# Statistics Learning Roadmap: [Your course, exam or thesis goal]

> A personal curriculum map for learning statistics in three levels (foundations, core inference and models,
> advanced), with the prerequisite graph, the matching template for every topic, "can do" targets, a 20-question
> diagnostic that tells you where to start, a 12-week plan with spacing and interleaving built in, a weekly retrieval
> routine and a progress tracker. It is for students starting or repeating a statistics course, master's and PhD
> students who need statistics for a thesis, and working analysts filling gaps. It speeds up learning by sending you
> straight to the topics you do not yet know, in an order where each topic builds on the last, and by scheduling
> practice the way memory research says works best. The worked examples use fictional data; replace them with your
> own.
> Source basis: the GAISE College Report (ASA 2016) recommendations, summarised in our own words, and the learning
> research of Dunlosky et al. (2013) and Weinstein and Sumeracki (2018).

<!--
Guidance: How to use this template
- Start with the diagnostic self-assessment. Answer all 20 questions without notes in about 20 minutes, then mark them with the Answer key.
- Use the routing table to find your starting level and week. Skip what you already know; do not skip the diagnostic.
- Copy the 12-week plan into your calendar. Keep the review and interleaving columns: they are what makes the plan faster than reading chapter by chapter.
- Every week, open the template listed for the new topic and complete its self-test and worked examples.
- Update the progress tracker on the same day each week and re-take the diagnostic in weeks 6 and 12.
- Related templates: academic/stats-formula-sheet, academic/stats-error-log, academic/stats-flashcards-spaced-review, academic/stats-worked-problem, academic/stats-practice-which-test, academic/stats-test-selector, academic/study-guide, education/cornell-notes, academic/lecture-notes, academic/thesis-full
-->

## Document control

<!-- Guidance: Name the goal (exam, thesis chapter, job task) and the date it must be met. The plan works backwards from that date. -->

| Field | Value |
|---|---|
| Course or project | [STAT 201 Inferential Statistics, Lakemoor University (fictional), or "thesis data analysis"] |
| Learner or analyst | [Your name] |
| Goal and deadline | [Final exam on YYYY-MM-DD / thesis results chapter by YYYY-MM-DD] |
| Data set | [Course practice data or your thesis data; examples here are fictional] |
| Software and versions | [R 4.5.1 and/or Python 3.14 with numpy, pandas, scipy, statsmodels] |
| Date | YYYY-MM-DD |
| Version | [0.1] |

## How this roadmap speeds up learning

<!-- Guidance: Read this once before the diagnostic. It explains why the plan looks different from a textbook's chapter order. -->

Statistics is a cumulative subject: confidence intervals need standard errors, standard errors need sampling
distributions, and regression needs nearly everything before it. Most learners lose time in two ways. They re-read
topics they already know because the textbook puts them first, and they skip the few prerequisites that make later
topics easy. The diagnostic fixes the first problem, the prerequisite graph fixes the second.

The plan then uses the six learning strategies that Weinstein and Sumeracki (2018) single out from the
cognitive psychology research, each built into a column or routine. In the review by Dunlosky et al. (2013), practice
testing and distributed (spaced) practice were rated high utility, and interleaving and elaborative interrogation
moderate utility:

| Strategy | What it means | Where it is in this roadmap |
|---|---|---|
| Retrieval practice | recalling from memory beats re-reading | weekly self-tests, flashcards, the diagnostic |
| Spacing | spreading practice over days and weeks beats cramming | review column: 1 week and 3 or more weeks back |
| Interleaving | mixing problem types trains you to choose the method | mixed practice column from week 4 |
| Elaboration | asking "why" and "how does this connect" | "can do" statements, Feynman check |
| Dual coding | pairing words with diagrams and charts | Mermaid decision trees and Vega-Lite charts in every template |
| Concrete examples | anchoring abstract ideas in specific cases | the same fictional settings in every template |

The concrete examples always use the same fictional settings (Lakemoor University, Brightwell Bakery, Harbour City
Library) so that you spend effort on the statistics, not on a new story each time. A seventh ingredient comes from
research on worked examples (Renkl and Atkinson 2003): study a solved problem, then a half-solved one, then solve one
alone. Every method template and academic/stats-worked-problem follow this fading pattern.

Structure aligned with the GAISE College Report (ASA 2016) and the topic dependencies of a standard two-semester
introductory and intermediate statistics sequence.

## GAISE College Report recommendations in brief

<!-- Guidance: The GAISE report is written for teachers, but each recommendation tells a learner what to expect and what to practise. Summarised here in our own words. -->

The American Statistical Association's GAISE College Report (2016) gives six recommendations for teaching
introductory statistics. In our words, and with what each means for you as a learner:

1. **Teach statistical thinking.** Statistics is an investigative process: pose a question, collect or find data,
   analyse, interpret. Include thinking about several variables at once. For you: always start from the question and
   the design, never from a formula (academic/stats-worked-problem steps 1 and 2).
2. **Focus on conceptual understanding.** Knowing why a method works and when it applies matters more than
   memorising procedures. For you: learn the concept cards (sampling distributions, p-values, intervals) before the
   method cards, and explain each in plain words.
3. **Integrate real data with a context and purpose.** For you: use your own course or thesis data in every
   template as soon as you can.
4. **Foster active learning.** For you: answer, compute and explain; do not just watch or read.
5. **Use technology to explore concepts and analyse data.** For you: run the R or Python code in each template,
   change the numbers and watch the output change; use simulations to see sampling variation.
6. **Use assessments to improve and evaluate learning.** For you: the diagnostic, the self-tests and the error log
   are assessments for learning, not grades.

## Curriculum map: three levels

<!-- Guidance: Each row is one topic with its prerequisite, its template and the "can do" target that tells you when you have learned it. Tick a topic only when you can do the target without notes. -->

**Level 1, foundations.** The language of data, describing data, probability and the idea that statistics vary from
sample to sample.

| ID | Topic | Prerequisites | Template (academic/) | Can do |
|---|---|---|---|---|
| L1.1 | Variables, measurement levels, coding | none | stats-variable-codebook | classify any variable as nominal, ordinal, interval or ratio and code it |
| L1.2 | Sampling and study design basics | L1.1 | stats-sampling-plan | tell an experiment from an observational study and name a bias source |
| L1.3 | Exploratory analysis, descriptive statistics | L1.1 | stats-eda-report | choose and compute centre and spread; draw and read a histogram and box plot |
| L1.4 | Data cleaning, missing data | L1.3 | stats-data-cleaning-log | log every cleaning step; explain MCAR, MAR and MNAR |
| L1.5 | Probability rules, conditional probability, Bayes' theorem | none | stats-probability-basics | solve a screening-test problem with a tree or two-way table |
| L1.6 | Discrete and continuous distributions | L1.5 | stats-distributions-sheet | pick binomial, Poisson or normal for a situation and compute a probability |
| L1.7 | Sampling distributions, SE, central limit theorem | L1.3, L1.6 | stats-sampling-distributions | explain why the SE of a mean is $s/\sqrt{n}$ and simulate it |

**Level 2, core inference and models.** Estimation, testing, the standard tests and simple regression, with effect
sizes, power and reporting.

| ID | Topic | Prerequisites | Template (academic/) | Can do |
|---|---|---|---|---|
| L2.1 | Confidence intervals | L1.7 | stats-confidence-intervals | build and correctly interpret a t interval and a Wilson interval |
| L2.2 | Hypothesis testing, p-values, errors, multiple testing | L1.7, L2.1 | stats-hypothesis-testing | state $H_0$ and $H_1$, interpret p, name Type I and II errors |
| L2.3 | Choosing a test | L2.2 | stats-test-selector, stats-practice-which-test | pick the method for 30 mixed scenarios with at least 80% accuracy |
| L2.4 | Assumptions and diagnostics | L2.3 | stats-assumption-checklist | check assumptions with plots and choose a remedy |
| L2.5 | t-tests (one-sample, Welch, pooled, paired) | L2.2 | stats-t-tests | run and report each with R and Python |
| L2.6 | Proportion tests | L2.2 | stats-proportion-tests | test and estimate one and two proportions |
| L2.7 | Contingency tables | L2.6 | stats-contingency-tables | run chi-square or Fisher's test, report Cramér's V and an odds ratio |
| L2.8 | Nonparametric tests | L2.5 | stats-nonparametric-tests | choose a rank-based test and say what it compares |
| L2.9 | One-way ANOVA and post hoc tests | L2.5 | stats-one-way-anova | fill an ANOVA table, run Tukey or Games-Howell |
| L2.10 | Correlation | L1.3, L2.2 | stats-correlation | compute Pearson and Spearman with CIs; explain why correlation is not causation |
| L2.11 | Linear regression (simple and multiple) | L2.10 | stats-linear-regression | fit, interpret and diagnose an OLS model |
| L2.12 | Effect sizes | L2.5, L2.9 | stats-effect-sizes | choose, compute and interpret d, g, r, $\eta^2$, V, OR |
| L2.13 | Power and sample size | L2.2, L2.12 | stats-power-sample-size | compute n for a t-test and a proportion |
| L2.14 | Reporting results | L2.5 | stats-results-reporting | write an APA-style results paragraph and table |

**Level 3, advanced.** Models for complex designs and outcomes, alternative inference frameworks, and the documents
of a full analysis.

| ID | Topic | Prerequisites | Template (academic/) | Can do |
|---|---|---|---|---|
| L3.1 | Factorial ANOVA, interactions | L2.9 | stats-factorial-anova | interpret an interaction plot and simple effects |
| L3.2 | Repeated measures | L2.5, L2.9 | stats-repeated-measures | check sphericity, apply Greenhouse-Geisser |
| L3.3 | ANCOVA | L2.9, L2.11 | stats-ancova | test homogeneity of slopes, report adjusted means |
| L3.4 | Logistic regression | L2.11 | stats-logistic-regression | interpret odds ratios and a confusion matrix |
| L3.5 | Count regression | L2.11 | stats-count-regression | fit Poisson, detect overdispersion, use an offset |
| L3.6 | Mixed models | L3.2, L2.11 | stats-mixed-models | fit a random-intercept model and report the ICC |
| L3.7 | Data transformations | L2.4 | stats-data-transformations | choose log or Box-Cox and back-transform correctly |
| L3.8 | Resampling | L2.1, L2.2 | stats-resampling-methods | run a seeded bootstrap CI and a permutation test |
| L3.9 | Estimation theory, maximum likelihood | L1.6, L2.1 | stats-estimation-mle | derive an MLE and run a likelihood ratio test |
| L3.10 | Bayesian inference | L1.5, L3.9 | stats-bayesian-inference | update a beta prior with binomial data and read a credible interval |
| L3.11 | Time series and ARIMA | L2.11 | stats-time-series-arima | read ACF and PACF, fit and evaluate a forecast |
| L3.12 | Reliability and factor analysis | L2.10 | stats-reliability-factor-analysis | compute Cronbach's alpha, decide factor retention |
| L3.13 | Experimental design | L1.2, L2.9 | stats-experiment-design | write a randomisation and blocking plan |
| L3.14 | Analysis plan and reports | L2.14 and the methods you use | stats-analysis-plan, stats-regression-model-report, stats-analysis-report | write a statistical analysis plan and a full report |

The learning tools apply at every level: stats-formula-sheet, stats-error-log, stats-flashcards-spaced-review,
stats-worked-problem and stats-practice-which-test.

## Prerequisite graph

<!-- Guidance: Before starting a topic, make sure every arrow into it comes from a topic you have ticked. If you are stuck on a topic, the cause is usually one arrow back. -->

Arrows point from a prerequisite to the topic that needs it. The graph is simplified: learning tools and reports are
left out, and some topics are grouped.

```mermaid
flowchart TD
  subgraph L1["Level 1 foundations"]
    VAR["Variables and measurement"] --> EDA["EDA and descriptive stats"]
    VAR --> DES["Sampling and study design"]
    EDA --> CLEAN["Data cleaning"]
    PROB["Probability and Bayes"] --> DIST["Distributions"]
    EDA --> SD["Sampling distributions and SE"]
    DIST --> SD
  end
  subgraph L2["Level 2 core inference and models"]
    SD --> CI["Confidence intervals"]
    CI --> HT["Hypothesis testing"]
    HT --> SEL["Choosing a test and assumptions"]
    HT --> TT["t-tests"]
    HT --> PROP["Proportions and contingency tables"]
    TT --> NP["Nonparametric tests"]
    TT --> AOV["One-way ANOVA"]
    HT --> COR["Correlation"]
    COR --> LR["Linear regression"]
    AOV --> ES["Effect sizes and power"]
    TT --> ES
  end
  subgraph L3["Level 3 advanced"]
    AOV --> FACT["Factorial and repeated measures"]
    LR --> ANC["ANCOVA"]
    AOV --> ANC
    LR --> GLM["Logistic and count regression"]
    FACT --> MIX["Mixed models"]
    LR --> MIX
    CI --> RES["Resampling"]
    DIST --> MLE["Estimation and MLE"]
    MLE --> BAY["Bayesian inference"]
    PROB --> BAY
    LR --> TS["Time series"]
    DES --> DOE["Experimental design"]
    AOV --> DOE
  end
```

## Diagnostic self-assessment

<!-- Guidance: Answer all 20 without notes and without a calculator except for simple arithmetic. Write your answers down. A guess marked as a guess counts as wrong for routing, so mark guesses with "?". -->

The diagnostic has four blocks of five questions. Each block maps to a part of the curriculum. Answer in about 20
minutes, then score each block from the Answer key (1 point per correct answer) and use the routing table.

**Block A: describing data (L1.1 to L1.4)**

1. For the data 2, 4, 4, 5, 10, what are the mean and the median?
2. Which is less affected by one very large value: the mean or the median?
3. What is the measurement level of "satisfaction rated 1 = very poor to 5 = very good"?
4. When computing a sample standard deviation, do you divide the sum of squared deviations by $n$ or by $n-1$?
5. A histogram of household income has a long tail to the right. Is the mean usually above or below the median?

**Block B: probability and distributions (L1.5 to L1.7)**

6. $P(A) = 0.3$, $P(B) = 0.5$, and $A$ and $B$ are independent. What is $P(A \text{ and } B)$?
7. A fair coin is tossed 3 times. What is the probability of exactly 2 heads?
8. About what percentage of a normal distribution lies within 2 standard deviations of the mean?
9. Exam scores are roughly normal with mean 70 and SD 10. What is the z-score of a score of 85?
10. A condition affects 1% of people. A test detects 90% of cases and gives a false positive for 9% of non-cases.
    If someone tests positive, is the chance they have the condition closer to 10% or to 90%?

**Block C: core inference (L2.1 to L2.5)**

11. A sample of $n = 36$ has SD $s = 12$. What is the standard error of the mean?
12. A 95% CI for a mean is [4.1, 7.9]. Would a two-sided test of $H_0: \mu = 5$ at $\alpha = 0.05$ reject $H_0$?
13. Complete the sentence correctly: "p = 0.03 means that..."
14. What is a Type I error?
15. The same 20 students are tested before and after a workshop. Which t-test compares the two means?

**Block D: models and method choice (L2.6 to L2.11 and Level 3 entry)**

16. Three independent groups, numeric outcome, compare means: which method?
17. Describe a correlation of $r = -0.8$ in words.
18. A regression line is $\hat{y} = 20 + 3x$. What is the predicted $y$ at $x = 5$, and what does the 3 mean?
19. The outcome is pass or fail and there are several predictors. Which regression model fits?
20. Two categorical variables summarised in a table of counts: which test checks for an association?

## Routing: where to start

<!-- Guidance: Use your block scores, not your total. A strong total can hide one weak block that will slow every later topic. -->

| Your block scores | Start at | Week in the 12-week plan | Why |
|---|---|---|---|
| A at most 3 or B at most 3 | Level 1 from L1.1 (or the weak block's first topic) | Week 1 (week 3 if only block B is weak) | later topics rest on these |
| A and B at least 4, C at most 3 | L1.7 sampling distributions, then Level 2 | Week 4 | inference needs the SE idea first |
| A, B, C at least 4, D at most 3 | L2.5 t-tests onward, with L2.3 choosing a test alongside | Week 6 | you know the logic; learn the methods and the method map |
| All blocks at least 4 | Level 3 topics your goal needs; use the full plan for review only | Week 9, or a custom plan | spend time where your goal is |

Goal-based shortcuts. **Exam in four weeks:** do the routing, then run weeks from your start point at double pace
and keep every review column. **Thesis analyst:** after routing, add your thesis method (for example L3.6 mixed
models) as early as its prerequisites allow, and start academic/stats-analysis-plan in the same week.
**Working analyst:** focus on L2.3, L2.4, L2.12 and L2.14 first: choosing, checking and reporting are the skills
that most change the quality of real analyses.

## 12-week plan

<!-- Guidance: Each week has one main new topic, a spaced review of earlier topics and, from week 4, a mixed (interleaved) practice set. Budget about 5 to 7 hours a week. If you start later than week 1, keep the review column of the skipped weeks as light review. -->

The plan covers Levels 1 and 2 plus a first Level 3 topic. The review column always contains one topic from the
previous week and one from at least three weeks earlier (in week 3 the oldest available topic, from week 1): this is
spacing. The mixed practice column contains problems
from several topics in shuffled order, so that you practise choosing the method rather than repeating one: this is
interleaving.

| Week | New topics (template) | Spaced review (1 week and 3+ weeks back) | Mixed practice (interleaved) | Retrieval check |
|---|---|---|---|---|
| 1 | L1.1 variables, L1.3 EDA (stats-variable-codebook, stats-eda-report) | none yet; take the diagnostic | none | self-tests of both templates |
| 2 | L1.2 study design, L1.4 cleaning (stats-sampling-plan, stats-data-cleaning-log) | L1.3 | 5 "experiment or observational?" items | 10 flashcards |
| 3 | L1.5 probability, L1.6 distributions (stats-probability-basics, stats-distributions-sheet) | L1.2; L1.1 | descriptive and design items mixed | 15 flashcards |
| 4 | L1.7 sampling distributions (stats-sampling-distributions) | L1.6; L1.3 | probability and distribution items mixed | run the CLT simulation from memory |
| 5 | L2.1 confidence intervals, L2.2 hypothesis testing (stats-confidence-intervals, stats-hypothesis-testing) | L1.7; L1.2 | 10 items from weeks 1 to 4 | write the CI meaning without notes |
| 6 | L2.5 t-tests, L2.4 assumptions (stats-t-tests, stats-assumption-checklist) | L2.2; L1.4 | stats-practice-which-test, first 10 scenarios | re-take the diagnostic |
| 7 | L2.6 proportions, L2.7 contingency tables (stats-proportion-tests, stats-contingency-tables) | L2.5; L1.6 | 10 scenarios mixing t, proportions and tables | worked-problem worksheet, one per method |
| 8 | L2.9 one-way ANOVA, L2.8 nonparametric (stats-one-way-anova, stats-nonparametric-tests) | L2.7; L2.1 | stats-practice-which-test, scenarios 11 to 20 | formula sheet rows from memory |
| 9 | L2.10 correlation, L2.11 regression (stats-correlation, stats-linear-regression) | L2.9; L2.2 | mixed set with regression added | explain $R^2$ to a non-statistician |
| 10 | L2.12 effect sizes, L2.13 power (stats-effect-sizes, stats-power-sample-size) | L2.11; L2.5 | all 30 scenarios, timed | error-log review of the month |
| 11 | L2.14 reporting, L2.3 test selection consolidated (stats-results-reporting, stats-test-selector) | L2.12; L2.7 | past exam or thesis-style questions | write a results paragraph from memory |
| 12 | One Level 3 topic your goal needs (for example stats-logistic-regression) | L2.14; L2.9 | full mock exam or full analysis on your data | re-take the diagnostic; compare with weeks 1 and 6 |

## Weekly retrieval routine

<!-- Guidance: Short, frequent sessions beat one long session. Keep the routine even in busy weeks: drop the new topic before you drop the review. -->

| Day | Activity (20 to 60 minutes) | Tool |
|---|---|---|
| Monday | learn the new topic: concept first, then Example A of its template | topic template |
| Tuesday | complete Example B (faded) and Exercise C without notes | topic template |
| Wednesday | flashcards due today; add 5 to 10 cards from the new topic | academic/stats-flashcards-spaced-review |
| Thursday | spaced review: self-test of the two review topics, cold | review templates |
| Friday | interleaved practice: the mixed set for the week, method choice first | academic/stats-practice-which-test |
| Saturday | one full worked problem on real or course data | academic/stats-worked-problem |
| Sunday | error-log review, update the progress tracker, plan next week | academic/stats-error-log, this roadmap |

Three rules make the routine work. Try before you look: answer from memory first, even if you expect to fail, because
an attempt followed by feedback is remembered better than reading the answer. Mix before you master: once two methods
are learned, practise them shuffled, because exams and real data never tell you which chapter a problem comes from.
Explain as you go: after each answer, say in one sentence why it is right.

## Worked examples with fading

<!-- Guidance: Example A shows a complete routing and plan for a fictional learner. Complete Example B, then do Exercise C for yourself: it becomes your own plan. -->

**Example A (fully worked).** A master's student at Lakemoor University (fictional) must analyse survey data from 120
students for a thesis in eight weeks. The outcome is whether a student used the campus tutoring service (yes or no),
with several predictors. Diagnostic block scores: A 5, B 4, C 3, D 2.

1. Routing: A and B at least 4, C at most 3, so start at L1.7 (week 4 of the plan).
2. Goal topic: a binary outcome with several predictors needs L3.4 logistic regression. Prerequisites from the graph:
   L2.11 linear regression, which needs L2.10 correlation, which needs L2.2 hypothesis testing.
3. Compressed plan (8 weeks): week 1 L1.7 and L2.1; week 2 L2.2 and L2.5; week 3 L2.6, L2.7 and L2.4; week 4 L2.10
   and L2.11; week 5 L3.4 logistic regression plus academic/stats-analysis-plan for the thesis; week 6 L2.12 and
   L2.14; week 7 analysis of the thesis data with academic/stats-regression-model-report; week 8 review and writing.
4. Spacing: each week keeps one review topic from the week before and one from three weeks back (for example week 4
   reviews L2.7 and L2.1).
5. Interleaving: from week 3, the Friday set mixes t-tests, proportion tests and contingency tables with regression
   scenarios.
6. Check: re-take the diagnostic in week 4. Block C should now be at least 4; if not, repeat L2.2 before L3.4.

**Example B (half worked).** An analyst at Brightwell Bakery (fictional) must compare the mean proving time of dough
across four flour suppliers and has scores A 5, B 5, C 4, D 2.

1. Routing: all of A, B and C are at least 4 and D is at most 3, so start at [ ] (week [ ] of the plan).
2. Goal topic: comparing means of four independent groups needs [ ]. Prerequisites from the graph: [ ].
3. If the variances differ strongly between suppliers, the template to open is [ ] and the method is [ ].
4. Spacing in the first week: review one topic from [ ] and one from [ ].
5. Interleaving: the Friday set should mix ANOVA scenarios with [ ] and [ ] scenarios.

**Exercise C (your turn).** Take the diagnostic, write your four block scores, apply the routing table and write your
own first four weeks in the progress tracker below. Then answer: which single prerequisite, if missing, would slow you
down most, and how will you check it in week 2?

## Progress tracker

<!-- Guidance: Update weekly. Rate each "can do" target from 1 (cannot start) to 5 (could teach it). A topic is done at 4 or more on two dates at least a week apart. -->

| Topic ID | Can do target (short) | Date 1 / rating | Date 2 / rating | Date 3 / rating | Done |
|---|---|---|---|---|---|
| *Example:* L1.7 | explain and simulate SE of a mean | YYYY-MM-DD / 2 | YYYY-MM-DD / 4 | YYYY-MM-DD / 4 | Y |
| *Example:* L2.5 | run and report Welch, pooled and paired t | YYYY-MM-DD / 3 | YYYY-MM-DD / [ ] | [ ] | [ ] |
| [ID] | [target] | YYYY-MM-DD / [ ] | YYYY-MM-DD / [ ] | YYYY-MM-DD / [ ] | [ ] |
| [ID] | [target] | YYYY-MM-DD / [ ] | YYYY-MM-DD / [ ] | YYYY-MM-DD / [ ] | [ ] |

Diagnostic history (scores out of 5 per block):

| Date | Block A | Block B | Block C | Block D | Total |
|---|---|---|---|---|---|
| *Example:* week 1 | 4 | 3 | 2 | 1 | 10 |
| *Example:* week 6 | 5 | 4 | 4 | 3 | 16 |
| *Example:* week 12 | 5 | 5 | 5 | 4 | 19 |
| YYYY-MM-DD | [ ] | [ ] | [ ] | [ ] | [ ] |

The chart shows the example learner's diagnostic profile over the term. Replace the values with your own: a block
that does not rise between weeks 1 and 6 tells you where to add spaced review.

```vega-lite
{
  "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
  "description": "Example diagnostic block scores in weeks 1, 6 and 12 (fictional learner).",
  "width": 360,
  "height": 200,
  "data": {"values": [
    {"week": "Week 1", "block": "A describe", "score": 4}, {"week": "Week 1", "block": "B probability", "score": 3},
    {"week": "Week 1", "block": "C inference", "score": 2}, {"week": "Week 1", "block": "D models", "score": 1},
    {"week": "Week 6", "block": "A describe", "score": 5}, {"week": "Week 6", "block": "B probability", "score": 4},
    {"week": "Week 6", "block": "C inference", "score": 4}, {"week": "Week 6", "block": "D models", "score": 3},
    {"week": "Week 12", "block": "A describe", "score": 5}, {"week": "Week 12", "block": "B probability", "score": 5},
    {"week": "Week 12", "block": "C inference", "score": 5}, {"week": "Week 12", "block": "D models", "score": 4}
  ]},
  "mark": "bar",
  "encoding": {
    "x": {"field": "block", "type": "nominal", "title": null},
    "xOffset": {"field": "week", "type": "nominal", "sort": ["Week 1", "Week 6", "Week 12"]},
    "y": {"field": "score", "type": "quantitative", "scale": {"domain": [0, 5]}, "title": "Score out of 5"},
    "color": {"field": "week", "type": "nominal", "sort": ["Week 1", "Week 6", "Week 12"], "title": "Diagnostic"}
  }
}
```

## Common mistakes when learning statistics

<!-- Guidance: These are study-process mistakes, not calculation mistakes. Calculation and concept mistakes go in academic/stats-error-log. -->

| Mistake | Why it slows you down | Better habit |
|---|---|---|
| Re-reading notes until they feel familiar | familiarity is not recall; it feels like learning but fades fast | close the notes and self-test |
| Studying one topic per day in blocks | you never practise choosing a method | interleave from week 4 |
| Cramming the week before the exam | spacing gives much better long-term retention for the same total time | short reviews spread over weeks |
| Skipping probability because "the software does it" | sampling distributions, p-values and Bayes all rest on it | do L1.5 and L1.7 properly |
| Learning formulas before ideas | you cannot tell when a formula applies | concept card first, then method card |
| Running code without predicting the output | you learn syntax, not statistics | predict the sign and rough size first |
| Treating the diagnostic as a grade | you hide gaps instead of fixing them | mark guesses as wrong for routing |
| Highlighting as the main study strategy | rated low utility by Dunlosky et al. (2013) | turn highlights into questions |

## Self-test questions

<!-- Guidance: Answer from memory, then check the Answer key. These test how well you understand the roadmap itself. -->

1. Name the six learning strategies built into this roadmap and one place each appears.
2. Why does the review column of the 12-week plan include a topic from three or more weeks earlier, not only last
   week's?
3. Using the prerequisite graph, list the chain of topics that leads from probability to Bayesian inference.
4. What is the difference between blocked and interleaved practice, and why is interleaving harder but better for
   statistics?
5. Your block scores are A 5, B 2, C 4, D 4. Where do you start, and why not at Level 3?

## My notes and next steps

<!-- Guidance: Write your route and the first concrete action. A plan without a first action on a date rarely starts. -->

My block scores: A [ ], B [ ], C [ ], D [ ]. Start at: [topic ID] in week [ ]. Goal topic: [ID and template].

First action (date and time): [YYYY-MM-DD, 19:00, take the self-test of academic/stats-sampling-distributions].

Confidence in the plan (1-5): [ ]. Open questions for the tutor or supervisor: [ ]. Errors to watch from my log:
[link to academic/stats-error-log].

## Sources and further reading

<!-- Guidance: The learning research behind the plan, and where to read further on statistics itself. -->

- GAISE College Report ASA Revision Committee (2016). *Guidelines for Assessment and Instruction in Statistics
  Education (GAISE) College Report 2016*. American Statistical Association.
- Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., and Willingham, D. T. (2013). Improving students' learning
  with effective learning techniques. *Psychological Science in the Public Interest*, 14(1), 4–58.
- Weinstein, Y., and Sumeracki, M. (2018). *Understanding How We Learn: A Visual Guide* (illustrated by O.
  Caviglioli). Routledge.
- Roediger, H. L., and Karpicke, J. D. (2006). Test-enhanced learning: taking memory tests improves long-term
  retention. *Psychological Science*, 17(3), 249–255.
- Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., and Rohrer, D. (2006). Distributed practice in verbal recall
  tasks: a review and quantitative synthesis. *Psychological Bulletin*, 132(3), 354–380.
- Rohrer, D., and Taylor, K. (2007). The shuffling of mathematics problems improves learning. *Instructional Science*,
  35(6), 481–498.
- Renkl, A., and Atkinson, R. K. (2003). Structuring the transition from example study to problem solving in cognitive
  skill acquisition: a cognitive load perspective. *Educational Psychologist*, 38(1), 15–22.
- NIST/SEMATECH e-Handbook of Statistical Methods, https://www.itl.nist.gov/div898/handbook/ (accessed 2026-10-25).
  Public domain.
- Further reading (by name only): de Smith, M. J. (2024). *Statistical Analysis Handbook*, 2024 edition. StatsRef,
  https://www.statsref.com/; *OpenIntro Statistics*.

## Answer key

<!-- Guidance: Mark the diagnostic strictly: a partly right answer is wrong for routing purposes. -->

**Diagnostic.**

1. Mean $= 25/5 = 5$; median $= 4$.
2. The median.
3. Ordinal (ordered categories; the gaps between levels are not guaranteed equal).
4. $n-1$.
5. Usually above the median: the long right tail pulls the mean up.
6. $0.3 \times 0.5 = 0.15$.
7. $\binom{3}{2}(0.5)^3 = 3/8 = 0.375$.
8. About 95%.
9. $z = (85-70)/10 = 1.5$.
10. Closer to 10%: $0.009/(0.009 + 0.0891) = 0.092$, about 9%. Most positives come from the large group without the
    condition.
11. $SE = 12/\sqrt{36} = 2$.
12. No: 5 lies inside the 95% CI, so a two-sided test at $\alpha = 0.05$ does not reject.
13. "...if $H_0$ were true, data at least as extreme as these would occur with probability 0.03." It is not the
    probability that $H_0$ is true.
14. Rejecting $H_0$ when it is true (a false positive).
15. The paired t-test (on the before-after differences).
16. One-way ANOVA (Welch's ANOVA if variances differ), followed by post hoc comparisons.
17. A strong negative linear association: higher $x$ goes with lower $y$.
18. $\hat{y} = 20 + 3 \times 5 = 35$. Each one-unit increase in $x$ is associated with a 3-unit increase in predicted
    $y$.
19. Logistic regression.
20. The chi-square test of independence (Fisher's exact test if expected counts are small).

**Example B.** Start at L2.5 t-tests with L2.3 choosing a test alongside (week 6 of the plan). Goal
topic L2.9 one-way ANOVA (academic/stats-one-way-anova); prerequisites L2.5 t-tests and L2.2 hypothesis testing. With
unequal variances: the same template, Welch's ANOVA followed by Games-Howell. Spacing: in the first week (plan week 6)
the review column gives L2.2 (previous plan week) and L1.4 (three or more weeks back); because this learner skipped
those weeks, treat them as light review. Interleaving: mix ANOVA with
t-test and nonparametric (Kruskal-Wallis) scenarios.

**Self-test.**

1. Retrieval practice (self-tests, diagnostic), spacing (review column), interleaving (mixed practice), elaboration
   (can-do statements, Feynman check), dual coding (Mermaid and Vega-Lite), concrete examples (the shared fictional
   settings). Worked examples with fading (each template's A, B, C) are the extra seventh ingredient.
2. When the test is weeks or months away, somewhat longer gaps between reviews produce better long-term retention
   (Cepeda et al. 2006); reviewing only last week's topic would let older topics fade before the exam.
3. Probability and Bayes, then distributions, then estimation and MLE, then Bayesian inference (with a direct arrow
   from probability to Bayesian inference as well).
4. Blocked practice repeats one problem type; interleaved practice mixes types. Interleaving feels harder because you
   must first decide which method applies, which is exactly the skill exams and real data demand.
5. Block B is at most 3, so start at the first Level 1 topic of that block, L1.5 probability (week 3). Level 3 methods rest
   on sampling distributions and probability; skipping them makes every later topic slower.

## Revision history

<!-- Guidance: Record each re-route, for example after the week 6 diagnostic. -->

| Version | Date | Author | Change |
|---|---|---|---|
| 0.1 | YYYY-MM-DD | [Name] | First version from template |
| [0.2] | YYYY-MM-DD | [Name] | [Re-routed after week 6 diagnostic] |