← Errata: The Busiest Crossing
The Commons Year · The case · ages 15-18
1. The Most Dangerous Crossing
The hammer rang once. A spark jumped off the anvil and did not go out. It waited. They followed.
The May issue of the Green Gazette had the biggest headline it had printed all year, and Tara had agreed to it.
STATION ROAD: THE GREEN'S MOST DANGEROUS CROSSING
Ollie in Year 10 had written it. It was his third big story, after the energy drinks and the bikes, and he had worked harder on it than on either. Since September, people had been sending the Gazette stories about near-misses at crossings round the Green: a car that came round the corner too fast, a van that did not stop at the zebra, a cyclist who nearly went into a pushchair. Ollie had put every one in a spreadsheet. Then he had counted them.
Station Road, by the station and the row of shops: six near-misses. School Lane, outside the primary school: two.
Station Road was where the lorries came through to the supermarket depot. It had no lights, only a zebra crossing with one of the bollards knocked sideways. Everyone on the Green had a story about it. The front page had a photograph of a lorry going past the zebra, very close, with a woman and a buggy waiting on the kerb.
The story had done what stories sometimes do. Mrs Fenwick from the residents' association had started a petition. It asked the council to move the crossing patrol, Mrs Adeyemi, the lollipop lady, from School Lane, where she had stood every morning and every afternoon for eleven years, to Station Road, where the danger was. It had four hundred signatures in a week.
On Monday there was a letter in the Gazette box. It was on the primary school's headed paper, with a drawing of a tree on it that a Year 2 child had done.
Dear Editor, it said. I read your front page with great interest. I am writing because the petition it has inspired would take our crossing patrol away from School Lane. I do not doubt that Station Road is dangerous. I would like to know, though, how your reporter decided that it is more dangerous than School Lane, because every morning at half past eight I stand at our gate and watch two hundred children cross a road, and I am not sure I agree. Yours, R. Banerjee, Headteacher.
Tara pinned it to the board above the back table at the Whetstone café. She read it twice.
She had been proud of the front page. Now she was uneasy. She did not know why yet.
2. Compared with What?
"I was going to say every near-miss in the story is real," Tara said.
She had brought the letter to the back table. Danya was there, drawing a map of the Green for a geography project, with a ruler and four colours of felt tip. Across from him sat Widen, who kept a notebook of what things cost, from bus fares to bridges, and who could not hear a number without asking what it should be compared with.
"I was going to say it like this," said Tara. "Parents reported all six at Station Road. Ollie checked every one. Two of them sent photos. Nothing was made up. Six is three times two. I can write back to Mr Banerjee and tell him so, politely."
She already had the sentence half written. Thank you for your letter. Every incident in our report was confirmed.
It felt good. It felt like the kind of answer an editor should give.
Widen read the front page, and then the letter, and then the front page again.
"Compared with what?" said Widen.
"Can I say one thing?" said Tara. "Compared with School Lane. Six against two."
"Widen the view. Six out of how many?" said Widen. "Two out of how many? One number on its own tells you almost nothing. Two numbers on their own tell you almost nothing twice."
"Hm. Six near-misses is six near-misses," said Tara.
"Is that a lot, or does it just sound like a lot?" said Widen. "If a million people crossed Station Road, six would be a miracle. If six people crossed it, six would be a disaster."
"Says who that the numbers are different?" said Danya, not looking up from his map.
"Nobody says it," said Widen. "That's the problem. Nobody's even asked how many people cross each road."
Tara looked at Mr Banerjee's letter. Two hundred children.
"How do we know how many people cross?" Danya asked.
Nobody knew. That was the problem.
3. The Count
Deed found it by the next afternoon.
Deed read council minutes for fun and kept the reports on her phone, and she found the thing Tara needed on page nineteen of a document nobody else on the Green had opened: the council's own traffic survey, done the year before, when they had been deciding whether Station Road needed lights.
"Go to the original document," said Deed, putting her phone on the table. "Not the petition. Not the front page. This. They stood people at both crossings with clickers for a week and counted everyone who crossed."
Tara leaned in.
"Station Road," said Deed. "About three thousand people crossing a day. It's the station, and the shops, and the bus stops on both sides. People cross there all day long, from six in the morning to midnight."
"Three thousand," said Tara.
"And School Lane," said Deed. "About two hundred a day. Nearly all of them at two times: between quarter past and twenty to nine in the morning, and again at quarter past three. Children, and the grown-ups bringing them. The rest of the day it's almost empty."
"So Station Road has fifteen times as many people crossing," said Danya, who had stopped drawing.
"Roughly," said Deed. "Read it where it was first written down. Page nineteen. Table four."
Tara copied both numbers into the pad she kept for corrections. Three thousand. Two hundred.
She felt something shift, the way it had in the spring with the bikes, and in the winter with the bar chart. It was the feeling of a true number turning out to be standing on the wrong ground.
4. Per Thousand
Widen took the pad and drew two boxes.
"Station Road," Widen said, writing in the first box. "Six near-misses. Three thousand people a day. Six divided by three thousand is two thousandths. So two for every thousand people who cross each day."
"And School Lane," said Widen, writing in the second box. "Two near-misses. Two hundred people a day. Two divided by two hundred is one hundredth, which is ten for every thousand."
Tara looked at the boxes.
Two for every thousand. Ten for every thousand.
"So School Lane is five times worse," said Danya slowly. "Not better. Worse."
"Person for person," said Widen. "If you're one person crossing, School Lane is where you're more likely to be in a near-miss. Five times more likely, on these numbers. Station Road has more near-misses because it has fifteen times more people. Busy places have more of everything. More near-misses. More lost umbrellas. More people saying hello."
"Hm. Then the headline's backwards," said Tara.
"Compared with what, though? The headline's a count," said Widen. "The count is true. Six really is more than two. But nobody crosses a road as a count. They cross it as one person."
Tara thought about Mrs Adeyemi in her yellow coat at School Lane, eleven years of half past eight. She thought about the petition, and the four hundred signatures, and the photograph of the lorry.
"Hm," said Tara.
5. Small Numbers
Tomas arrived while they were still looking at the two boxes. He carried a twenty-sided dice in his pocket for explaining chance and took it out, as he usually did, before he had sat down.
He read the boxes. Then he read the front page. Then he rolled the dice on the table and watched it settle on a seven.
"How surprising is this?" said Tomas. "That's my question. Two near-misses at School Lane in a year. Six at Station Road. Those are tiny numbers."
"They're real numbers," said Tara.
"They're real," said Tomas. "And they're tiny. Next year School Lane could easily have one, or four, just by chance. Station Road could have three, or nine. Real things are noisy. A rate made out of a count of two wobbles a lot. If School Lane has one next year, its rate halves. If it has four, its rate doubles. Nothing about the road would have changed."
"That's not fair. So we can't say anything?" said Danya.
"We can say something," said Tomas. "Just not everything. A gap of five times is big. Bigger than the wobble, probably. It's enough to say the front page compared the wrong things, and that School Lane is not the safe one. It isn't enough to say exactly how dangerous either road is. Nobody can say that from one year and eight near-misses."
"Widen the view again. Put the near-misses nobody reported next to it," said Widen.
Tomas nodded. "What would ordinary mess look like? A lot of near-misses never get sent to a newspaper. Especially if the person in them is six."
Tara wrote that down too, in the margin of her pad, and underlined it.
6. The Box
Attest came last, carrying the Gazette's red pen. Attest subbed every story before it went to print and circled any number without a name next to it. The May front page had come back with one red circle, round the words six near-misses. Next to it Attest had written: out of?
"Who says so?" said Attest. "That was my question. I wrote it, and then I let it go, because the six were all checked."
"I saw it," said Tara. "I thought you meant check the six."
"Who says so? I meant: out of how many," said Attest. "But I didn't follow it through. Nobody did, until Widen asked."
"Let me listen first," Tara said, before anyone could start telling her what to write.
She took her pad and wrote three headings across the top: what we printed, what the count says, what we can't know.
Under the first she wrote Station Road most dangerous: 6 v 2. Under the second she wrote 3,000 a day v 200 a day; per thousand, 2 v 10. The third column took longer: small numbers wobble, then near-misses nobody reports, then one year only.
"Hm. So what does a clarification like this have to carry?" Tara asked.
"Every claim names its source," said Attest. "Ollie's six and two, and where they came from: reports to the Gazette. The council's crossing count, named, page and table. Then the rate, per thousand people crossing, worked out plainly. Then a sentence saying the numbers are small. And then what it means, without overclaiming."
"Do we say Station Road is safe?"
"No," said Attest. "We never said it was safe, and it isn't. It has lorries and a broken bollard. We say we compared two counts of a different size. Put a name next to it."
"Hm. That's a lot for one box," said Tara.
"Four sentences," said Attest. "Five if you're unlucky."
Tara looked at the petition again. Four hundred names.
"I think we missed someone," Tara said slowly. "The children. We asked parents to send in near-misses. Who sends in a near-miss for a six-year-old? Mrs Adeyemi's been standing there for eleven years. We never asked her what she sees."
Nobody answered at once.
"A correction names its source too," said Attest. "Who you ask is your call. That's your bit."
7. Four People and a Pen
Mrs Hallam, who advised the Gazette and signed off every issue, came in at four. Ollie came with her. Mrs Fenwick came at quarter past, with the petition in a ring binder. Mr Banerjee came straight from school, still wearing his lanyard. Mrs Adeyemi came last, still in her yellow coat, with her lollipop sign folded under her arm.
Ollie spoke first.
"Every one of the six happened," he said. "I checked them all. Two of them had photos. And Station Road has lorries, and no lights, and a bollard that's been knocked over since February. If I'd left that out, I'd have been hiding something real. People are frightened of that road. They're right to be."
It was the strongest version of his argument, and every word of it was true.
Mrs Fenwick spoke next.
"I've lived by Station Road for thirty years," she said. "I've seen a man knocked off his bike there. I don't care about rates. I care that I'm frightened every time I take my grandson to the station. That's why I started the petition. Somebody has to do something."
Then Mrs Adeyemi put her lollipop sign on the table, folded, very carefully.
"Can I tell you what I see?" she said. "I see a car come round that corner by the church too fast, about once a week. I see a child step out behind a parked van, because she's seen her friend on the other side. I put my sign out and I step in front, and the car stops, and nobody sends a letter to the newspaper about it. It isn't a near-miss if it doesn't happen. It doesn't happen because I'm there."
Nobody said anything for a while.
"I don't want Station Road to be dangerous either," said Mr Banerjee quietly. "I just want someone to count the children."
"How do we know how many near-misses she stopped?" said Danya.
"We don't," said Tomas. "That's the trouble with things that don't happen. They're very hard to count."
Mrs Hallam took the corrections box out of her bag. It was the small grey panel at the bottom of page two, with a border round it and room for a few lines. She had used it eight times that year. She set it on the table in front of Tara, with the May front page beside it.
On the table in front of Tara was the front page, with the lorry and the buggy and the six. There was Deed's phone, open at page nineteen, table four. There was Widen's pad with its two boxes: 2 per thousand and 10 per thousand. There was Attest's red circle: out of? There was Mrs Fenwick's ring binder with four hundred names, and Mrs Adeyemi's folded sign, and one letter on paper with a tree drawn on it by a child in Year 2.
"You're the editor," said Mrs Hallam. "What does it say?"
She handed Tara the pen.
Tara looked at the empty box.
(Write the clarification Tara prints under the May front page.)
The spark dimmed to a warm dot and settled back on the anvil. The Green was just the Green again.
Back on the Green
That evening Lan, who was seven, came home from the park and announced that the swings were much more dangerous than the slide, because three people had fallen off the swings that week and only one off the slide.
Danya asked her how many people had been on the swings.
Lan thought. She said everybody, all the time, because the swings were the best thing in the park, and there was a queue.
Danya asked how many had been on the slide.
Lan said hardly anybody, because the slide was wet.
She went quiet for a moment. Then she said that perhaps the slide was the dangerous one, actually, and she would go on it carefully tomorrow, when it was dry.
Afterword. The idea in this case is that a count needs to be compared with how many had the chance: a rate, not a raw number. A busy road has more near-misses than a quiet one simply because more people use it, so the fair question is how many near-misses there are for every thousand people crossing. Judged that way, the quiet road in this case was five times riskier per person. The case also warns about small numbers: when you are counting two or six of something, chance alone can double or halve the count from one year to the next, so a rate made from a tiny count should be held loosely. Before you trust a claim that one place has "the most" of anything, ask out of how many, and how sure such small numbers can make you. You can practise comparing counts with rates in InferForge, and reading where numbers come from in NewsForge.
Saved. The next chapter will be here whenever you come back.
Who you met
- Widen One number means little without something to compare it with from NewsForge
- Deed Go to the original document, not a summary of a summary from NewsForge
- Danya a child of the Green Asks "how do we know?"
- Tomas Ask how surprising a result would be, including how surprisingly neat from InferForge
- Attest Every claim names its source, and a correction names one too from NewsForge
- Tara a child of the Green Listens longest, speaks last
Every recurring character has a short tune, so you can tell who is on stage before a word is said. The tunes play only when you tap, and the Reading Access sound switch turns them off.
The Honest Page
Which parts of this story are true, stretched or made up?
True
- A rate compares a count with how many had the chance: accidents per thousand journeys, say, rather than accidents alone. Ignoring how many had the chance, and judging by the count, is sometimes called base rate neglect. Source
- Road safety bodies compare roads by rates, such as casualties per million vehicle-kilometres or per number of people using a crossing, because a busy road will have more incidents than a quiet one even if it is safer for each person. Source
- In the case, six near-misses for three thousand daily crossings is two per thousand; two for two hundred is ten per thousand; ten is five times two.
Stretched
- In the case, the council has a simple count of how many people cross each road every day. What we simplified: Real crossing counts are done on a few sample days and vary with weather, school terms and events, and near-misses are often never reported at all. With counts as small as two and six, a single year can mislead either way.
Made up
- The Green Gazette, its May front page, the petition, the council's count, Ollie, Mrs Fenwick, Mrs Adeyemi and Mr Banerjee are made up. The idea of comparing rates rather than counts is real.