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// Get the T Value, sample mean // and standard deviation based on the data const alphaIndex = tTableConfidence.indexOf(halfAlpha); if (alphaIndex > -1) { // Subtract 2 instead of 1 because list is 0 based let tValue; const degreeFreedom = array.length - 2; if (1 <= degreeFreedom && degreeFreedom <= 30) { tValue = tTableList[degreeFreedom][alphaIndex]; } else if (31 <= degreeFreedom && degreeFreedom <= 60) { tValue = tTableList[31][alphaIndex]; } else if (61 <= degreeFreedom && degreeFreedom <= 120) { tValue = tTableList[32][alphaIndex]; } else { tValue = tTableList[33][alphaIndex]; } const sampleMean = mean(array); const sd = standardDeviation(array); // high and low distribution const low = sampleMean - tValue * (sd / Math.sqrt(degreeFreedom)); const high = sampleMean + tValue * (sd / Math.sqrt(degreeFreedom)); return md` ### T Distribution: Sample Mean: **${sampleMean.toFixed(4)}** Standard Deviation: **${sd.toFixed(4)}** T Value: **${tValue.toFixed(3)}** T Distribution: **\[${low.toFixed(2)}; ${high.toFixed(2)}\]** `; } }35:T724,tTableList = [ [3.078, 6.314, 12.076, 31.821, 63.657, 318.310, 636.620], [1.886, 2.920, 4.303, 6.965, 9.925, 22.326, 31.598], [1.638, 2.353, 3.182, 4.541, 5.841, 10.213, 12.924], [1.533, 2.132, 2.776, 3.747, 4.604, 7.173, 8.610], [1.476, 2.015, 2.571, 3.365, 4.032, 5.893, 6.869], [1.440, 1.943, 2.447, 3.143, 3.707, 5.208, 5.959], [1.415, 1.895, 2.365, 2.998, 3.499, 4.785, 5.408], [1.397, 1.860, 2.306, 2.896, 3.355, 4.501, 5.041], [1.383, 1.833, 2.262, 2.821, 3.250, 4.297, 4.781], [1.372, 1.812, 2.228, 2.764, 3.169, 4.144, 4.587], [1.363, 1.796, 2.201, 2.718, 3.106, 4.025, 4.437], [1.356, 1.782, 2.179, 2.681, 3.055, 3.930, 4.318], [1.350, 1.771, 2.160, 2.650, 3.012, 3.852, 4.221], [1.345, 1.761, 2.145, 2.624, 2.977, 3.787, 4.140], [1.341, 1.753, 2.131, 2.602, 2.947, 3.733, 4.073], [1.337, 1.746, 2.120, 2.583, 2.921, 3.686, 4.015], [1.333, 1.740, 2.110, 2.567, 2.898, 3.646, 3.965], [1.330, 1.734, 2.101, 2.552, 2.878, 3.610, 3.922], [1.328, 1.729, 2.093, 2.539, 2.861, 3.579, 3.883], [1.325, 1.725, 2.086, 2.528, 2.845, 3.552, 3.850], [1.323, 1.721, 2.080, 2.518, 2.831, 3.527, 3.819], [1.321, 1.717, 2.074, 2.508, 2.819, 3.505, 3.792], [1.319, 1.714, 2.069, 2.500, 2.807, 3.485, 3.767], [1.318, 1.711, 2.064, 2.492, 2.797, 3.467, 3.745], [1.316, 1.708, 2.060, 2.485, 2.787, 3.450, 3.725], [1.315, 1.706, 2.056, 2.479, 2.779, 3.425, 3.707], [1.314, 1.703, 2.052, 2.473, 2.771, 3.421, 3.690], [1.313, 1.701, 2.048, 2.467, 2.763, 3.408, 3.674], [1.311, 1.699, 2.045, 2.462, 2.756, 3.396, 3.659], [1.310, 1.697, 2.042, 2.457, 2.750, 3.385, 3.646], [1.303, 1.684, 2.021, 2.423, 2.704, 3.307, 3.551], [1.296, 1.671, 2.000, 2.390, 2.660, 3.232, 3.460], [1.289, 1.658, 1.980, 2.358, 2.617, 3.160, 3.373], [1.282, 1.645, 1.960, 2.326, 2.576, 3.090, 3.291] ]36:[{"id":"3b9b01dc0d30baa0e6b2b6942935d0ae8413b37987e71d075395d0a752cd0ba46277ac4ee2716ca80ba385f45c28d54c07251e1896016ea8ec74641afdcc3fc6","href":"https://static.observableusercontent.com/files/3b9b01dc0d30baa0e6b2b6942935d0ae8413b37987e71d075395d0a752cd0ba46277ac4ee2716ca80ba385f45c28d54c07251e1896016ea8ec74641afdcc3fc6","name":"title.jpg","type":"image/jpeg","lastModified":1596746081916.567,"size":440456}] 31:{"id":"c5284acd0fb11cb0","slug":"derek-banas-statistics","title":"Derek Banas Statistics","thumbnail":"0877e9cec0ff83b3465b2783bf993a7429d2f2ff2c8788594f2af55ffa25be4c","access_level":"public","create_time":"$D2020-08-06T20:30:16.995Z","update_time":"$D2020-08-09T23:07:02.476Z","view_time":null,"first_public_time":"$D2020-08-06T20:42:40.369Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"b5ee25cc13065361","login":"a1ip","name":"Philippe Rigovanov","avatar_url":"https://avatars-next.observableusercontent.com/6359e02dc30dad37dc8aeff508f64823d0f57f42e9b940688bdd1af508bb839c","tier":"starter_2024"},"version":72,"publish_version":72,"role":null,"authored":false,"authors":[{"type":"individual","id":"968f76daa2a26d11","login":"a1ip","name":"Philippe Rigovanov","avatar_url":"https://avatars-next.observableusercontent.com/6359e02dc30dad37dc8aeff508f64823d0f57f42e9b940688bdd1af508bb839c","tier":null}],"members":[{"type":"individual","id":"968f76daa2a26d11","login":"a1ip","name":"Philippe Rigovanov","avatar_url":"https://avatars-next.observableusercontent.com/6359e02dc30dad37dc8aeff508f64823d0f57f42e9b940688bdd1af508bb839c","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Derek Banas Statistics","cells":[{"id":2,"value":"md`# Derek Banas Statistics`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":0,"value":"md`

${Object.assign(await FileAttachment(\"title.jpg\").image(), {\n alt: 'Title slide',\n style: 'width: 100%; max-width: 1920px;'\n})}\n\n## Functions from [Derek Banas](https://twitter.com/newthinktank)'s [\"Statistics with Python\"](http://www.newthinktank.com/2020/07/statistics-every-day/) tutorial series`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"function mean(array) {\n const valSum = sum(array);\n return valSum / array.length;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"function median(array) {\n if (array.length % 2 === 0) {\n const j = Math.floor(array.length / 2);\n const i = j - 1;\n return (array[i] + array[j]) / 2;\n } else {\n const k = Math.floor(array.length / 2);\n return array[k];\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"function mode(array) {\n if (!array.length) return [];\n const frequencies = [];\n\n // Calculate frequencies\n array.forEach(e => {\n const frequenciesMember = frequencies.find(el => el.element === e);\n if (frequenciesMember) {\n frequencies[frequencies.indexOf(frequenciesMember)].frequency =\n frequenciesMember.frequency + 1;\n } else {\n frequencies.push({ element: e, frequency: 1 });\n }\n });\n\n // Create array of modes\n let maxFrequency = 0;\n let modes = [];\n frequencies.forEach(el => {\n if (el.frequency > maxFrequency) {\n modes = [].concat(el.element);\n maxFrequency = el.frequency;\n } else if (el.frequency === maxFrequency) modes.push(el.element);\n });\n\n // If every value appears same amount of times\n if (modes.length === frequencies.length) modes = [];\n return modes;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"function variance(array) {\n const meanVal = mean(array);\n const numerator = array.reduce((acc, curr) => acc + (curr - meanVal) ** 2, 0);\n const denominator = array.length - 1;\n return numerator / denominator;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"function standardDeviation(array) {\n return variance(array) ** .5;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"function coefficientOfVariation(array) {\n return standardDeviation(array) / mean(array);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"function covariance(array) {\n // Use a list comprehension to get all values\n // stored in the 1st & 2nd list\n const [list1, list2] = array;\n // Pass those lists to get their means\n const list1Mean = mean(list1),\n list2Mean = mean(list2);\n let numerator = 0;\n\n // We must have the same number of elements\n // in both lists\n if (list1.length === list2.length) {\n const denominator = list1.length - 1;\n for (let i = 0; i < list1.length; i++) {\n // Find (xi - x mean) * (yi - y mean)\n numerator += (list1[i] - list1Mean) * (list2[i] - list2Mean);\n }\n return numerator / denominator;\n } else {\n console.log(\n \"Error : You must have the same number of values in both lists\"\n );\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"function correlationCoefficient(array) {\n // Use a list comprehension to get all values\n // stored in the 1st & 2nd list\n const [list1, list2] = array;\n // Pass those lists to get their standard deviations\n const list1SD = standardDeviation(list1),\n list2SD = standardDeviation(list2);\n const denominator = list1SD * list2SD;\n let numerator = 0;\n // Get the covariance\n numerator = covariance(array);\n return numerator / denominator;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":46,"value":"function normalizeList(array) {\n const sdList = standardDeviation(array);\n return array.map(e => (e - mean(array)) / sdList);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"function standardError(array) {\n const sdList = standardDeviation(array);\n return sdList / Math.sqrt(array.length);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":57,"value":"function getZCode(zCodeArea, posZCodeMatrix = posZCodeList) {\n // Get index for first closest matching value in Z Table\n // Define what I'm looking for\n // Trim the 0 from the area because it isn't used in the\n // list of table values\n const zCodeAreaHead = zCodeArea.toFixed(3).slice(1);\n const regex = new RegExp(\"\\\\\" + zCodeAreaHead + \"\\\\d{2}\");\n // Iterate the multidimensional list\n for (let i = 0; i < posZCodeMatrix.length; i++) {\n for (let j = 0; j < posZCodeMatrix[0].length; j++) {\n if (posZCodeMatrix[i][j].search(regex) != -1) {\n // Combine column and row values into Z Code\n return .1 * parseFloat(i) + .01 * parseFloat(j);\n }\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"function getConfidenceInterval(sampleMean, confidence, sd, sampleSize) {\n // Formula (x,y) = x̄ ± Z(α/2) * σ/√n\n // x̄ : Sample Mean\n // α : Alpha (1 - Confidence)\n // σ : Standard Deviation\n // n : Sample Size\n const alphaVal = 1 - confidence;\n const criticalProbability = 1 - alphaVal / 2;\n const zCode = getZCode(criticalProbability);\n const marginOfError = zCode * (sd / Math.sqrt(sampleSize));\n const low = sampleMean - zCode * (sd / Math.sqrt(sampleSize));\n const high = sampleMean + zCode * (sd / Math.sqrt(sampleSize));\n return md`\nAlpha: **${alphaVal.toFixed(3)}**\n\nCritical Probability: **${criticalProbability.toFixed(3)}**\n\nZ Code: **${zCode.toFixed(3)}**\n\nMargin of Error: **${marginOfError.toFixed(3)}**\n\nConfidence Interval: **\\[${low.toFixed(2)}; ${high.toFixed(\n 2\n )}\\]**\n`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":64,"value":"tTableConfidence = [\n '0.1000',\n '0.0500',\n '0.0250',\n '0.0100',\n '0.0050',\n '0.0010',\n '0.0005'\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":69,"value":"breakPadKMs = [\n 58500,\n 58700,\n 62800,\n 57220,\n 62750,\n 59370,\n 57720,\n 60920,\n 61910,\n 59260,\n 63550,\n 60520,\n 58710,\n 57340,\n 60660,\n 57750,\n 60430,\n 60050,\n 62970,\n 58870\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":67,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":61,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"mdAppendix = md`## Appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"function sum(array) {\n return array.reduce(function(a, b) {\n return a + b;\n }, 0);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 32:"$31:body"