29:null 2a:["$","title",null,{"children":"One-Way ANOVA Box Plot | ARussell-23 | Observable"}] 2f:T48f,# One-Way ANOVA Box Plot ## 3-5 Group Comparison This test is used to test the (null) hypothesis that three or more populations have equal means – in other words you can use it to tell if at least one of your populations has a statistically significant difference (p-value) in its average compared to the others. It is an extension of the T-Test to three or more groups and assumes that the populations have roughly equal variances. Unlike the T-Test, a significant result tells you that differences exist somewhere among the groups – but not which specific pairs differ. For that, a post-hoc test such as Tukey HSD is recommended. n=30 per group is a safe minimum. ## How to use this notebook 1. Create your CSV with exactly these three column names: * participant_id — a unique row identifier * group — your group label (any label you like, e.g. "Control", "Treatment 1", "Treatment 2") * score — the numeric value you are comparing 2. In the group settings below, make sure the group name fields exactly match the labels used in your CSV — including capitalization and spacing 3. Click the Upload CSV button below and select your file 30:T64d,// Creates the settings controls for the chart // The number of group name fields and color pickers matches the selected groupCount // All arrays are pre-populated up to 5 but only the active ones are shown viewof settings = Inputs.form({ // Y axis label — same as T-Test axisLabel: Inputs.text({ label: "Vertical axis label", value: "Score" }), // Group name fields — one per group // slice(0, groupCount) trims the array to only show fields for active groups // for example if groupCount is 3, only Group 1, Group 2, Group 3 appear ...Object.fromEntries( // creates an array of 5 possible group name inputs // then trims it to the number of active groups ["Group 1", "Group 2", "Group 3", "Group 4", "Group 5"] .slice(0, groupCount) .map((label, i) => [ // the key becomes groupName0, groupName1, groupName2 etc `groupName${i}`, Inputs.text({ label: `Group ${i + 1} name`, value: label }) ]) ), // Color pickers — one per group, trimmed to active groups // default colors are evenly spaced samples from d3.interpolateWarm // users should check their chosen colors at https://projects.susielu.com/viz-palette ...Object.fromEntries( [ // default colors for up to 5 groups ["#6d003a", "Group 1 color"], ["#cf4343", "Group 2 color"], ["#f4a340", "Group 3 color"], ["#c5e021", "Group 4 color"], ["#00c4b4", "Group 5 color"] ] .slice(0, groupCount) .map(([defaultColor, label], i) => [ `color${i}`, Inputs.color({ label, value: defaultColor }) ]) ) })31:T4c5,// Creates a variable named 'groups' — an array containing one entry per active group // Instead of separate groupA, groupB, groupC variables like the T-Test notebook, // we use a single array so the chart and stats cells work for 3, 4, or 5 groups // groups[0] is Group 1, groups[1] is Group 2, and so on groups = { // Build an array of group name strings from the settings cell // settings.groupName0, settings.groupName1 etc. are the values from the name text inputs // Array.from() creates an array of a given length // the second argument is a function that runs once per item to generate each value const groupNames = Array.from( { length: groupCount }, (_, i) => settings[`groupName${i}`] ); // For each group name, filter the full dataset down to just rows matching that name // This replaces the separate groupA, groupB, groupC filter cells from the T-Test notebook // .map() runs a function once per group name and collects the results into a new array return groupNames.map(name => // filter keeps only rows where the group column exactly matches this group's name // === means strictly equal to — same value and same type data.filter(d => d.group === name) ); }32:Tdd4,// Creates a variable named 'anova' containing the one-way ANOVA results // ANOVA asks: is the variance between group means larger than // the variance within groups? If yes, at least one group differs significantly anova = { // ---- STEP 1: COLLECT ALL SCORES ---- // Pull all scores from every active group into one flat array // .flat() collapses an array of arrays into a single array const allScores = groups.map(g => g.map(d => d.score)).flat(); // Calculate the grand mean — the average of all scores across all groups // this is the reference point that between-group variance is measured against const grandMean = d3.mean(allScores); // Total number of participants across all groups const N = allScores.length; // Number of groups const k = groupCount; // ---- STEP 2: CALCULATE BETWEEN-GROUP SUM OF SQUARES ---- // Between-group SS measures how much the group means differ from the grand mean // A large value means the groups are spread far apart from each other // reduce() accumulates a running total across all groups const ssBetween = groups.reduce((sum, group) => { // mean score for this group const groupMean = d3.mean(group.map(d => d.score)); // each group contributes: its size × (its mean - grand mean) squared // squaring removes negative values so differences don't cancel out return sum + group.length * Math.pow(groupMean - grandMean, 2); }, 0); // ---- STEP 3: CALCULATE WITHIN-GROUP SUM OF SQUARES ---- // Within-group SS measures how much individual scores vary around their own group mean // A large value means scores within groups are spread out — noisy data const ssWithin = groups.reduce((sum, group) => { const groupMean = d3.mean(group.map(d => d.score)); // each participant contributes: (their score - their group mean) squared return sum + group.reduce((s, d) => s + Math.pow(d.score - groupMean, 2), 0 ); }, 0); // ---- STEP 4: CALCULATE DEGREES OF FREEDOM ---- // Degrees of freedom roughly reflects the number of independent pieces of information // dfBetween = number of groups minus 1 const dfBetween = k - 1; // dfWithin = total participants minus number of groups const dfWithin = N - k; // ---- STEP 5: CALCULATE MEAN SQUARES ---- // Mean squares are sums of squares divided by their degrees of freedom // This normalizes the values so they can be fairly compared // msBetween = average variance between groups const msBetween = ssBetween / dfBetween; // msWithin = average variance within groups const msWithin = ssWithin / dfWithin; // ---- STEP 6: CALCULATE THE F-STATISTIC ---- // The F-statistic is the ratio of between-group variance to within-group variance // F = 1 means groups vary no more than you would expect by chance // F >> 1 means between-group differences are larger than within-group noise const F = msBetween / msWithin; // ---- STEP 7: CALCULATE THE P-VALUE ---- // jStat.centralF.cdf() gives the probability of getting an F value this small // subtracting from 1 gives the probability of getting this large or larger by chance // a small p-value means the result is unlikely to be due to chance const p = 1 - jStat.centralF.cdf(F, dfBetween, dfWithin); // ---- STEP 8: RETURN RESULTS ---- return { fStatistic: F.toFixed(3), dfBetween, dfWithin, pValue: p.toFixed(4), // significant if p is less than 0.05 significant: p < 0.05 ? "Significant (p < 0.05)" : "Not Significant (p ≥ 0.05)" }; }33:T4bf,// Creates a variable named 'summaryStats' for the summary table // maps over all active groups and calculates descriptive statistics for each // the number of rows in the table matches the number of active groups summaryStats = groups.map((group, i) => { // pull just the score numbers out of each row into a plain sorted array const sorted = group.map(d => d.score).sort(d3.ascending); // return one row of statistics per group return { // pulls the group name from the settings cell using the index i group: settings[`groupName${i}`], // number of participants in this group n: group.length, // average score rounded to 2 decimal places mean: d3.mean(sorted).toFixed(2), // standard deviation rounded to 2 decimal places standardDeviation: d3.deviation(sorted).toFixed(2), // lowest score in this group min: d3.min(sorted), // 25th percentile — lower edge of the box firstQuartile: d3.quantile(sorted, 0.25), // middle value — line inside the box median: d3.quantile(sorted, 0.5), // 75th percentile — upper edge of the box thirdQuartile: d3.quantile(sorted, 0.75), // highest score in this group max: d3.max(sorted) }; })34:T22d1,// Creates the complete ANOVA box plot chart as a single SVG // All elements are drawn inside one SVG so it exports cleanly to Illustrator chart = { // ---- STEP 1: FIXED DIMENSIONS ---- // Everything is fixed pixel values — no responsiveness, no layout shifts const svgWidth = 620; const svgHeight = 580; const marginTop = 80; const marginRight = 30; const marginBottom = 60; const marginLeft = 70; const plotWidth = svgWidth - marginLeft - marginRight; const plotHeight = svgHeight - marginTop - marginBottom; // ---- STEP 2: CALCULATE DYNAMIC X POSITIONS ---- // Instead of fixed xA and xB, we calculate one x position per group // groups are spaced evenly across the plot width // Array.from() creates an array with one entry per group const xPositions = Array.from( { length: groupCount }, // i is the index (0, 1, 2...) // we divide the plot into (groupCount + 1) equal sections // and place each group center at section i+1 // this keeps equal space before the first group and after the last (_, i) => marginLeft + plotWidth * ((i + 1) / (groupCount + 1)) ); // Box half-width shrinks as more groups are added so boxes don't overlap // with 3 groups boxes are wider, with 5 groups they are narrower const boxHalfWidth = (plotWidth / (groupCount + 1)) * 0.35; // Whisker cap half-width — 80% of box half-width const capHalfWidth = boxHalfWidth * 0.8; // ---- STEP 3: Y SCALE ---- // Identical to T-Test — converts a score value to a pixel position const y = value => marginTop + plotHeight * (1 - (value - yMin) / (yMax - yMin)); // ---- STEP 4: CREATE THE SVG ELEMENT ---- const svg = d3.create("svg") .attr("width", svgWidth) .attr("height", svgHeight) .style("background", "white") .style("font-family", "sans-serif") .style("font-size", "12px"); // ---- STEP 5: DRAW GRID LINES ---- // Identical to T-Test d3.ticks(yMin, yMax, 8).forEach(tickValue => { svg.append("line") .attr("x1", marginLeft) .attr("x2", marginLeft + plotWidth) .attr("y1", y(tickValue)) .attr("y2", y(tickValue)) .attr("stroke", "#e0e0e0") .attr("stroke-width", 1); }); // ---- STEP 6: DRAW Y AXIS ---- // Identical to T-Test // vertical axis line svg.append("line") .attr("x1", marginLeft).attr("y1", marginTop) .attr("x2", marginLeft).attr("y2", marginTop + plotHeight) .attr("stroke", "#333") .attr("stroke-width", 1); // y axis ticks and labels d3.ticks(yMin, yMax, 8).forEach(tickValue => { svg.append("line") .attr("x1", marginLeft - 5) .attr("x2", marginLeft) .attr("y1", y(tickValue)) .attr("y2", y(tickValue)) .attr("stroke", "#333") .attr("stroke-width", 1); svg.append("text") .attr("x", marginLeft - 8) .attr("y", y(tickValue)) .attr("dominant-baseline", "middle") .attr("text-anchor", "end") .attr("fill", "#333") .text(tickValue); }); // rotated y axis label svg.append("text") .attr("transform", `rotate(-90) translate(${-(marginTop + plotHeight / 2)}, ${marginLeft - 45})`) .attr("text-anchor", "middle") .attr("fill", "#333") .attr("font-size", "13px") .text(settings.axisLabel); // ---- STEP 7: DRAW X AXIS ---- // horizontal axis line svg.append("line") .attr("x1", marginLeft) .attr("x2", marginLeft + plotWidth) .attr("y1", marginTop + plotHeight) .attr("y2", marginTop + plotHeight) .attr("stroke", "#333") .attr("stroke-width", 1); // group labels below the axis — one per active group // forEach loops over xPositions, running once per group xPositions.forEach((xCenter, i) => { svg.append("text") .attr("x", xCenter) .attr("y", marginTop + plotHeight + 25) .attr("text-anchor", "middle") .attr("fill", "#333") // pulls the group name from settings using the index i .text(settings[`groupName${i}`]); }); // x axis title svg.append("text") .attr("x", marginLeft + plotWidth / 2) .attr("y", svgHeight - 10) .attr("text-anchor", "middle") .attr("fill", "#333") .attr("font-size", "13px") .text("Group"); // ---- STEP 8: DRAW BOX PLOTS ---- // Loop over all active groups and draw each one // forEach runs once per group, passing the x center position and index i xPositions.forEach((xCenter, i) => { // get the statistics and color for this group const s = stats[i]; // pulls the color from settings using the index i const color = settings[`color${i}`]; // WHISKER LINE — vertical line from lower to upper whisker svg.append("line") .attr("x1", xCenter).attr("x2", xCenter) .attr("y1", y(s.lowerWhisker)) .attr("y2", y(s.upperWhisker)) .attr("stroke", color) .attr("stroke-width", 2.5); // LOWER WHISKER CAP svg.append("line") .attr("x1", xCenter - capHalfWidth) .attr("x2", xCenter + capHalfWidth) .attr("y1", y(s.lowerWhisker)) .attr("y2", y(s.lowerWhisker)) .attr("stroke", color) .attr("stroke-width", 2.5); // UPPER WHISKER CAP svg.append("line") .attr("x1", xCenter - capHalfWidth) .attr("x2", xCenter + capHalfWidth) .attr("y1", y(s.upperWhisker)) .attr("y2", y(s.upperWhisker)) .attr("stroke", color) .attr("stroke-width", 2.5); // BOX — rectangle from Q1 to Q3 svg.append("rect") .attr("x", xCenter - boxHalfWidth) .attr("y", y(s.q3)) .attr("width", boxHalfWidth * 2) .attr("height", y(s.q1) - y(s.q3)) .attr("fill", color) .attr("fill-opacity", 0.3) .attr("stroke", color) .attr("stroke-width", 1.5); // MEDIAN LINE svg.append("line") .attr("x1", xCenter - boxHalfWidth) .attr("x2", xCenter + boxHalfWidth) .attr("y1", y(s.median)) .attr("y2", y(s.median)) .attr("stroke", color) .attr("stroke-width", 2.5); // MEAN SQUARE — open square at the mean value const squareSize = 10; svg.append("rect") .attr("x", xCenter - squareSize / 2) .attr("y", y(s.mean) - squareSize / 2) .attr("width", squareSize) .attr("height", squareSize) .attr("fill", "none") .attr("stroke", color) .attr("stroke-width", 2); }); // ---- STEP 9: DRAW DATA POINTS ---- // Loop over every row in the dataset and draw a solid black dot // The dot is placed at the x position of its group plus a random jitter data.forEach(d => { // find which group index this row belongs to by matching the group name // findIndex returns the position of the first match in the array const i = Array.from( { length: groupCount }, (_, i) => settings[`groupName${i}`] ).findIndex(name => name === d.group); // if the group name doesn't match any active group, skip this row if (i === -1) return; // random horizontal jitter — same as T-Test const jitter = (Math.random() - 0.5) * 24; svg.append("circle") .attr("cx", xPositions[i] + jitter) .attr("cy", y(d.score)) .attr("r", 3) .attr("fill", "black") .attr("fill-opacity", 1); }); // ---- STEP 10: DRAW SIGNIFICANCE BAR ---- // For ANOVA the bracket spans all groups — from the first to the last // Unlike T-Test which connects two specific groups, // ANOVA only tells us that differences exist somewhere among all groups // so the bracket spans the full width from group 1 to the last group // x position of the first group const x1 = xPositions[0]; // x position of the last group const x2 = xPositions[xPositions.length - 1]; // y position of the horizontal bracket line const barY = 28; // y position of the vertical ticks dropping down from the bracket const tickY = 40; // horizontal bracket line spanning all groups svg.append("line") .attr("x1", x1).attr("y1", barY) .attr("x2", x2).attr("y2", barY) .attr("stroke", "black") .attr("stroke-width", 1.5); // left vertical tick svg.append("line") .attr("x1", x1).attr("y1", barY) .attr("x2", x1).attr("y2", tickY) .attr("stroke", "black") .attr("stroke-width", 1.5); // right vertical tick svg.append("line") .attr("x1", x2).attr("y1", barY) .attr("x2", x2).attr("y2", tickY) .attr("stroke", "black") .attr("stroke-width", 1.5); // p-value label centered above the bracket // handles the case where p rounds to 0.0000 by showing p < 0.0001 instead const pLabel = anova.pValue === "0.0000" ? "p < 0.0001" : `p = ${anova.pValue}`; svg.append("text") .attr("x", (x1 + x2) / 2) .attr("y", barY - 6) .attr("text-anchor", "middle") .attr("font-size", "13px") .attr("fill", "black") .text(`${pLabel} — ${anova.significant}`); // ---- STEP 11: RETURN THE SVG ---- return svg.node(); }35:T648,// ---- CAPTION GENERATOR ---- // Builds a formatted caption from the chart settings and ANOVA results // Updates automatically whenever settings or data change caption = { // Determine whether the groups show a significant difference const significant = parseFloat(anova.pValue) < 0.05; // Build a comma-separated list of all active group names // slice(0, -1) takes all but the last name // join(", ") connects them with commas // then we add "and" before the last name const groupNames = Array.from({ length: groupCount }, (_, i) => settings[`groupName${i}`]); const groupList = groupNames.slice(0, -1).join(", ") + " and " + groupNames[groupNames.length - 1]; // significance phrase const showPhrase = significant ? "show" : "do not show"; // handle p value that rounds to 0.0000 const pDisplay = anova.pValue === "0.0000" ? "p < 0.0001" : `p = ${anova.pValue}`; // bold opening sentence const boldSentence = `${groupList} groups ${showPhrase} a significant difference when assessed based on ${settings.axisLabel} (${pDisplay}).`; // regular body sentence const regularSentence = `Box plot of ${settings.axisLabel} scores across ${groupCount} groups. Box indicates first through third quartile with median line, whiskers are 1.5 IQR, open square represents mean. Analysis of statistical significance at the 0.05 level was determined through a one-way ANOVA.`; return html`

${boldSentence} ${regularSentence}

`; }36:Tcaf,// ---- ALT TEXT GENERATOR ---- // Builds detailed alt text following a consistent formula // Updates automatically whenever settings, data, or test results change altText = { // y axis range and increment — identical to T-Test // d3.ticks() generates the same tick values that appear on the y axis const ticks = d3.ticks(yMin, yMax, 8); // the lowest tick value shown on the y axis const yAxisMin = ticks[0]; // the highest tick value shown on the y axis const yAxisMax = ticks[ticks.length - 1]; // the increment between ticks — subtract first tick from second to get the step size const yAxisIncrement = ticks[1] - ticks[0]; // build an array of active group names from the settings cell const groupNames = Array.from({ length: groupCount }, (_, i) => settings[`groupName${i}`]); // comma separated list of group names for the opening sentence // slice(0, -1) takes all but the last, join connects with commas // then we add "and" before the final name const groupList = groupNames.slice(0, -1).join(", ") + " and " + groupNames[groupNames.length - 1]; // handle p value that rounds to 0.0000 — show < 0.0001 instead const pDisplay = anova.pValue === "0.0000" ? "< 0.0001" : anova.pValue; // build outlier phrase for each group // map() runs once per group and returns a descriptive phrase // .toFixed(1) rounds outlier values to 1 decimal place for clean reading const outlierPhrases = groups.map((group, i) => { const s = stats[i]; // filter keeps only points that fall outside the whisker range const outliers = group.filter(d => d.score < s.lowerWhisker || d.score > s.upperWhisker); return outliers.length === 0 ? "No outliers are present." : `${outliers.length} outlier${outliers.length > 1 ? "s are" : " is"} present at ${outliers.map(d => d.score.toFixed(1)).join(", ")}.`; }); // build one paragraph per group // .toFixed(1) rounds each stat to 1 decimal place for clean reading const groupParagraphs = groupNames.map((name, i) => { const s = stats[i]; return `${name} has a box indicating first through third quartile spanning from ${s.q1.toFixed(1)} to ${s.q3.toFixed(1)}, with a median line at ${s.median.toFixed(1)}. The whiskers, representing 1.5 IQR, span from ${s.lowerWhisker.toFixed(1)} to ${s.upperWhisker.toFixed(1)}. ${outlierPhrases[i]}`; }).join("\n\n"); // build the full alt text string // template literals with backticks allow multi-line strings and variable insertion const text = `Box plot showing ${settings.axisLabel} scores across ${groupCount} groups with associated p value. The groups are: ${groupList}. The y-axis is labelled ${settings.axisLabel} and ranges from ${yAxisMin} to ${yAxisMax} in increments of ${yAxisIncrement}. ${groupParagraphs} The p-value equals ${pDisplay}.`; // render the alt text in a textarea so it is easy to select and copy // into a presentation or document return html`

Alt text:

`; }37:T119c,// ---- TUKEY HSD POST-HOC TEST ---- // Calculates Tukey HSD for every possible pair of active groups // Returns an array of results — one row per pair — for display in the table below tukey = { // ---- STEP 1: RECALCULATE WITHIN-GROUP MEAN SQUARE ---- // msWithin is the average variance within groups — our measure of noise // we recalculate it here so this cell is self-contained and doesn't depend on the anova cell internals const N = data.length; const k = groupCount; // within-group sum of squares — how much scores vary around their own group mean const ssWithin = groups.reduce((sum, group) => { const groupMean = d3.mean(group.map(d => d.score)); return sum + group.reduce((s, d) => s + Math.pow(d.score - groupMean, 2), 0); }, 0); // degrees of freedom within groups = total participants minus number of groups const dfWithin = N - k; // within-group mean square = ssWithin divided by its degrees of freedom const msWithin = ssWithin / dfWithin; // ---- STEP 2: CRITICAL Q VALUE LOOKUP TABLE ---- // The critical q value is the threshold the q statistic must exceed to be significant // These values come from the Studentized Range Distribution table at p=0.05 // rows are number of groups (k), columns are degrees of freedom within groups // we use the largest df value that does not exceed our actual dfWithin const qTable = { 3: { 5: 4.60, 6: 4.34, 7: 4.16, 8: 4.04, 9: 3.95, 10: 3.88, 12: 3.77, 15: 3.67, 20: 3.58, 30: 3.49, 40: 3.44, 60: 3.40, 120: 3.36, 1000: 3.31 }, 4: { 5: 5.22, 6: 4.90, 7: 4.68, 8: 4.53, 9: 4.41, 10: 4.33, 12: 4.20, 15: 4.08, 20: 3.96, 30: 3.85, 40: 3.79, 60: 3.74, 120: 3.68, 1000: 3.63 }, 5: { 5: 5.67, 6: 5.30, 7: 5.06, 8: 4.89, 9: 4.76, 10: 4.65, 12: 4.51, 15: 4.37, 20: 4.23, 30: 4.10, 40: 4.04, 60: 3.98, 120: 3.92, 1000: 3.86 } }; // find the closest df entry that does not exceed our actual dfWithin // Object.keys() gets all the df values from the table for this k // .map(Number) converts them from strings to numbers // .filter() keeps only values less than or equal to our actual dfWithin // .at(-1) takes the last (largest) value that still doesn't exceed dfWithin const dfKeys = Object.keys(qTable[k]).map(Number).filter(d => d <= dfWithin); // if no df value is small enough, fall back to the smallest available const dfLookup = dfKeys.length > 0 ? dfKeys.at(-1) : Object.keys(qTable[k]).map(Number)[0]; // look up the critical q value for this k and df combination const qCritical = qTable[k][dfLookup]; // ---- STEP 3: COMPARE EVERY PAIR OF GROUPS ---- // the number of pairs = k * (k-1) / 2 // with 3 groups: 3 pairs, with 4 groups: 6 pairs, with 5 groups: 10 pairs const results = []; // outer loop goes from group 0 to the second-to-last group // inner loop goes from the group after i to the last group // this ensures each pair is only compared once for (let i = 0; i < groupCount; i++) { for (let j = i + 1; j < groupCount; j++) { // get the scores and sample size for each group in this pair const scoresI = groups[i].map(d => d.score); const scoresJ = groups[j].map(d => d.score); const nI = scoresI.length; const nJ = scoresJ.length; // mean difference between the two groups — always positive using Math.abs() const meanDiff = Math.abs(d3.mean(scoresI) - d3.mean(scoresJ)); // standard error for this pair // this formula handles unequal sample sizes between groups const se = Math.sqrt(msWithin / 2 * (1 / nI + 1 / nJ)); // q statistic — the Tukey test statistic for this pair // larger q means a bigger difference relative to within-group noise const q = meanDiff / se; // this pair is significant if q exceeds the critical value from the table const significant = q > qCritical; // add this pair's results to the results array results.push({ // group names pulled from settings using the index comparison: `${settings[`groupName${i}`]} vs ${settings[`groupName${j}`]}`, // mean difference rounded to 2 decimal places meanDifference: meanDiff.toFixed(2), // q statistic rounded to 3 decimal places qStatistic: q.toFixed(3), // critical q value for reference — same for all pairs qCritical: qCritical.toFixed(3), // significance label result: significant ? "Significant" : "Not Significant" }); } } return results; }38:[{"id":"7d13a25889d8ec7a9dc71cf0aa5b801f2b5054993bafcea7f7eec88ee450d3763f20b7981072340c8ac357104c467d9ccd58b033860995e1fbe4a2ce04d499e0","href":"https://static.observableusercontent.com/files/7d13a25889d8ec7a9dc71cf0aa5b801f2b5054993bafcea7f7eec88ee450d3763f20b7981072340c8ac357104c467d9ccd58b033860995e1fbe4a2ce04d499e0","name":"anova_data.csv","type":"text/csv","lastModified":1782488845486.847,"size":2620}] 2d:{"id":"d987aae82836a847","slug":null,"title":"One-Way ANOVA Box Plot","thumbnail":"09838e7ac5edcfbd231fcbf9b9bce3b47a63252e787f4a214ef1bd50ff85aece","access_level":"public","create_time":"$D2026-06-26T15:42:18.189Z","update_time":"$D2026-06-26T17:09:14.765Z","view_time":null,"first_public_time":"$D2026-06-26T15:42:18.189Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"e6c86544478da089","login":"arussell-23","name":"ARussell-23","avatar_url":"https://avatars-next.observableusercontent.com/8afab74a991063029ac3160ea38fecac0cb44f2bedfed2b819070571df7c84f5","tier":"starter_2024"},"version":105,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"20e4cf6ac4650492","login":"arussell-23","name":"ARussell-23","avatar_url":"https://avatars-next.observableusercontent.com/8afab74a991063029ac3160ea38fecac0cb44f2bedfed2b819070571df7c84f5","tier":null}],"members":[{"type":"individual","id":"20e4cf6ac4650492","login":"arussell-23","name":"ARussell-23","avatar_url":"https://avatars-next.observableusercontent.com/8afab74a991063029ac3160ea38fecac0cb44f2bedfed2b819070571df7c84f5","tier":null,"role":"editor"},{"type":"team","id":"e6c86544478da089","login":"arussell-23","name":"ARussell-23","avatar_url":"https://avatars-next.observableusercontent.com/8afab74a991063029ac3160ea38fecac0cb44f2bedfed2b819070571df7c84f5","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"One-Way ANOVA Box Plot","cells":[{"id":0,"value":"$2f","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":103,"value":"viewof csvFile = Inputs.file({ label: \"Upload CSV\", accept: \".csv\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"data = {\n if (csvFile === null) return [];\n const text = await csvFile.text();\n return d3.csvParse(text, d3.autoType);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"// Creates a dropdown selector for the number of groups\n// viewof exposes both the widget and its current value to other cells\n// other cells reference 'groupCount' to know how many groups are active\n// when the user changes this, every cell that depends on it automatically reruns\nviewof groupCount = Inputs.select(\n // the options available in the dropdown\n [3, 4, 5],\n {\n // the label displayed next to the dropdown\n label: \"Number of groups\",\n // the default selection when the notebook first loads\n value: 3\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"// Creates a variable named 'stats' — an array containing box plot statistics for each group\n// stats[0] is Group 1's statistics, stats[1] is Group 2's, and so on\n// This replaces the separate statsA, statsB, statsC cells from the T-Test notebook\nstats = groups.map(group => {\n\n // pull just the score numbers out of each row into a plain array\n const sorted = group.map(d => d.score).sort(d3.ascending);\n\n // calculate quartiles\n const q1 = d3.quantile(sorted, 0.25);\n const q3 = d3.quantile(sorted, 0.75);\n // IQR = interquartile range = distance between Q1 and Q3\n const iqr = q3 - q1;\n\n // whisker ends stop at the furthest real data point within 1.5x IQR\n const lowerWhisker = d3.min(sorted.filter(v => v >= q1 - 1.5 * iqr));\n const upperWhisker = d3.max(sorted.filter(v => v <= q3 + 1.5 * iqr));\n\n // return all statistics for this group as a single object\n return {\n q1,\n q3,\n median: d3.quantile(sorted, 0.5),\n mean: d3.mean(sorted),\n lowerWhisker,\n upperWhisker\n };\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"// Calculates the minimum y axis value with a 10% buffer below the data\n// pulled out into its own cell so both the chart and altText cells can reference it\nyMin = {\n const allScores = data.map(d => d.score);\n const dataMin = d3.min(allScores);\n const dataMax = d3.max(allScores);\n const buffer = (dataMax - dataMin) * 0.10;\n return dataMin - buffer;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"// Calculates the maximum y axis value with a 10% buffer above the data\n// pulled out into its own cell so both the chart and altText cells can reference it\nyMax = {\n const allScores = data.map(d => d.score);\n const dataMin = d3.min(allScores);\n const dataMax = d3.max(allScores);\n const buffer = (dataMax - dataMin) * 0.10;\n return dataMax + buffer;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"// Imports jStat, a statistics library, from the web\n// jStat handles the complex probability math needed to calculate the p-value\njStat = require(\"jstat@1.9.6/dist/jstat.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"// Displays the summary statistics as a readable table\nInputs.table(summaryStats)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":43,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":49,"value":"// Creates a download button for the chart\n// Downloads the chart as a single clean SVG file for Illustrator or Figma\nDOM.download(\n () => new Blob(\n [new XMLSerializer().serializeToString(chart)],\n { type: \"image/svg+xml\" }\n ),\n \"anova_chart.svg\",\n \"Download chart as SVG\"\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":65,"value":"## Tukey HSD Post-Hoc Test\n\nA significant ANOVA result tells you that differences exist *somewhere* among the groups – but not which specific pairs differ. The Tukey HSD (Honestly Significant Difference) test answers that question by comparing every possible pair of groups against a critical threshold value.\n\nIf the q statistic for a pair exceeds the critical value, that pair is considered significantly different at the 0.05 level.\n\nSignificance between specific pairs can be represented on the chart with asterisks or additional significance bars between groups. This can be done by opening the downloaded SVG in a vector editing program such as Adobe Illustrator or Figma.\n\n**Only interpret these results if the ANOVA result is significant.**","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":51,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"// Displays the Tukey HSD results as a readable table\n// Each row is one pair of groups\n// Note: only interpret these results if the ANOVA result is significant\nInputs.table(tukey)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W38","stdlib":"1","titling":"auto"}} 2e:"$2d:body"