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It covers how to interpret sample statistics versus population parameters, key measurement terms such as mean, median, standard deviation, and correlation, and the dangers of taking data at face value. The material explains representativeness, bias, limitations, correlation versus causation, and guidance for common data “slicing” metrics like proportions, percentiles, percent change, percentage points, quantiles, and quartiles.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/sanders-analytics-intro-to-statistics-cheat-sheets-2025/571680/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/sanders-analytics-intro-to-statistics-cheat-sheets-2025/571680.png","ImageObject",442,249,{"name":88,"@type":89},"GGG","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-21","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":47},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are the core questions to ask about the data before interpreting results?","Question",{"text":108,"@type":109},"The cheatsheets emphasize understanding available variables, the data’s origin story (observational, experimental, aggregated, or survey), representativeness and sampling bias, missing measurements, and whether the dataset measures the intended construct.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How should sample size adequacy be evaluated?",{"text":113,"@type":109},"A general rule of thumb is to look for at least 1000 representative cases, and to consider the statistical power of the tests used, aiming for at least 0.8 or 0.9 when reported.",{"name":115,"@type":106,"acceptedAnswer":116},"What is the difference between correlation and causation?",{"text":117,"@type":109},"Correlation indicates an association between variables but does not establish which variable causes the change. 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Sanders, Ph. D.  \n[SandersAnalytics.org](SandersAnalytics.org)[ ](SandersAnalytics.org)+1 424-256-5960  \n+33 07 80 83 18 20  \nTable of Contents  \nSymbols & Questions to Ask of Data  \nFoundations & Fundamentals  \nVisualizations  \nHypothesis Testing  \nGoing Deeper  \n1  \n3  \n7  \n11  \n12  \nSymbol Cheat Sheet  \nPage 1  \n| Sample statistic | Population parameter | Description |\n| --- | --- | --- |\n| n | N | number of members of sample or population |\n|  “x-bar” | μ “mu” or  | mean |\n| M or Med or  “x-tilde” | (none) | median |\n| s | σ “sigma” or  | standard deviation For variance, apply a squared symbol (s² or σ²) . |\n| r | ρ “rho” | coefficient of linear correlation |\n| ̂p “p-hat” | p | proportion |\n\n\n| Mathematical Symbol |  | Description |\n| --- | --- | --- |\n| Greek letter capital sigma |  | Sum |\n| | Greek letter chi | Chi-square (hypothesis test of independence) |\n| 􁹂 Greek letter alpha |  | In statistics, alpha refers to the significance level (see page 12) |\n| |x| |  | Absolute value : |-5| = |5| = 5\u003Cbr>The distance between that value and the origin (or zero) along the real number line. |\n\nQuestions to ask about the data  \nDo not take data at face value  \nPage 2  \nEverything depends on the quality of the data, so you need to understand it in order to evaluate the quality of the study.  \nAll data is created/generated and, therefore, is the result of subjective decisions. It is incumbent upon us to understand the biases, objectives, and values of those who created the datasets with which we work as far as possible.  \nQuestions  \n1. What information is available in the data?  \na. What variables are present?  \nb. How are the variables defined? Do they cover all the possible outcomes that need to be considered?  \nc. What values do they take on and are these reasonable?  \n2. What is the data origin story? [Ultimately, is the data reliable?]  \na. Is the underlying data observational, experimental, aggregated, or survey response data?  \nb. Who collected the data?  \nc. How was it collected?  \n3. Is the data representative?  \na. Is there sampling bias?  \nb. What did the authors do with outliers?  \n4. What data is missing or was not collected?  \na. How did the research team handle missing values?  \nb. Did they overlook data that should have been collected?  \n5. Do the data measure what the research team wanted to measure?  \n6. Are there any identifiable ideological effects in the dataset construction?  \na. If your dataset were your only source, what information would be left out?  \nb. Would the results be biased in any way?  \n7. Does the data need to be transformed to be useful?  \nFoundations Sample Size  \nPage 3  \n population: the complete set of individuals, events, or objects that are the focus of a study  \n sample: a representative subset of a population  \n Is the sample size large enough? The general rule of thumb is at least 1000 cases that are representative of the population.  \n Look at the statistical power of the tests used (if reported) . The power should be at least 0.8 or 0.9.(Indicates that the sample size is large enough and that the results are trustworthy.)  \nEvaluating Data  \n What variables are present, absent, and how are they defined? Which are independent and dependent?  \n How was the data set constructed?  \n Is generalizing from this sample to the population valid?  \n Representativeness: composition of the sample mirrors the proportions seen in the general population. Representativeness is necessary so that reliable inferences may be made from the specific sample to the population.  \n Is the data biased? Bias occurs when a sample is not representative of the target population. A related type of bias occurs when study participants do not have an equally likely chance of being placed in each of the study’s groups, known as random sampling  \n Limitations: There are limitations in every study, so be sure to look for them and briefly report on t","cbCaipZ8q6MYxlcp","https://ap.wps.com/l/cbCaipZ8q6MYxlcp","pdf",2154428,"English","# Table of Contents\n## Symbols & Questions to Ask of Data\n## Foundations & Fundamentals\n## Visualizations\n## Hypothesis Testing\n## Going Deeper\n# Symbol Cheat Sheet\n## Questions to ask about the data\n## Foundations Sample Size\n## Evaluating Data\n## Correlation vs. Causation\n## Percentages & Other Ways of Slicing Data","[{\"question\":\"What are the core questions to ask about the data before interpreting results?\",\"answer\":\"The cheatsheets emphasize understanding available variables, the data’s origin story (observational, experimental, aggregated, or survey), representativeness and sampling bias, missing measurements, and whether the dataset measures the intended construct.\"},{\"question\":\"How should sample size adequacy be evaluated?\",\"answer\":\"A general rule of thumb is to look for at least 1000 representative cases, and to consider the statistical power of the tests used, aiming for at least 0.8 or 0.9 when reported.\"},{\"question\":\"What is the difference between correlation and causation?\",\"answer\":\"Correlation indicates an association between variables but does not establish which variable causes the change. The document warns about confounding factors and notes that rigorous experimental designs can suggest causality but are rarely conclusive proof.\"}]","Sanders Analytics - Intro to Statistics - Cheat Sheets - 2025 | PDF",1791923096,6]