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believe","The way statistics are presented can make them more persuasive","Humans struggle to visualize large numbers, making presentation crucial",1,{"id":37,"data":38,"type":39,"maxContentLevel":19,"version":35},"a759ff7f-977b-4d45-9c65-24ac0069b1bf",{"type":39,"intro":40},10,[41,42],"Why do humans struggle to grasp large numbers in statistics?","How can visual aids help in understanding big numbers?",[44,60,75],{"id":45,"data":46,"type":35,"maxContentLevel":19,"version":19,"reviews":49},"588cec50-09bd-4a54-ba5b-029877c54053",{"type":35,"contentRole":25,"markdownContent":47,"audioMediaId":48},"According to Arthur James Balfour, “there are three kinds of falsehoods: lies, damned lies and statistics.” But what did he mean by this? Well, he, along with others, argues that it's possible to prove anything by the misleading use of statistics. In fact, there are a number of influential books that have been written on it.\n\nHowever, **the fundamental use of statistics when arguing is to prove that something is true**. Moreover, **you can use statistics as a yardstick** to measure the relative importance of problems. Imagine that you’re the director of a medical research company who’s looking to invest in a new treatment. You’d far sooner try to treat Covid, a disease affecting millions, than to treat an extremely rare type of elbow injury that only affects a hundred thousand people globally.\n\n![Graph](image://1fe6b78c-aa4a-4d1d-ad2c-34e1cfa63ba6 \"X-ray of an elbow. Image: MB, CC BY-SA 2.5 \u003Chttps://creativecommons.org/licenses/by-sa/2.5>, via Wikimedia Commons\")","77c11ca3-b45d-465e-b20d-75045faf58f2",[50],{"id":51,"data":52,"type":53,"version":35,"maxContentLevel":19},"205025f6-4e77-4433-bd37-0c90948862b7",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":54,"binaryCorrect":56,"binaryIncorrect":58},11,[55],"Statistics are always a source of indisputable proof.",[57],"FALSE",[59],"TRUE",{"id":61,"data":62,"type":35,"maxContentLevel":19,"version":19,"reviews":65},"7e9534f7-a6d6-46b6-bf70-7040bdaadb8d",{"type":35,"contentRole":25,"markdownContent":63,"audioMediaId":64},"Often two people engaged in an argument will both have their own **competing statistics**. One person will say one thing and back it up and another will produce a similar statistic for the other side. But **how does the audience distinguish between the 2 competing statistics**?\n\nWell, there are two things that they evaluate. First of all, they evaluate the **credibility** of the facts. Does it fall in line with what they think the rough number would be? Does it come from a reliable source? Often, statistics will hit home more effectively when they come from a source trusted by the audience. While liberal audiences have tended to favor the news channel CNN, conservative ones have traditionally prefered Fox News. Similarly, **while establishment supporters like to use government statistics, anti-establishment figures are more critical of them**.\n\n![Graph](image://277d485b-e097-40e6-81d1-b89b1cfc3cd3 \"Behind the scenes of the Fox News channel newsroom. Image: Spud of Inside Cable news, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons\")","1d6ec37a-3994-40ea-9ca7-607d03cc2202",[66],{"id":67,"data":68,"type":53,"version":35,"maxContentLevel":19},"69c0bf47-bb45-4db3-a5f9-4356b95a110b",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":69,"binaryCorrect":71,"binaryIncorrect":73},[70],"Which of these parties are more likely to use government figures in a debate?",[72],"Establishment supporters",[74],"Anti-establishment figures",{"id":76,"data":77,"type":35,"maxContentLevel":19,"version":25,"reviews":80},"e37a3eb5-dbf5-4f32-8199-a0c316483e60",{"type":35,"contentRole":25,"markdownContent":78,"audioMediaId":79},"Secondly, **people can be more or less persuaded by a statistic based on its presentation**. Has it been contextualized? Is it easy to visualize? Is it attention grabbing? Do they feel it's relevant to them? Often, this is where battles over statistics are won and lost.\n\n**It can be difficult for people to visualize numbers**. It is easy for us to think of 10 people - you would just imagine a recent birthday party or gathering. It is even possible to visualize hundreds. For those who often go to concerts and sports games, it might even be within the realm of possibility to visualize thousands. But **the human brain has not evolved to visualize any numbers bigger than that**.\n\n![Graph](image://1c18a052-5256-4986-af34-a0e9d120e7f7 \"A 19th century infographic visualising the size of Napoleon's armies. Image: Public domain via Wikimedia\")\n\nThis is a problem spoken about by EH Gombrich. In his *Little History of the World*, he says it's almost impossible for us to imagine the passing of millions of years because we have no personal experience to compare it to. Similarly, it is impossible for us to visualize a million people, or 18 billion coffee grinds because we’ve never had any relatable experience.\n\nAs a result, **the presentation of statistics**, both in audible and written forms, is almost as important as those statistics themselves.","380c969f-ceb6-4afa-b401-fa661b911dea",[81,90],{"id":82,"data":83,"type":53,"version":35,"maxContentLevel":19},"7560f5bf-3d79-4ab4-b6e8-c736dd042326",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":84,"binaryCorrect":86,"binaryIncorrect":88},[85],"Do all audiences have the same conception of source credibility for statistics?",[87],"No",[89],"Yes",{"id":91,"data":92,"type":53,"version":35,"maxContentLevel":19},"661fc9e1-83c7-4b87-967e-1778b2fb44c5",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":93,"binaryCorrect":95,"binaryIncorrect":97},[94],"Which of these would be the most effective rhetorical presentation of the number of people in the French Army?",[96],"Four football stadiums' worth",[98],"208,000",{"id":100,"data":101,"type":25,"version":20,"maxContentLevel":19,"summaryPage":103,"introPage":111,"pages":117},"b10d6871-e7ac-452f-aac2-2164ee427c68",{"type":25,"title":102},"Visualizing Statistics",{"id":104,"data":105,"type":19,"maxContentLevel":19,"version":25},"03aa6c10-7ccc-40fc-89c6-883058acc394",{"type":19,"summary":106},[107,108,109,110],"Imagining tiny things like nanometers is tough because we’ve never seen them","Air travel seems dangerous until you know 0.002% of flights had accidents in 2009","Context helps: 1 in 48 people in the UK identify as gay, making it easier to picture","Dividing big numbers by relatable ones makes stats easier to understand",{"id":112,"data":113,"type":39,"maxContentLevel":19,"version":35},"f43980a6-55d2-48fc-97fc-87fcc0f1bae5",{"type":39,"intro":114},[115,116],"What's the coolest way to show off huge numbers in a graph?","How can you spot trends in a sea of data?",[118,133,138],{"id":119,"data":120,"type":35,"maxContentLevel":19,"version":25,"reviews":123},"53e33672-6368-4031-8d59-6966ab4b30d2",{"type":35,"contentRole":25,"markdownContent":121,"audioMediaId":122},"One of the things that’s difficult to imagine is **things which are very small**. For example, **while we can picture a yard, it is more difficult for us to imagine a nanometer**. Even if we know there are a million nanometers in a millimeter, we still can’t imagine it very easily because we’ve never seen something that size.\n\nFor example, imagine that you were arguing about the safety of air travel. Saying that in 2009 there were 763 air travel accidents might make it seem frequent. In fact, if you presented the statistics in isolation, you might be led to believe that airplanes are very dangerous. However, if you were also told that roughly the same number of people died by bedsheet strangulation each year, it makes the number seem much smaller. After all, nobody refuses to go to sleep.","95c88f15-6dc3-47a2-98c6-2075162acef2",[124],{"id":125,"data":126,"type":53,"version":35,"maxContentLevel":19},"41dfecb6-7130-42e1-942e-c1595bda6fba",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":127,"binaryCorrect":129,"binaryIncorrect":131},[128],"In rhetoric, what's the most effective way of conveying how small a probability is?",[130],"Compare them to other probabilities of normal events",[132],"Show them as percentages",{"id":134,"data":135,"type":35,"maxContentLevel":19,"version":19},"900e9e19-4b9a-40c6-a1bd-549b3f6bf60a",{"type":35,"contentRole":25,"markdownContent":136,"audioMediaId":137},"Moreover, if you look at the total number of air journeys, the statistic is further contextualized. In 2009, there were 29.5 million air journeys in the world. That means that 0.002% of journeys ended in death. That’s a far cry from the 763 that looked like such a big number earlier.\n\n![Graph](image://ccb2f27a-1696-4688-8cfd-a5d995739203 \"Plane crash damage. Image: Staselnik, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons\")","c254533b-c6f9-4688-9b7f-648c70d5e921",{"id":139,"data":140,"type":35,"maxContentLevel":19,"version":19,"reviews":143},"cff20b36-dd27-4116-b096-0dbd7188ef21",{"type":35,"contentRole":25,"markdownContent":141,"audioMediaId":142},"The most common way of **visualizing large statistics** is by **contextualizing** them. For example, we can’t picture 1.4 million people identifying as gay in the UK. However, if you were told that 1 in 48 people in Britain self-identified as gay, it is far easier to picture. **Everyone knows 50 people so they can visualize the statistics**.\n\nSimilarly, it would be difficult for us to understand the significance of the fact that 375,000 cars sold each year are electric. In fact, it might seem like a huge number. However, if we were told that only 1 in 5 cars are electric, it helps us get a better picture of the environmental impact of new cars sold.\n\n![Graph](image://41e7374b-81c0-4268-8cd5-70b3f9376d07 \"Electric Renault charging. Image: werner hillebrand-hansen, CC BY-SA 2.0 \u003Chttps://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons\")\n\nTypically, **finding another number to divide the large number by is key to understanding its relative significance**, and showing it to a population.","4791f495-c7ed-4dff-8d7e-8fcb22239960",[144],{"id":145,"data":146,"type":53,"version":35,"maxContentLevel":19},"06d6c7ed-dbd8-4a29-9f11-ae2819cbb18c",{"type":53,"reviewType":20,"spacingBehaviour":35,"clozeQuestion":147,"clozeWords":149},[148],"We can help an audience understand large numbers by relaying them as fractions or percentages of total population sizes",[150],"total population sizes",{"id":152,"data":153,"type":25,"version":19,"maxContentLevel":19,"summaryPage":155,"introPage":163,"pages":169},"16122908-7e2c-408e-8d4f-c2b20b8aa7be",{"type":25,"title":154},"Believability of Statistics",{"id":156,"data":157,"type":19,"maxContentLevel":19,"version":35},"912f2e32-fc7f-4356-9413-0887c2feab3d",{"type":19,"summary":158},[159,160,161,162],"True statistics can be disbelieved if they don't match expectations","Explaining how statistics are calculated makes them more believable","Multiple attribution makes resources seem larger than they are","The Brexit bus misled by suggesting money could fund multiple things at once",{"id":164,"data":165,"type":39,"maxContentLevel":19,"version":35},"52dfdfd9-771e-480a-8ca1-0393290fd201",{"type":39,"intro":166},[167,168],"What is 'multiple attribution' in statistics?","How can 'multiple attribution' be used to mislead in arguments?",[170,183,198],{"id":171,"data":172,"type":35,"maxContentLevel":19,"version":19,"reviews":175},"8871199e-a896-4c4c-8f43-dd19d2345091",{"type":35,"contentRole":25,"markdownContent":173,"audioMediaId":174},"Another strange thing about statistics is that **they aren’t always believable just because they’re true**. A Stanford study showed that, even once told something is true, **people are still prone to not believing it if it doesn’t fit with their expectations**. Additionally, some statistics which are true, people don’t believe. For example, 41% of Americans think that humans co-existed with dinosaurs, despite us having missed each other by 64 million years.\n\n![Graph](image://f66e5b4e-f803-4f68-a762-876918a27fb6 \"Man stands by dinosaur tracks. Image: Dill Tom, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons\")\n\nAs a result, **it is often important to help explain the methodology behind the statistics obtained**. Rather than just spouting the statistic and offhandedly attributing it to its source, it can be useful to explain the methodology behind its calculation and finding. That way, people are more likely to believe it.","265e93b9-0373-496d-b03d-a1dcd16060a1",[176],{"id":177,"data":178,"type":53,"version":35,"maxContentLevel":19},"b516d329-f1c8-4bd4-9ee5-8f4cb197e9d9",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":179,"binaryCorrect":181,"binaryIncorrect":182},[180],"Should you trust that just because a statistic is true, people will find it credible?",[87],[89],{"id":184,"data":185,"type":35,"maxContentLevel":19,"version":19,"reviews":188},"7c65b7b0-d80e-4f62-98b5-5674064ff4a1",{"type":35,"contentRole":25,"markdownContent":186,"audioMediaId":187},"One common statistical fallacy is **multiple attribution**. This occurs when people take a statistic and try to state that it can be used for multiple things.\n\n![Graph](image://818ed671-aae1-40ac-9736-a9e7cff9a911 \"Vote Leave poster in a window. Image: DAVID HOLT from London, England, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons\")\n\nIn the 2016 Brexit referendum, the VoteLeave campaign drove a bus round the country with an infamous claim written on the side. It said that Britain’s exit from the European Union would save the country £350 million *per week*. That’s equivalent to 10,500 new nurses, 13,000 policemen or approximately two hospitals.","09e271cf-4846-4c3e-bda4-8dc20ab35957",[189],{"id":190,"data":191,"type":53,"version":35,"maxContentLevel":19},"9b280fe4-c02e-41f0-a22f-5acebdd01501",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":192,"binaryCorrect":194,"binaryIncorrect":196},[193],"What statistical fallacy can make resources seem larger than they are?",[195],"Multiple Attribution",[197],"Sunk Cost",{"id":199,"data":200,"type":35,"maxContentLevel":19,"version":19,"reviews":203},"882e84b6-b931-4e4c-bf49-98c3737c0aec",{"type":35,"contentRole":25,"markdownContent":201,"audioMediaId":202},"The problem with this is that people imagined it going to the nurses **and** the policemen **and** the new hospitals. This led to the satisfaction of multiple different interest groups - those who wanted increased policing and those who wanted increased medical funding. As a result, **both groups largely voted for the leave campaign**. However, the money cannot be used twice.\n\n![Graph](image://1dbe00b4-765d-4827-a989-aa90e347433c \"Congregation of Greater Manchester Police officers. Image: Terry from uk, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons\")\n\n**By providing multiple uses for a resource - whether it be money or barrels of oil - you can make it seem larger than it actually is**.","eaba80f2-8bfc-460f-a724-e09a62dc2394",[204],{"id":205,"data":206,"type":53,"version":35,"maxContentLevel":19},"93891482-836b-46a6-a4a3-8705c3458b01",{"type":53,"reviewType":20,"spacingBehaviour":35,"clozeQuestion":207,"clozeWords":209},[208],"Multiple attribution occurs when you show multiple potential expenditures equivalent to a resource that can only occur in isolation",[210],"Multiple attribution",{"id":212,"data":213,"type":25,"version":25,"maxContentLevel":19,"summaryPage":215,"introPage":223,"pages":229},"72bfe41a-0737-42e4-95bb-0a9b777e02a9",{"type":25,"title":214},"Correlation and Causation in Statistics",{"id":216,"data":217,"type":19,"maxContentLevel":19,"version":35},"39554053-785b-4373-ac55-05c65d9f6b42",{"type":19,"summary":218},[219,220,221,222],"Correlation doesn't always mean causation","Spurious correlations are coincidences with no real-world link","Mechanizing explains how one event leads to another","More than one link? Mechanize to show causality",{"id":224,"data":225,"type":39,"maxContentLevel":19,"version":35},"bbdad443-821d-4a1b-ade7-3cb43c5d9dfc",{"type":39,"intro":226},[227,228],"What does 'mechanizing' mean in statistics?","How can 'mechanizing' explain causal links between correlated stats?",[230,254,259],{"id":231,"data":232,"type":35,"maxContentLevel":19,"version":25,"reviews":235},"b53faf34-c163-428f-a04b-29bf89cee1e1",{"type":35,"contentRole":25,"markdownContent":233,"audioMediaId":234},"Another common statistical fallacy is assuming that **correlation** always implies **causation**. However, this is not always the case. Sometimes, 2 statistics might have similar patterns but have no real world relation to each other. We call these ‘**spurious correlations**.’\n\n![Graph](image://d43ea895-15c0-4b1e-8283-7c1d7604a501 \"Mozzarella cheese in a bowl. Image: Luigi Versaggi, CC BY-SA 2.0 \u003Chttps://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons\")\n\nFor example, there is a high mathematical correlation between consumption of mozzarella cheese and the number of civil engineering doctorates awarded from 2000 to 2009. However, **this does not mean that eating mozzarella increases the quality of civil engineering education**. The coincidence of the 2 statistics is simply that - a coincidence. Similarly, there is a 95.24% correlation between the number of people who drowned after falling out of a fishing boat and the marriage rate in Kentucky. However, **there is little evidence to suggest that people are getting married in Kentucky because people are falling out of fishing boats**.","aa7cced0-267f-49e6-b776-1cc72fcc990d",[236,245],{"id":237,"data":238,"type":53,"version":35,"maxContentLevel":19},"4429edb5-d2b0-4282-9497-e227df30094c",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":239,"binaryCorrect":241,"binaryIncorrect":243},[240],"Which of these statements is true?",[242],"Correlation may not mean causation",[244],"Correlation implies causation",{"id":246,"data":247,"type":53,"version":35,"maxContentLevel":19},"8d0fe5d5-b932-4e55-84aa-0a580cb6232f",{"type":53,"reviewType":25,"spacingBehaviour":35,"binaryQuestion":248,"binaryCorrect":250,"binaryIncorrect":252},[249],"What is it called when two statistics follow each other's patterns?",[251],"Correlation",[253],"Causation",{"id":255,"data":256,"type":35,"maxContentLevel":19,"version":25},"10dbe3af-f531-4074-9150-3b2215b4a09e",{"type":35,"contentRole":25,"markdownContent":257,"audioMediaId":258},"As a result, it is important, when being presented with a statistic, **to think about whether or not it is possible that a correlation was caused simply by the benefit of coincidence, or whether it is actually real mathematically**. One way of getting around the spurious correlation fallacy is to show causal links. **When you outline a series of steps from one thing that happened to lead to it causing another, we call that process ‘mechanizing’**.\n\n![Graph](image://61ffba1b-2935-4947-813a-6f1fb8a88b2f \"Capsized fishing boat. Image: Calistemon, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons\")","c7eaba96-c5f9-49d2-af36-c320292cd66e",{"id":260,"data":261,"type":35,"maxContentLevel":19,"version":25,"reviews":264},"fdc4c767-354f-43f0-9650-1e79a374aadc",{"type":35,"contentRole":25,"markdownContent":262,"audioMediaId":263},"For example, you might ‘mechanize’ that the reason why an increase in sports car ownership led to more crashes is because sports cars drive faster and are harder to control. By explaining the reason why 2 statistics might have a correlation, you can show that the correlation isn’t a spurious one.\n\nTypically, **if a statistic is the kind that has an obvious link, explaining the causality is not necessary**. However, if your concept is slightly further afield - such as explaining why the rise in domestic cats is lowering the spread of avian disease across continents, you might need to fill in the blanks with the extra steps. The 2 statistics look like a coincidence unless you explain that domestic cats are eating the birds; therefore, stopping them from migrating.\n\nIn short, a good rule of thumb is that if your statistics require more than 1 link, it is usually a good idea to mechanize the link.\n\n![Graph](image://5f77527e-dc0f-4c24-a179-2def4d89b2db \"Two domestic cats. Image: Jeremy Foo, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons\")","6faa34a9-a360-41a1-8fee-abd0a668b122",[265],{"id":266,"data":267,"type":53,"version":35,"maxContentLevel":19},"614edfa0-f811-47ad-9510-4f545e8fc768",{"type":53,"reviewType":35,"spacingBehaviour":35,"activeRecallQuestion":268,"activeRecallAnswers":270},[269],"What is it called when you explain the logical steps or processes that cause a statistic to behave in a certain way?",[271],"Mechanization",[273,445,557,695],{"id":23,"data":24,"type":25,"version":19,"maxContentLevel":19,"summaryPage":27,"introPage":36,"pages":274},[275,322,376],{"id":45,"data":46,"type":35,"maxContentLevel":19,"version":19,"reviews":49,"parsed":276},{"data":277,"body":280,"toc":320},{"title":278,"description":279},"","According to Arthur James Balfour, “there are three kinds of falsehoods: lies, damned lies and statistics.” But what did he mean by this? Well, he, along with others, argues that it's possible to prove anything by the misleading use of statistics. In fact, there are a number of influential books that have been written on it.",{"type":281,"children":282},"root",[283,290,310],{"type":284,"tag":285,"props":286,"children":287},"element","p",{},[288],{"type":289,"value":279},"text",{"type":284,"tag":285,"props":291,"children":292},{},[293,295,301,303,308],{"type":289,"value":294},"However, ",{"type":284,"tag":296,"props":297,"children":298},"strong",{},[299],{"type":289,"value":300},"the fundamental use of statistics when arguing is to prove that something is true",{"type":289,"value":302},". Moreover, ",{"type":284,"tag":296,"props":304,"children":305},{},[306],{"type":289,"value":307},"you can use statistics as a yardstick",{"type":289,"value":309}," to measure the relative importance of problems. Imagine that you’re the director of a medical research company who’s looking to invest in a new treatment. You’d far sooner try to treat Covid, a disease affecting millions, than to treat an extremely rare type of elbow injury that only affects a hundred thousand people globally.",{"type":284,"tag":285,"props":311,"children":312},{},[313],{"type":284,"tag":314,"props":315,"children":319},"img",{"alt":316,"src":317,"title":318},"Graph","image://1fe6b78c-aa4a-4d1d-ad2c-34e1cfa63ba6","X-ray of an elbow. Image: MB, CC BY-SA 2.5 \u003Chttps://creativecommons.org/licenses/by-sa/2.5>, via Wikimedia Commons",[],{"title":278,"searchDepth":25,"depth":25,"links":321},[],{"id":61,"data":62,"type":35,"maxContentLevel":19,"version":19,"reviews":65,"parsed":323},{"data":324,"body":326,"toc":374},{"title":278,"description":325},"Often two people engaged in an argument will both have their own competing statistics. One person will say one thing and back it up and another will produce a similar statistic for the other side. But how does the audience distinguish between the 2 competing statistics?",{"type":281,"children":327},[328,347,366],{"type":284,"tag":285,"props":329,"children":330},{},[331,333,338,340,345],{"type":289,"value":332},"Often two people engaged in an argument will both have their own ",{"type":284,"tag":296,"props":334,"children":335},{},[336],{"type":289,"value":337},"competing statistics",{"type":289,"value":339},". One person will say one thing and back it up and another will produce a similar statistic for the other side. But ",{"type":284,"tag":296,"props":341,"children":342},{},[343],{"type":289,"value":344},"how does the audience distinguish between the 2 competing statistics",{"type":289,"value":346},"?",{"type":284,"tag":285,"props":348,"children":349},{},[350,352,357,359,364],{"type":289,"value":351},"Well, there are two things that they evaluate. First of all, they evaluate the ",{"type":284,"tag":296,"props":353,"children":354},{},[355],{"type":289,"value":356},"credibility",{"type":289,"value":358}," of the facts. Does it fall in line with what they think the rough number would be? Does it come from a reliable source? Often, statistics will hit home more effectively when they come from a source trusted by the audience. While liberal audiences have tended to favor the news channel CNN, conservative ones have traditionally prefered Fox News. Similarly, ",{"type":284,"tag":296,"props":360,"children":361},{},[362],{"type":289,"value":363},"while establishment supporters like to use government statistics, anti-establishment figures are more critical of them",{"type":289,"value":365},".",{"type":284,"tag":285,"props":367,"children":368},{},[369],{"type":284,"tag":314,"props":370,"children":373},{"alt":316,"src":371,"title":372},"image://277d485b-e097-40e6-81d1-b89b1cfc3cd3","Behind the scenes of the Fox News channel newsroom. Image: Spud of Inside Cable news, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons",[],{"title":278,"searchDepth":25,"depth":25,"links":375},[],{"id":76,"data":77,"type":35,"maxContentLevel":19,"version":25,"reviews":80,"parsed":377},{"data":378,"body":380,"toc":443},{"title":278,"description":379},"Secondly, people can be more or less persuaded by a statistic based on its presentation. Has it been contextualized? Is it easy to visualize? Is it attention grabbing? Do they feel it's relevant to them? Often, this is where battles over statistics are won and lost.",{"type":281,"children":381},[382,394,410,418,431],{"type":284,"tag":285,"props":383,"children":384},{},[385,387,392],{"type":289,"value":386},"Secondly, ",{"type":284,"tag":296,"props":388,"children":389},{},[390],{"type":289,"value":391},"people can be more or less persuaded by a statistic based on its presentation",{"type":289,"value":393},". Has it been contextualized? Is it easy to visualize? Is it attention grabbing? Do they feel it's relevant to them? Often, this is where battles over statistics are won and lost.",{"type":284,"tag":285,"props":395,"children":396},{},[397,402,404,409],{"type":284,"tag":296,"props":398,"children":399},{},[400],{"type":289,"value":401},"It can be difficult for people to visualize numbers",{"type":289,"value":403},". It is easy for us to think of 10 people - you would just imagine a recent birthday party or gathering. It is even possible to visualize hundreds. For those who often go to concerts and sports games, it might even be within the realm of possibility to visualize thousands. But ",{"type":284,"tag":296,"props":405,"children":406},{},[407],{"type":289,"value":408},"the human brain has not evolved to visualize any numbers bigger than that",{"type":289,"value":365},{"type":284,"tag":285,"props":411,"children":412},{},[413],{"type":284,"tag":314,"props":414,"children":417},{"alt":316,"src":415,"title":416},"image://1c18a052-5256-4986-af34-a0e9d120e7f7","A 19th century infographic visualising the size of Napoleon's armies. Image: Public domain via Wikimedia",[],{"type":284,"tag":285,"props":419,"children":420},{},[421,423,429],{"type":289,"value":422},"This is a problem spoken about by EH Gombrich. In his ",{"type":284,"tag":424,"props":425,"children":426},"em",{},[427],{"type":289,"value":428},"Little History of the World",{"type":289,"value":430},", he says it's almost impossible for us to imagine the passing of millions of years because we have no personal experience to compare it to. Similarly, it is impossible for us to visualize a million people, or 18 billion coffee grinds because we’ve never had any relatable experience.",{"type":284,"tag":285,"props":432,"children":433},{},[434,436,441],{"type":289,"value":435},"As a result, ",{"type":284,"tag":296,"props":437,"children":438},{},[439],{"type":289,"value":440},"the presentation of statistics",{"type":289,"value":442},", both in audible and written forms, is almost as important as those statistics themselves.",{"title":278,"searchDepth":25,"depth":25,"links":444},[],{"id":100,"data":101,"type":25,"version":20,"maxContentLevel":19,"summaryPage":103,"introPage":111,"pages":446},[447,479,499],{"id":119,"data":120,"type":35,"maxContentLevel":19,"version":25,"reviews":123,"parsed":448},{"data":449,"body":451,"toc":477},{"title":278,"description":450},"One of the things that’s difficult to imagine is things which are very small. For example, while we can picture a yard, it is more difficult for us to imagine a nanometer. Even if we know there are a million nanometers in a millimeter, we still can’t imagine it very easily because we’ve never seen something that size.",{"type":281,"children":452},[453,472],{"type":284,"tag":285,"props":454,"children":455},{},[456,458,463,465,470],{"type":289,"value":457},"One of the things that’s difficult to imagine is ",{"type":284,"tag":296,"props":459,"children":460},{},[461],{"type":289,"value":462},"things which are very small",{"type":289,"value":464},". For example, ",{"type":284,"tag":296,"props":466,"children":467},{},[468],{"type":289,"value":469},"while we can picture a yard, it is more difficult for us to imagine a nanometer",{"type":289,"value":471},". Even if we know there are a million nanometers in a millimeter, we still can’t imagine it very easily because we’ve never seen something that size.",{"type":284,"tag":285,"props":473,"children":474},{},[475],{"type":289,"value":476},"For example, imagine that you were arguing about the safety of air travel. Saying that in 2009 there were 763 air travel accidents might make it seem frequent. In fact, if you presented the statistics in isolation, you might be led to believe that airplanes are very dangerous. However, if you were also told that roughly the same number of people died by bedsheet strangulation each year, it makes the number seem much smaller. After all, nobody refuses to go to sleep.",{"title":278,"searchDepth":25,"depth":25,"links":478},[],{"id":134,"data":135,"type":35,"maxContentLevel":19,"version":19,"parsed":480},{"data":481,"body":483,"toc":497},{"title":278,"description":482},"Moreover, if you look at the total number of air journeys, the statistic is further contextualized. In 2009, there were 29.5 million air journeys in the world. That means that 0.002% of journeys ended in death. That’s a far cry from the 763 that looked like such a big number earlier.",{"type":281,"children":484},[485,489],{"type":284,"tag":285,"props":486,"children":487},{},[488],{"type":289,"value":482},{"type":284,"tag":285,"props":490,"children":491},{},[492],{"type":284,"tag":314,"props":493,"children":496},{"alt":316,"src":494,"title":495},"image://ccb2f27a-1696-4688-8cfd-a5d995739203","Plane crash damage. Image: Staselnik, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons",[],{"title":278,"searchDepth":25,"depth":25,"links":498},[],{"id":139,"data":140,"type":35,"maxContentLevel":19,"version":19,"reviews":143,"parsed":500},{"data":501,"body":503,"toc":555},{"title":278,"description":502},"The most common way of visualizing large statistics is by contextualizing them. For example, we can’t picture 1.4 million people identifying as gay in the UK. However, if you were told that 1 in 48 people in Britain self-identified as gay, it is far easier to picture. Everyone knows 50 people so they can visualize the statistics.",{"type":281,"children":504},[505,530,535,543],{"type":284,"tag":285,"props":506,"children":507},{},[508,510,515,517,522,524,529],{"type":289,"value":509},"The most common way of ",{"type":284,"tag":296,"props":511,"children":512},{},[513],{"type":289,"value":514},"visualizing large statistics",{"type":289,"value":516}," is by ",{"type":284,"tag":296,"props":518,"children":519},{},[520],{"type":289,"value":521},"contextualizing",{"type":289,"value":523}," them. For example, we can’t picture 1.4 million people identifying as gay in the UK. However, if you were told that 1 in 48 people in Britain self-identified as gay, it is far easier to picture. ",{"type":284,"tag":296,"props":525,"children":526},{},[527],{"type":289,"value":528},"Everyone knows 50 people so they can visualize the statistics",{"type":289,"value":365},{"type":284,"tag":285,"props":531,"children":532},{},[533],{"type":289,"value":534},"Similarly, it would be difficult for us to understand the significance of the fact that 375,000 cars sold each year are electric. In fact, it might seem like a huge number. However, if we were told that only 1 in 5 cars are electric, it helps us get a better picture of the environmental impact of new cars sold.",{"type":284,"tag":285,"props":536,"children":537},{},[538],{"type":284,"tag":314,"props":539,"children":542},{"alt":316,"src":540,"title":541},"image://41e7374b-81c0-4268-8cd5-70b3f9376d07","Electric Renault charging. Image: werner hillebrand-hansen, CC BY-SA 2.0 \u003Chttps://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons",[],{"type":284,"tag":285,"props":544,"children":545},{},[546,548,553],{"type":289,"value":547},"Typically, ",{"type":284,"tag":296,"props":549,"children":550},{},[551],{"type":289,"value":552},"finding another number to divide the large number by is key to understanding its relative significance",{"type":289,"value":554},", and showing it to a population.",{"title":278,"searchDepth":25,"depth":25,"links":556},[],{"id":152,"data":153,"type":25,"version":19,"maxContentLevel":19,"summaryPage":155,"introPage":163,"pages":558},[559,605,645],{"id":171,"data":172,"type":35,"maxContentLevel":19,"version":19,"reviews":175,"parsed":560},{"data":561,"body":563,"toc":603},{"title":278,"description":562},"Another strange thing about statistics is that they aren’t always believable just because they’re true. A Stanford study showed that, even once told something is true, people are still prone to not believing it if it doesn’t fit with their expectations. Additionally, some statistics which are true, people don’t believe. For example, 41% of Americans think that humans co-existed with dinosaurs, despite us having missed each other by 64 million years.",{"type":281,"children":564},[565,584,592],{"type":284,"tag":285,"props":566,"children":567},{},[568,570,575,577,582],{"type":289,"value":569},"Another strange thing about statistics is that ",{"type":284,"tag":296,"props":571,"children":572},{},[573],{"type":289,"value":574},"they aren’t always believable just because they’re true",{"type":289,"value":576},". A Stanford study showed that, even once told something is true, ",{"type":284,"tag":296,"props":578,"children":579},{},[580],{"type":289,"value":581},"people are still prone to not believing it if it doesn’t fit with their expectations",{"type":289,"value":583},". Additionally, some statistics which are true, people don’t believe. For example, 41% of Americans think that humans co-existed with dinosaurs, despite us having missed each other by 64 million years.",{"type":284,"tag":285,"props":585,"children":586},{},[587],{"type":284,"tag":314,"props":588,"children":591},{"alt":316,"src":589,"title":590},"image://f66e5b4e-f803-4f68-a762-876918a27fb6","Man stands by dinosaur tracks. Image: Dill Tom, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons",[],{"type":284,"tag":285,"props":593,"children":594},{},[595,596,601],{"type":289,"value":435},{"type":284,"tag":296,"props":597,"children":598},{},[599],{"type":289,"value":600},"it is often important to help explain the methodology behind the statistics obtained",{"type":289,"value":602},". Rather than just spouting the statistic and offhandedly attributing it to its source, it can be useful to explain the methodology behind its calculation and finding. That way, people are more likely to believe it.",{"title":278,"searchDepth":25,"depth":25,"links":604},[],{"id":184,"data":185,"type":35,"maxContentLevel":19,"version":19,"reviews":188,"parsed":606},{"data":607,"body":609,"toc":643},{"title":278,"description":608},"One common statistical fallacy is multiple attribution. This occurs when people take a statistic and try to state that it can be used for multiple things.",{"type":281,"children":610},[611,623,631],{"type":284,"tag":285,"props":612,"children":613},{},[614,616,621],{"type":289,"value":615},"One common statistical fallacy is ",{"type":284,"tag":296,"props":617,"children":618},{},[619],{"type":289,"value":620},"multiple attribution",{"type":289,"value":622},". This occurs when people take a statistic and try to state that it can be used for multiple things.",{"type":284,"tag":285,"props":624,"children":625},{},[626],{"type":284,"tag":314,"props":627,"children":630},{"alt":316,"src":628,"title":629},"image://818ed671-aae1-40ac-9736-a9e7cff9a911","Vote Leave poster in a window. Image: DAVID HOLT from London, England, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons",[],{"type":284,"tag":285,"props":632,"children":633},{},[634,636,641],{"type":289,"value":635},"In the 2016 Brexit referendum, the VoteLeave campaign drove a bus round the country with an infamous claim written on the side. It said that Britain’s exit from the European Union would save the country £350 million ",{"type":284,"tag":424,"props":637,"children":638},{},[639],{"type":289,"value":640},"per week",{"type":289,"value":642},". That’s equivalent to 10,500 new nurses, 13,000 policemen or approximately two hospitals.",{"title":278,"searchDepth":25,"depth":25,"links":644},[],{"id":199,"data":200,"type":35,"maxContentLevel":19,"version":19,"reviews":203,"parsed":646},{"data":647,"body":649,"toc":693},{"title":278,"description":648},"The problem with this is that people imagined it going to the nurses and the policemen and the new hospitals. This led to the satisfaction of multiple different interest groups - those who wanted increased policing and those who wanted increased medical funding. As a result, both groups largely voted for the leave campaign. However, the money cannot be used twice.",{"type":281,"children":650},[651,676,684],{"type":284,"tag":285,"props":652,"children":653},{},[654,656,661,663,667,669,674],{"type":289,"value":655},"The problem with this is that people imagined it going to the nurses ",{"type":284,"tag":296,"props":657,"children":658},{},[659],{"type":289,"value":660},"and",{"type":289,"value":662}," the policemen ",{"type":284,"tag":296,"props":664,"children":665},{},[666],{"type":289,"value":660},{"type":289,"value":668}," the new hospitals. This led to the satisfaction of multiple different interest groups - those who wanted increased policing and those who wanted increased medical funding. As a result, ",{"type":284,"tag":296,"props":670,"children":671},{},[672],{"type":289,"value":673},"both groups largely voted for the leave campaign",{"type":289,"value":675},". However, the money cannot be used twice.",{"type":284,"tag":285,"props":677,"children":678},{},[679],{"type":284,"tag":314,"props":680,"children":683},{"alt":316,"src":681,"title":682},"image://1dbe00b4-765d-4827-a989-aa90e347433c","Congregation of Greater Manchester Police officers. Image: Terry from uk, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons",[],{"type":284,"tag":285,"props":685,"children":686},{},[687,692],{"type":284,"tag":296,"props":688,"children":689},{},[690],{"type":289,"value":691},"By providing multiple uses for a resource - whether it be money or barrels of oil - you can make it seem larger than it actually is",{"type":289,"value":365},{"title":278,"searchDepth":25,"depth":25,"links":694},[],{"id":212,"data":213,"type":25,"version":25,"maxContentLevel":19,"summaryPage":215,"introPage":223,"pages":696},[697,757,791],{"id":231,"data":232,"type":35,"maxContentLevel":19,"version":25,"reviews":235,"parsed":698},{"data":699,"body":701,"toc":755},{"title":278,"description":700},"Another common statistical fallacy is assuming that correlation always implies causation. However, this is not always the case. Sometimes, 2 statistics might have similar patterns but have no real world relation to each other. We call these ‘spurious correlations.’",{"type":281,"children":702},[703,729,737],{"type":284,"tag":285,"props":704,"children":705},{},[706,708,713,715,720,722,727],{"type":289,"value":707},"Another common statistical fallacy is assuming that ",{"type":284,"tag":296,"props":709,"children":710},{},[711],{"type":289,"value":712},"correlation",{"type":289,"value":714}," always implies ",{"type":284,"tag":296,"props":716,"children":717},{},[718],{"type":289,"value":719},"causation",{"type":289,"value":721},". However, this is not always the case. Sometimes, 2 statistics might have similar patterns but have no real world relation to each other. We call these ‘",{"type":284,"tag":296,"props":723,"children":724},{},[725],{"type":289,"value":726},"spurious correlations",{"type":289,"value":728},".’",{"type":284,"tag":285,"props":730,"children":731},{},[732],{"type":284,"tag":314,"props":733,"children":736},{"alt":316,"src":734,"title":735},"image://d43ea895-15c0-4b1e-8283-7c1d7604a501","Mozzarella cheese in a bowl. Image: Luigi Versaggi, CC BY-SA 2.0 \u003Chttps://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons",[],{"type":284,"tag":285,"props":738,"children":739},{},[740,742,747,749,754],{"type":289,"value":741},"For example, there is a high mathematical correlation between consumption of mozzarella cheese and the number of civil engineering doctorates awarded from 2000 to 2009. However, ",{"type":284,"tag":296,"props":743,"children":744},{},[745],{"type":289,"value":746},"this does not mean that eating mozzarella increases the quality of civil engineering education",{"type":289,"value":748},". The coincidence of the 2 statistics is simply that - a coincidence. Similarly, there is a 95.24% correlation between the number of people who drowned after falling out of a fishing boat and the marriage rate in Kentucky. However, ",{"type":284,"tag":296,"props":750,"children":751},{},[752],{"type":289,"value":753},"there is little evidence to suggest that people are getting married in Kentucky because people are falling out of fishing boats",{"type":289,"value":365},{"title":278,"searchDepth":25,"depth":25,"links":756},[],{"id":255,"data":256,"type":35,"maxContentLevel":19,"version":25,"parsed":758},{"data":759,"body":761,"toc":789},{"title":278,"description":760},"As a result, it is important, when being presented with a statistic, to think about whether or not it is possible that a correlation was caused simply by the benefit of coincidence, or whether it is actually real mathematically. One way of getting around the spurious correlation fallacy is to show causal links. When you outline a series of steps from one thing that happened to lead to it causing another, we call that process ‘mechanizing’.",{"type":281,"children":762},[763,781],{"type":284,"tag":285,"props":764,"children":765},{},[766,768,773,775,780],{"type":289,"value":767},"As a result, it is important, when being presented with a statistic, ",{"type":284,"tag":296,"props":769,"children":770},{},[771],{"type":289,"value":772},"to think about whether or not it is possible that a correlation was caused simply by the benefit of coincidence, or whether it is actually real mathematically",{"type":289,"value":774},". One way of getting around the spurious correlation fallacy is to show causal links. ",{"type":284,"tag":296,"props":776,"children":777},{},[778],{"type":289,"value":779},"When you outline a series of steps from one thing that happened to lead to it causing another, we call that process ‘mechanizing’",{"type":289,"value":365},{"type":284,"tag":285,"props":782,"children":783},{},[784],{"type":284,"tag":314,"props":785,"children":788},{"alt":316,"src":786,"title":787},"image://61ffba1b-2935-4947-813a-6f1fb8a88b2f","Capsized fishing boat. Image: Calistemon, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons",[],{"title":278,"searchDepth":25,"depth":25,"links":790},[],{"id":260,"data":261,"type":35,"maxContentLevel":19,"version":25,"reviews":264,"parsed":792},{"data":793,"body":795,"toc":825},{"title":278,"description":794},"For example, you might ‘mechanize’ that the reason why an increase in sports car ownership led to more crashes is because sports cars drive faster and are harder to control. By explaining the reason why 2 statistics might have a correlation, you can show that the correlation isn’t a spurious one.",{"type":281,"children":796},[797,801,812,817],{"type":284,"tag":285,"props":798,"children":799},{},[800],{"type":289,"value":794},{"type":284,"tag":285,"props":802,"children":803},{},[804,805,810],{"type":289,"value":547},{"type":284,"tag":296,"props":806,"children":807},{},[808],{"type":289,"value":809},"if a statistic is the kind that has an obvious link, explaining the causality is not necessary",{"type":289,"value":811},". However, if your concept is slightly further afield - such as explaining why the rise in domestic cats is lowering the spread of avian disease across continents, you might need to fill in the blanks with the extra steps. The 2 statistics look like a coincidence unless you explain that domestic cats are eating the birds; therefore, stopping them from migrating.",{"type":284,"tag":285,"props":813,"children":814},{},[815],{"type":289,"value":816},"In short, a good rule of thumb is that if your statistics require more than 1 link, it is usually a good idea to mechanize the link.",{"type":284,"tag":285,"props":818,"children":819},{},[820],{"type":284,"tag":314,"props":821,"children":824},{"alt":316,"src":822,"title":823},"image://5f77527e-dc0f-4c24-a179-2def4d89b2db","Two domestic cats. Image: Jeremy Foo, CC BY 2.0 \u003Chttps://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons",[],{"title":278,"searchDepth":25,"depth":25,"links":826},[],{"left":4,"top":4,"width":828,"height":828,"rotate":4,"vFlip":6,"hFlip":6,"body":829},24,"\u003Cpath fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\" d=\"m9 18l6-6l-6-6\"/>",{"left":4,"top":4,"width":828,"height":828,"rotate":4,"vFlip":6,"hFlip":6,"body":831},"\u003Cpath fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\" d=\"M4 5h16M4 12h16M4 19h16\"/>",1778179309065]