is split by age: the driver is legally responsible for making sure any passenger under 17 is belted or properly restrained, and it is the driver who collects the penalty if they are not; passengers aged 17 and over answer for themselves.

The penalty is the same whether it is your own belt or an under-17 you failed to restrain: a fixed-charge notice of €120 with 3 penalty points if paid within 28 days, rising to €180 if paid between days 29 and 56, and 5 penalty points on a court conviction. That €120 figure is current: it doubled from €60 on 27 October 2022, when fines for sixteen road-safety offences were raised together. It is worth naming, because older material, including a couple of pages on this very site that we are correcting, still shows the pre-2022 figures.

The boring-basics trioIrish fixed-charge penalty (paid within 28 days)On court conviction
No seat belt (driver, or allowing an under-17 unrestrained)€120 + 3 penalty points5 penalty points
Speeding€160 + 3 penalty points5 penalty points, max fine €1,000
Handheld mobile phone€120 + 3 penalty points5 penalty points, max fine €2,000

Notice what that table is. It is the boring-basics trio from the research, transplanted into Irish law almost one for one. The seat belt sat at the top of the study's robustness ladder; speed was the next most Bayesian-robust variable; the mobile phone stood in for distraction, which the wider evidence treats as a genuine killer. These are not this year's frightening headline. They are the dull, well-established fundamentals, and the Irish penalty-points system is, in effect, betting its enforcement on the same three levers the statistics keep pointing at.

⚠️ Ireland's belt-wearing recovered in 2024, but the last few percent are exactly the lever that matters

The Road Safety Authority's most recent observational survey (published March 2025) shows belt-wearing recovered in 2024 after the 2023 dip: drivers back up to 97%, front-seat passengers to 96%, and rear-seat wearing to 96%. That is a rebound, not a solved problem. Read what is left against the study you have just met. The one variable the whole ecological analysis could not shake, and the one the causal research says removes roughly half your fatal risk, still has a few percent of Irish occupants riding unbelted, with rear-seat and rural compliance the parts that keep lagging. A newer RSA survey may since have been published, so treat these as the 2024 baseline and check the latest RSA Safe Road Use reports page before quoting a figure. The direction of the point does not depend on the decimal.

One forward pointer, and then we leave it, because it is a separate subject: the study's headline variable was cannabis, and Irish law does treat drug-driving seriously, with its own testing regime and penalties. That belongs in its own guide and we will give it one. It is not the point here. The point here is that when you sort the same evidence by certainty rather than by drama, the levers that rise to the top are the three plain ones you already control every time you turn the key.

Section 6

What this evidence cannot tell you

A guide about reading statistics honestly has to hold itself to the same standard. The panel study we built this on has real soft edges, and naming them is part of the lesson, not a retreat from it.

🧪 The honest small print

It is an ecological design. Every variable is a state-level average. The study links state cannabis-use rates to state death rates, not impaired individuals to their own crashes. Ecological data can mislead, and no conclusion about any individual driver follows from it. The belt's sturdiness here is an association across states, which is why we lean on the individual-level NHTSA evidence for the causal claim.

It is US data, 2010 to 2016. One country, seven years, a window in which US road deaths actually rose 14.6%, against a long-run fall from 54,589 in 1972 to 37,806 in 2016. Nothing here is automatically an Irish number, and we have not treated it as one.

Some of the sturdiness depends on the optimistic prior. Marijuana, alcohol and mobile phones were sturdy only under the friendliest assumption. That is a genuine finding, but a conditional one, and the paper's abstract and conclusion state those associations more confidently than the all-priors picture in its own Table 3 strictly supports. We have reported the table, not the abstract.

Associations are not causes. Even the seat belt's all-priors sturdiness is, within this study, an association. We have been explicit that the causal proof for belts comes from elsewhere. Do not let anyone, us included, quietly upgrade a robust association into a proven cause.

We have deliberately not adjudicated the cannabis question. This guide uses marijuana only as the fragile foil. Whether and how cannabis impairs driving, and what Irish drug-driving law requires, is a real subject with its own literature that we will treat separately, not settle in a footnote here.

The causal belt figures mix sources. The 45% and 60% fatality reductions are from NHTSA's rigorous individual-level analysis; the injury-reduction and some rear-seat figures come from NHTSA and IIHS summary materials rather than a single primary report, and the "unbelted passenger as projectile" percentages come from named peer-reviewed studies, not from a road-safety agency. We have attributed each to its own source rather than blurring them together.

The Irish penalties and wearing rate are current as verified, but figures change. The €120, €160 and points values reflect the law after the October 2022 increases; the wearing rates are the 2024 survey. Legal amounts and survey numbers both move, so check the live RSA and Citizens Information pages before relying on an exact figure.

Section 7

Our verdict

The final verdict

A study built to measure a frightening thing handed its most certain result to a boring one. Across 357 US state-years, stress-tested against a vast number of reasonable models, exactly one variable stayed sturdy under every assumption the authors tried. Not marijuana, not speed, not alcohol, not the mobile phone. The plain seat belt, sturdy under the demanding, the sceptical and the generous priors alike, with a t-statistic of -6.06 to match. The scary headline variable was real but fragile; the unglamorous basic was bulletproof.

That is the statistics lesson, and it generalises well past this one paper: for statistical certainty, well-measured fundamentals beat frightening headlines. When a number alarms you, ask whether it survives being pushed. The findings that hold their sign and their strength under every reasonable assumption tend to be the dull, clean-measured basics, and those are the ones worth acting on first. Remember too that the panel study only shows the belt as the sturdiest association; the reason to actually wear one is the separate, causal-grade evidence that a belt removes something like half of your risk of dying.

So the one line to keep: the highest-confidence levers on your own safety are not this week's headline, they are the seat belt, your speed and your phone, the three plain things you control every time you drive. Belt up, everyone in the car, every trip. It is the least glamorous habit on the road and the single finding the evidence is most certain about.

Sources & further reading

References

  1. Fowles, R. & Loeb, P. D. (2021). "The association between marijuana and motor vehicle crashes." Journal of Transport & Health 21:101043. The foil study for this guide: a balanced panel of 50 states plus DC, 2010 to 2016 (357 state-years), road deaths per 100 million vehicle-miles, stress-tested with Leamer/Bayesian s-values under wide, pessimistic and optimistic priors. Seat belt use is the only variable sturdy under all three priors (s = -2.04, -2.38, -13.50; t = -6.06); speed is sturdy under two; marijuana, alcohol and cell phones under the optimistic prior only; the recreational-legalisation dummy is fragile under every prior (t = -0.27). All figures read directly from the paper's Table 3. https://doi.org/10.1016/j.jth.2021.101043
  2. Leamer, E. E. (2014, 2016). The "sturdy values" (s-value) and Extreme Bounds methodology that Fowles and Loeb apply, distinguishing simple correlations that "are a feature of the data" from partial coefficients "cooked up by the analyst." Method described in the paper's Sections 4 and 5; original developments in Leamer's work on specification searches.
  3. Kahane, C. J. (2000). "Fatality Reduction by Safety Belts for Front-Seat Occupants of Cars and Light Trucks." NHTSA Technical Report DOT HS 809 199. The causal anchor: three-point belts reduce front-seat fatal-injury risk by about 45% in passenger cars and 60% in light trucks and vans, from FARS crash data. crashstats.nhtsa.dot.gov
  4. Kahane, C. J. (2017). "Fatality Reduction by Seat Belts in the Center Rear Seat and Comparison of Occupants' Relative Fatality Risk at Various Seating Positions." NHTSA Technical Report DOT HS 812 369. Centre-rear three-point belts reduce fatality risk by about 58% in passenger cars (95% CI 41% to 69%) and 75% in light trucks and vans (95% CI 63% to 84%). crashstats.nhtsa.dot.gov (PDF)
  5. Insurance Institute for Highway Safety, "Seat belts" research topic. Summarises NHTSA's figures: about 45% fatal and 50% moderate-to-critical injury reduction for front-seat car occupants, and 60% / 65% for SUV, van and pickup occupants. iihs.org
  6. World Health Organisation, "Road traffic injuries" fact sheet ("wearing a seat-belt can reduce the risk of death among vehicle occupants by up to 50%") and WHO Global Status Report on Road Safety 2015 (differentiated 45 to 50% front-seat / ~25% rear-seat reduction, as summarised in the GRSP Seat-belts Fact Sheet, Dec 2015). who.int
  7. MacLennan, P. A. et al. (2004); Bose, D., Arregui-Dalmases, C. et al. (2013), Accident Analysis & Prevention; Ichikawa, M. et al. (2002), The Lancet. Peer-reviewed evidence that unbelted occupants endanger others: exposure to unbelted occupants raises injury/death risk to other occupants by ~40% (MacLennan); an unbelted rear passenger behind a belted driver raises that driver's fatality risk by ~137% (Bose); front occupants had roughly double the death risk when the person directly behind was unbelted (Ichikawa). Attributed to the academic studies, not to a safety agency.
  8. Road Safety Authority, Seat Belt Wearing Observational Survey 2024 (published March 2025). Drivers 97%, front-seat passengers 96%, rear-seat passengers 96%, a rebound from the 2023 dip (drivers 95%, front-seat 94%, rear-seat 95% overall and 92% on rural roads). A later survey may supersede these; verify at the RSA Safe Road Use reports page. rsa.ie
  9. Citizens Information & Road Safety Authority. Irish seat-belt law (driver and all passengers must wear where fitted; driver responsible for passengers under 17), the current penalties (seat belt €120 + 3 points; speeding €160 + 3 points; handheld phone €120 + 3 points; 5 points on conviction), and the 27 October 2022 fine increases. citizensinformation.ie · rsa.ie
  10. Cannabis-and-crash literature, reviewed within Fowles & Loeb (2021). Cited here only to note the wider debate, not adjudicated in this guide: Asbridge, Hayden & Cartwright (2012, BMJ) meta-analysis finding cannabis roughly doubles serious-crash risk; Arkell et al. (2020, JAMA) randomised trial on THC/CBD and lane-weaving; and the counter-studies (Aydelotte et al. 2017; Hansen et al. 2018) finding no clear legalisation effect. A dedicated Smart Driving Academy guide on cannabis and driving is planned.

Related on this site: Why drivers really crash · Young men, risk and the worry gap · Careless or clueless? Why young drivers really crash · Irish road traffic law · Driving Science hub