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统计学学习工具包

学习路线图、概率、概率分布、抽样分布、假设检验、置信区间、公式表、方法卡片、检验选择指南、练习题集、错题本和记忆卡片。

第 1 步

规划

  1. Statistics Learning Roadmap Template (Diagnostic and 12-Week Plan)

    完整

    Statistics curriculum map in three levels – prerequisite graph, template per topic, can-do targets, 20-question diagnostic with routing, 12-week spaced and interleaved plan, progress tracker

    GAISE College Report (ASA 2016, summarised); Dunlosky et al. (2013); Weinstein and Sumeracki (2018); Cepeda et al. (2006); Rohrer and Taylor (2007)
第 2 步

学习

  1. Probability Basics Concept Card Template (Statistics, R and Python)

    完整

    Probability concept card: axioms, addition and multiplication rules, conditional probability, independence, total probability, Bayes' theorem with a natural-frequency tree, counting, expectation and variance, seeded R and Python simulations

    Kolmogorov (1933) axioms; Bayes (1763); Gigerenzer and Hoffrage (1995) natural frequencies; NIST/SEMATECH e-Handbook 1.3.6; GAISE College Report (name)

  2. Probability Distributions Reference Sheet Template (Statistics, R and Python)

    完整

    Distributions reference: 16 discrete and continuous distributions with pmf/pdf, support, mean, variance and uses, a relationship map, R d/p/q/r and scipy.stats equivalents with parameterisation traps, verified lookups and a which-distribution self-test

    NIST/SEMATECH e-Handbook 1.3.6; R stats and SciPy documentation; Student (1908); Weibull (1951)

  3. Sampling Distributions and CLT Concept Card Template (Statistics, R and Python)

    完整

    Sampling distributions concept card: population vs sample, standard error, Central Limit Theorem and when n is large enough, SE of a proportion and a difference in means, origin of the t distribution, seeded R and Python simulation with a Vega-Lite chart

    Student (1908); Central Limit Theorem (Laplace 1812); NIST/SEMATECH e-Handbook; GAISE College Report (name)

  4. Hypothesis Testing Concept Card Template (Statistics, R and Python)

    完整

    Logic of significance testing: H0/H1, p-values, Type I/II errors, power, one- vs two-sided, TOST, Bonferroni, Holm and Benjamini-Hochberg, ASA statement

    Fisher (1925); Neyman and Pearson (1933); Holm (1979); Benjamini and Hochberg (1995); ASA Statement on P-Values (2016); NIST/SEMATECH e-Handbook ch. 7

  5. Confidence Intervals Concept Card Template (Statistics, R and Python)

    完整

    Meaning and construction of confidence intervals: z and t for means, Wald vs Wilson for proportions, Welch difference, width vs n, link to tests, bootstrap preview, coverage simulation

    Neyman (1937); Wilson (1927); Welch (1947); Efron (1979); Brown, Cai and DasGupta (2001); NIST/SEMATECH e-Handbook

  6. Statistics Formula Sheet Template (KaTeX, Verified in R and Python)

    完整

    Course-wide statistics formula sheet in KaTeX – descriptive, probability, SEs, CIs, tests, ANOVA, regression, GLM links, effect sizes, power, Bayes – with use-when and common-slip notes

    NIST/SEMATECH e-Handbook of Statistical Methods; Welch (1947); Wilson (1927); Nelder and Wedderburn (1972); Cohen (1988); GAISE College Report (ASA 2016, name)
第 3 步

练习

  1. Statistical Test Selector Template (Statistics, Decision Trees, R and Python)

    完整

    Choosing a statistical test or model: five questions, three decision trees and master tables with effect sizes, R and Python functions

    NIST/SEMATECH e-Handbook of Statistical Methods; Student (1908); Welch (1947); Mann and Whitney (1947); McNemar (1947); Nelder and Wedderburn (1972); ASA p-value statement (2016, name)

  2. t-Tests Method Card Template (Statistics, R and Python)

    完整

    One-sample, Welch and pooled independent, and paired t-tests with hand calculation, R and Python code, Hedges' g and APA-style reporting

    Student (1908); Welch (1947); Satterthwaite (1946); Hedges (1981); NIST/SEMATECH e-Handbook 1.3.5.3; APA JARS-Quant (name)

  3. Proportion Tests Method Card Template (Statistics, R and Python)

    完整

    One- and two-proportion tests (exact binomial, z, 2x2 chi-square link), Wilson and Newcombe intervals, risk difference, relative risk and odds ratio, A/B test framing

    Wilson (1927); Clopper and Pearson (1934); Yates (1934); Newcombe (1998); Agresti and Coull (1998); NIST/SEMATECH e-Handbook; APA JARS-Quant (name)

  4. Contingency Tables Method Card Template (Statistics, R and Python)

    完整

    Chi-square goodness of fit and independence, standardised residuals, Yates defaults, Fisher's exact, McNemar, Cramér's V, phi, odds ratio and relative risk, Simpson's paradox

    Pearson (1900); Fisher (1922, 1935); Yates (1934); McNemar (1947); Cramér (1946); Simpson (1951); NIST/SEMATECH e-Handbook 1.3.5.15

  5. One-Way ANOVA Method Card Template (Statistics, R and Python)

    完整

    Classic and Welch one-way ANOVA, ANOVA table by hand, Tukey HSD, Games-Howell, planned contrasts, eta squared with CI and omega squared

    Fisher (1925); Welch (1951); Tukey (1949); Games and Howell (1976); Hays (1963); Steiger (2004); NIST/SEMATECH e-Handbook 7.4

  6. Correlation Method Card Template (Statistics, R and Python)

    完整

    Correlation method card – Pearson, Spearman, Kendall, partial correlation, Fisher z CIs, influence, restriction of range and confounding, with R and Python

    Pearson (1896); Spearman (1904); Kendall (1938); Fisher (1915, 1921); Anscombe (1973); Steiger (1980); NIST/SEMATECH e-Handbook

  7. Linear Regression Method Card Template (Statistics, R and Python)

    完整

    Simple and multiple OLS regression: least squares, coefficient tests and CIs, R² and F test, dummies, interactions, diagnostics, HC3 robust SEs, prediction vs confidence intervals, with R and Python

    Least squares (Legendre 1805); Cook (1977); White (1980); MacKinnon and White (1985) HC3; NIST/SEMATECH e-Handbook ch. 4; APA JARS-Quant (name)

  8. Which Test Practice Set Template (Statistics, 30 Interleaved Scenarios)

    完整

    Interleaved practice for choosing a statistical method: 30 mixed scenarios, scoring rubric, confusable pairs and an answer key with reasons

    Dunlosky et al. (2013); Weinstein and Sumeracki (2018); Rohrer and Taylor (2007); Roediger and Karpicke (2006); GAISE College Report (ASA 2016, name)

  9. Statistics Worked Problem Worksheet Template (8 Steps, R and Python)

    完整

    Eight-step statistics problem-solving worksheet – restate, design, method, assumptions, compute, interpret, Feynman check, reflect – with full, faded and unsolved examples

    Pólya (1945); Renkl and Atkinson (2003) faded worked examples; Chi et al. (1989) self-explanation; Welch (1947); GAISE Pre-K-12 (2007) and GAISE II (2020) problem-solving process (name)
第 4 步

Well-Architected 评审

  1. Statistics Error Log Template (Mistake Journal and 25 Misconceptions)

    标准

    Statistics mistake journal – log table, six-type error taxonomy, 25 classic misconceptions with the correct idea and fixing template, fix-it drills, weekly review routine

    Greenland et al. (2016) misinterpretation guide; ASA p-value statement (Wasserstein and Lazar 2016); Roediger and Karpicke (2006); Cepeda et al. (2006)

  2. Statistics Flashcards Template (72 Cards, Leitner Boxes, Spaced Review)

    标准

    72 statistics flashcards by topic in Q/A format with Leitner boxes, a 1-3-7-14-30 day review calendar (R and Python), card-writing rules, Anki export note and tracking table

    Leitner (1972) box system; Cepeda et al. (2006); Karpicke and Roediger (2008); Kornell (2009)

  3. Study Guide Template

    标准

    Exam study guide: overview, topic confidence checklist, concepts, KaTeX formulas, practice Q&A, spaced repetition, exam-day plan