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통계학 학습 키트

학습 로드맵, 확률, 확률분포, 표본분포, 가설검정, 신뢰구간, 공식 정리, 방법 카드, 검정 선택 가이드, 연습 문제, 오답 노트, 플래시카드.

1단계

계획

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

    전체

    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)
2단계

학습

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

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)
3단계

실전 연습

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

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)

    전체

    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)
4단계

Well-Architected 검토

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

    표준

    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)

    표준

    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

    표준

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