[{"data":1,"prerenderedAt":291},["ShallowReactive",2],{"guide:statistics-for-student-research":3},{"title":4,"description":5,"slug":6,"category":7,"stage":8,"readingMinutes":9,"updated":10,"featured":11,"order":12,"related":13,"resources":17,"tags":26,"body":31,"toc":279},"Use statistics that strengthen the work","Summarize variation, choose analysis from the study design, and separate visible, statistical, and practical importance.","statistics-for-student-research","Analyze","Doing the work",10,"2026-09-22",false,6,[14,15,16],"plan-your-first-study","make-clear-research-graphs","explain-why-research-matters",[18,22],{"title":19,"url":20,"note":21},"NIST\u002FSEMATECH e-Handbook of Statistical Methods","https:\u002F\u002Fwww.itl.nist.gov\u002Fdiv898\u002Fhandbook\u002F","Authoritative reference for distributions, uncertainty, testing, and experimental design.",{"title":23,"url":24,"note":25},"American Statistical Association — Statement on p-values","https:\u002F\u002Fwww.amstat.org\u002Fasa\u002Ffiles\u002Fpdfs\u002Fp-valuestatement.pdf","What p-values do and do not establish.",[27,28,29,30],"statistics","p-values","confidence intervals","effect size",{"type":32,"children":33},"root",[34,42,49,54,100,105,111,116,121,126,130,136,148,176,190,196,201,230,235,241,246,252,257,263,268],{"type":35,"tag":36,"props":37,"children":38},"element","p",{},[39],{"type":40,"value":41},"text","Statistics cannot repair a weak design. They help you describe the evidence, quantify uncertainty, and decide how far a conclusion can travel.",{"type":35,"tag":43,"props":44,"children":46},"h2",{"id":45},"start-with-the-data-you-actually-have",[47],{"type":40,"value":48},"Start with the data you actually have",{"type":35,"tag":36,"props":50,"children":51},{},[52],{"type":40,"value":53},"Plot the observations before choosing a test. Look for shape, clusters, outliers, missing values, ceiling\u002Ffloor effects, and changes in variability.",{"type":35,"tag":55,"props":56,"children":57},"ul",{},[58,72,83,95],{"type":35,"tag":59,"props":60,"children":61},"li",{},[62,64,70],{"type":40,"value":63},"Use the ",{"type":35,"tag":65,"props":66,"children":67},"strong",{},[68],{"type":40,"value":69},"mean",{"type":40,"value":71}," when the arithmetic average matches the question and extreme values are not distorting the summary.",{"type":35,"tag":59,"props":73,"children":74},{},[75,76,81],{"type":40,"value":63},{"type":35,"tag":65,"props":77,"children":78},{},[79],{"type":40,"value":80},"median",{"type":40,"value":82}," when the middle observation is more representative of a skewed distribution or when extremes are influential.",{"type":35,"tag":59,"props":84,"children":85},{},[86,88,93],{"type":40,"value":87},"Always pair center with ",{"type":35,"tag":65,"props":89,"children":90},{},[91],{"type":40,"value":92},"variability",{"type":40,"value":94},": range, interquartile range, standard deviation, or another measure appropriate to the data.",{"type":35,"tag":59,"props":96,"children":97},{},[98],{"type":40,"value":99},"Report the sample size and what counts as an independent sample.",{"type":35,"tag":36,"props":101,"children":102},{},[103],{"type":40,"value":104},"Three repeated readings from one sensor may show repeatability. They do not establish how the sensor performs across different devices, days, environments, or populations.",{"type":35,"tag":43,"props":106,"children":108},{"id":107},"show-uncertainty-honestly",[109],{"type":40,"value":110},"Show uncertainty honestly",{"type":35,"tag":36,"props":112,"children":113},{},[114],{"type":40,"value":115},"Error bars are not self-explanatory. State whether they show standard deviation, standard error, a confidence interval, or something else.",{"type":35,"tag":36,"props":117,"children":118},{},[119],{"type":40,"value":120},"A confidence interval estimates a range produced by a model and sampling procedure. It is not a guarantee that every future result will fall inside it, and it does not erase bias in the sample or measurement.",{"type":35,"tag":36,"props":122,"children":123},{},[124],{"type":40,"value":125},"Effect size answers “how much?” Statistical testing addresses how compatible the observed result is with a specified model or null hypothesis. Practical importance asks whether the size matters in the real system.",{"type":35,"tag":127,"props":128,"children":129},"statistics-meaning-diagram",{},[],{"type":35,"tag":43,"props":131,"children":133},{"id":132},"understand-what-a-p-value-is-not",[134],{"type":40,"value":135},"Understand what a p-value is not",{"type":35,"tag":36,"props":137,"children":138},{},[139,141,146],{"type":40,"value":140},"A p-value is calculated under assumptions, including a null model. It is ",{"type":35,"tag":65,"props":142,"children":143},{},[144],{"type":40,"value":145},"not",{"type":40,"value":147},":",{"type":35,"tag":55,"props":149,"children":150},{},[151,156,161,166,171],{"type":35,"tag":59,"props":152,"children":153},{},[154],{"type":40,"value":155},"the probability that your hypothesis is true;",{"type":35,"tag":59,"props":157,"children":158},{},[159],{"type":40,"value":160},"the probability that the result happened “by chance” in ordinary language;",{"type":35,"tag":59,"props":162,"children":163},{},[164],{"type":40,"value":165},"the size or importance of an effect;",{"type":35,"tag":59,"props":167,"children":168},{},[169],{"type":40,"value":170},"proof that the study is unbiased or reproducible;",{"type":35,"tag":59,"props":172,"children":173},{},[174],{"type":40,"value":175},"a substitute for showing the data and design.",{"type":35,"tag":36,"props":177,"children":178},{},[179,181,188],{"type":40,"value":180},"Do not turn ",{"type":35,"tag":182,"props":183,"children":185},"code",{"className":184},[],[186],{"type":40,"value":187},"p \u003C 0.05",{"type":40,"value":189}," into “proved.” Report the exact value when appropriate, the effect estimate, uncertainty, sample, and limitations.",{"type":35,"tag":43,"props":191,"children":193},{"id":192},"choose-analysis-from-the-design",[194],{"type":40,"value":195},"Choose analysis from the design",{"type":35,"tag":36,"props":197,"children":198},{},[199],{"type":40,"value":200},"Ask these questions before naming a test:",{"type":35,"tag":202,"props":203,"children":204},"ol",{},[205,210,215,220,225],{"type":35,"tag":59,"props":206,"children":207},{},[208],{"type":40,"value":209},"What type of outcome is measured: continuous, count, binary, category, time-to-event, rank, or something else?",{"type":35,"tag":59,"props":211,"children":212},{},[213],{"type":40,"value":214},"Are groups independent, paired, or repeatedly measured?",{"type":35,"tag":59,"props":216,"children":217},{},[218],{"type":40,"value":219},"How was the sample selected or assigned?",{"type":35,"tag":59,"props":221,"children":222},{},[223],{"type":40,"value":224},"What distributional and independence assumptions are plausible?",{"type":35,"tag":59,"props":226,"children":227},{},[228],{"type":40,"value":229},"Is the question a difference, association, prediction, estimation, or equivalence question?",{"type":35,"tag":36,"props":231,"children":232},{},[233],{"type":40,"value":234},"Consult a knowledgeable teacher or mentor when the analysis affects a major claim. An advanced-looking test is not better if its assumptions do not fit.",{"type":35,"tag":43,"props":236,"children":238},{"id":237},"correlation-is-not-causation",[239],{"type":40,"value":240},"Correlation is not causation",{"type":35,"tag":36,"props":242,"children":243},{},[244],{"type":40,"value":245},"An association may reflect reverse causation, selection, measurement error, or a third variable. Causal language requires a design and assumptions that justify it—not merely a small p-value or a machine-learning model with high accuracy.",{"type":35,"tag":43,"props":247,"children":249},{"id":248},"avoid-multiple-comparison-fishing",[250],{"type":40,"value":251},"Avoid multiple-comparison fishing",{"type":35,"tag":36,"props":253,"children":254},{},[255],{"type":40,"value":256},"If you test many outcomes, subgroups, time points, or model variants, some may look unusual by chance. Define a primary question, distinguish planned analyses from exploration, and disclose the full set of relevant comparisons. Do not hide trials or keep changing tests until one crosses a threshold.",{"type":35,"tag":43,"props":258,"children":260},{"id":259},"plan-sample-size-before-collection",[261],{"type":40,"value":262},"Plan sample size before collection",{"type":35,"tag":36,"props":264,"children":265},{},[266],{"type":40,"value":267},"Required sample size depends on the effect worth detecting, expected variability, design, acceptable uncertainty, and analysis—not a universal minimum. A small careful pilot can estimate procedure reliability, but broad claims from tiny samples are rarely justified.",{"type":35,"tag":269,"props":270,"children":273},"guide-callout",{"title":271,"tone":272},"Minimum reporting set","action",[274],{"type":35,"tag":36,"props":275,"children":276},{},[277],{"type":40,"value":278},"Show the observations when practical; define the sample and exclusions; report center, variability, effect size, uncertainty, and analysis assumptions; distinguish planned from exploratory work; keep unfavorable trials visible.",{"title":280,"searchDepth":281,"depth":281,"links":282},"",3,[283,285,286,287,288,289,290],{"id":45,"depth":284,"text":48},2,{"id":107,"depth":284,"text":110},{"id":132,"depth":284,"text":135},{"id":192,"depth":284,"text":195},{"id":237,"depth":284,"text":240},{"id":248,"depth":284,"text":251},{"id":259,"depth":284,"text":262},1790164659676]