24:null 25:["$","title",null,{"children":"Samplingfördelning för en andel - ändlig population | Mattias Villani | Observable"}] 2a:T809,Antag att vi är intresserade av en andel i en population. T ex andelen som skulle rösta på socialdemokraterna om det var val i Sverige idag. Vi tar ett stickprov från populationen, dvs väljer slumpmässigt ut ${tex`n`} personer och frågar vilka de skulle rösta på. För ett givet stickprov med ${tex`n`} observationer skattar vi populationsandelen ${tex`p`} med stickprovsandelen ${tex`\hat p`}. Om vi hade fått ett annat stickprov så skulle vi säkerligen ha fått en annan skattning ${tex`\hat p`}. **Samplingfördelningen** för **estimatorn** ${tex`\hat p`} talar om hur mycket ${tex`\hat p`} kan variera sett över *alla möjliga stickprov* av en viss storlek ${tex`n`}. Se notebooken [samplingfordeling-for-ändlig-population](samplingfordeling-for-andlig-population) för en illustration av detta i en mycket liten population med ett fåtal observationer. För större populationer är det i praktiken omöjligt att gå igenom alla möjliga stickprov, de är helt enkelt för många! Men det brukar räcka bra att dra några hundra stickprov och titta på fördelningen av ${tex`\hat p`} i dessa stickprov. I många fall kan vi också härleda samplingfördelningen matematiskt, men här använder vi oss av simulering för att få en mer intuitiv känsla för begreppet samplingfördelning. I figuren nedan undersöker vi andelen överlevande på Titanic med simulering. I fallet med Titanic är det egentligen ingen mening att skatta någonting eftersom vi faktiskt har tillgång till hela population med 2208 personer. Vi vet att ungefär 32% överlevde katastrofen. Men vi låtsas som om vi inte vet det, och att vi bara har ett stickprov tillgängligt för att skatta andelen överlevande. Då kan vi också jämföra med facit: ca 32% överlevande. Du väljer urvalsstorleken ${tex`n`} för varje stickprov och antal stickprov. För varje stickprov som programmet drar från populationen beräknas andelen överlevande ${tex`\hat p`}. Histogrammet plottar sen upp alla dessa skattningar ${tex`\hat p`} för de olika stickproven.2b:[] 28:{"id":"640ecbe957010f68","slug":"samplingfordelning-for-andel-andlig_pop","title":"Samplingfördelning för en andel - ändlig population","thumbnail":"17f009faaf3f1ba79215d4554523e5429e4e677e358957f1e893468b4beb232f","access_level":"public","create_time":"$D2023-02-06T21:15:57.800Z","update_time":"$D2023-02-19T15:21:28.264Z","view_time":null,"first_public_time":"$D2023-02-06T21:15:57.800Z","fork":{"id":"9489415a5c3d1f6e","slug":"samplingfordeling-for-andlig-population","title":"Samplingfördelning - leksakspopulation","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"stars":0,"starred":false,"owner":{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024"},"version":1434,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null}],"members":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":{"id":"209e13808f44ed11","slug":"sda1","title":"SDA1","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Samplingfördelning för en andel - ändlig population","cells":[{"id":38,"value":"# Samplingfördelning för en andel - ändlig population","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1360,"value":"$2a","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1071,"value":"viewof settings = Inputs.form([\n Inputs.range([1, titanic.length], {value: 10, step: 1, label: tex`\\text{Stickprovsstorlek, }n`}), \n Inputs.range([10, 1000], {value: 100, step: 10, label: tex`\\text{Antal stickprov: }`})\n])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1314,"value":"plt = Plot.plot({\n x: {\n domain: [0,1.02],\n label: \"Andelen överlevande i stickprovet\",\n },\n y: {\n axis: true,\n label: \"Antal stickprov\"\n },\n marks: [\n Plot.rectY(samplingdist_data, Plot.binX({y: \"count\"}, {x: \"mean\", fill: \"orange\", thresholds: d3.range(0, 1.02, 0.01)})),\n Plot.ruleX([popmean], {stroke: \"steelblue\", strokeWidth: 2}),\n Plot.ruleY([0]),\n Plot.ruleX([0]),\n Plot.text({x: popmean, y: 5}, {x: \"x\", y: \"y\", text: \"hh\"})\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nHär följer bara kod och detaljer som du antagligen inte vill läsa.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1252,"value":"ss = require('simple-statistics')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":888,"value":"#### Functions","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1250,"value":"function sample_finite_pop(data, n, nRep){\n // Sample nRep samples of size n from the data and return the mean in each sample\n var props = [];\n for (let i = 0; i < nRep; ++i) {\n props.push({sample: i+1, mean: d3.mean(ss.sample(survive_titanic, settings[0]).map(d => d.survived))})\n }\n return props;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1236,"value":"import {titanic} from \"@mattiasvillani/histogram\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1259,"value":"survive_titanic = titanic.map(d => ({survived: d.Survived == \"Alive\" ? 1 : 0, Class: d.Class}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1304,"value":"samplingdist_data = sample_finite_pop(survive_titanic, settings[0], settings[1])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1325,"value":"popmean = d3.mean(survive_titanic.map(d => d.survived))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":202,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":58,"value":"viewof md_colour = Inputs.color({label: \"Highlight color cells\", value: \"#F5F5DC\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2b","stdlib":"1","titling":"auto"}} 29:"$28:body"