ECON20003 Quantitative Methods 2

How ECON20003 is assessed

Dates, weights and the test venue are indicative (from a recent Semester 1 subject guide) and are subject to confirmation — always check your own unit outline and Canvas/LMS for the authoritative timetable.

What ECON20003 covers

The whole subject → one exam-ready map. Each topic links to its free chapter guide.

It teaches you to identify the right quantitative technique, run it in R/RStudio, and interpret the results — spanning estimation and hypothesis testing of a mean, normality diagnostics and nonparametric tests, comparing two populations, inferences on variances and proportions, ANOVA, χ² frequency analysis, simple and multiple regression with the general F-test, heteroskedasticity and dummy variables, binary logit/probit models, cross-validation with ridge and LASSO, and time-series regression with autocorrelation and unit-root testing.

It is assessed by three assignments (10% each), a mid-semester test (10%), tutorial participation and weekly homework (10%), and a closed-book end-of-semester exam worth 50% that is also a hurdle — you must pass the exam to pass the subject, even if your coursework already totals 50%.

The exam supplies a formula sheet identical to the Canvas one plus statistical tables, so the marks come not from memorising formulas but from choosing the right test among look-alikes, reading R printouts correctly, and writing the full five-step reasoning chain.

Worked example · free

One-sample t-test for a mean (closed-book, formula-sheet style)

Key terms

Point-estimator properties

Three things we want of an estimator θ̂ of a parameter θ: unbiasedness (E(θ̂) = θ), efficiency (smallest variance among unbiased estimators), and consistency (θ̂ collapses onto θ as n → ∞). The sample mean X̄ is the standard example for μ.

Standard error (SE)

The standard deviation of a sample statistic across all possible samples. For a sample mean it is σ/√n (or S/√n when σ is unknown); it shrinks as n grows, which is why larger samples estimate more precisely.

Five-step hypothesis test

The spine of every ECON20003 exam answer: (1) state H₀ and H₁, (2) give the test statistic and its distribution under H₀, (3) state the decision rule (critical value or p-value), (4) make the statistical decision, (5) write a plain-English conclusion in context. Marks attach to each step, and failing to reject H₀ is never the same as accepting it.

Parametric vs nonparametric test

A parametric test (t, F, ANOVA) assumes a distributional form, usually normality; a nonparametric test (sign, Wilcoxon, Kruskal-Wallis) works on ranks or signs and makes weaker assumptions. When normality fails, you switch to the matching nonparametric alternative.

Reading an R printout

The exam-critical skill of locating the Estimate, Std. Error, t value, Pr(>|t|) and significance codes, the residual standard error, Multiple and Adjusted R², the F-statistic and its p-value, and the diagnostic blocks (Breusch-Pagan, White, Durbin-Watson, Breusch-Godfrey, VIF, Shapiro-Wilk, Wilcoxon, Kruskal-Wallis) on a stylised RStudio output.

Which-test decision tree

The habit of classifying any prompt before computing: identify the data and the goal (estimate, test one mean/variance/proportion, compare two groups, ANOVA across several, model with regression, or analyse a time series), then check assumptions (normality, equal variance) to land on the correct parametric or nonparametric procedure.

ECON20003 FAQ

Questions students ask in each ECON20003 chapter

When do I use Z instead of t?

Use Z only when the population standard deviation σ is genuinely known (rare in practice). The moment you estimate the spread with the sample S — which is almost always — switch to t with df = n − 1. For large n the two give nearly identical answers, but the exam rewards naming the correct distribution. Chapter 01 · Estimation & Hypothesis Testing of a Population Mean

How do I decide between the t-test, the Wilcoxon signed-rank test and the sign test?

First check normality (Q-Q plot, skew/kurt ratios, Shapiro-Wilk). If the data look normal, use the t-test. If they are non-normal but roughly symmetric, use the Wilcoxon signed-rank test. If they are non-normal and skewed, fall back to the sign test, which only assumes a median exists. Chapter 02 · Normality & Nonparametric One-Sample Tests

How do I know whether to use the pooled or the Welch t-test?

Run the F-test of equal variances first. If it does not reject H₀ (variances look equal), use the pooled t-test; if it rejects (variances differ), use Welch. When in doubt, Welch is the safer default because it stays valid even when variances are unequal. Chapter 03 · Comparing Two Population Central Locations

Why does R's two-proportion result not exactly match my hand Z²?

R reports a continuity-corrected χ² statistic by default, which nudges the value to account for using a continuous distribution to approximate discrete counts. Your uncorrected Z² will be close but not identical — both lead to the same decision in almost every case, so explain the discrepancy rather than treating it as an error. Chapter 04 · Inferences on Variances & Proportions (χ², t, F)

If ANOVA rejects, which group is different?

ANOVA's F-test only says at least one mean differs — it does not identify which. You then run a post-hoc multiple-comparison procedure to find the specific pairs that differ, controlling the overall error rate. Chapter 05 · One-Way ANOVA & Nonparametric Alternatives

Why is a prediction interval wider than a confidence interval at the same x?

A confidence interval captures uncertainty about the average response at that x; a prediction interval must also capture the scatter of a single new observation around that average, so it adds an extra variance term (a +1 inside the standard-error root) and is always wider. Chapter 06 · Correlation & Simple Linear Regression

What's the difference between R² and adjusted R²?

R² never falls when you add a predictor, so it rewards stuffing the model with variables. Adjusted R² subtracts a penalty for each extra predictor and can decrease, so it is the right tool for comparing models with different numbers of regressors. Chapter 07 · Multiple Regression, the General F-test & Specification

If heteroskedasticity is present, are my coefficient estimates wrong?

No — the OLS coefficients stay unbiased. What breaks is the standard errors, which become incorrect and make the t and F tests unreliable. The standard fix is to report White (heteroskedasticity-robust) standard errors, or to use weighted least squares; you do not need to discard the model. Chapter 08 · Heteroskedasticity & Dummy Independent Variables

Why prefer logit or probit over the linear probability model?

The LPM can predict probabilities below 0 or above 1, which is nonsensical, and it carries inherent heteroskedasticity. Logit and probit squeeze the linear index through an S-shaped link that keeps predictions strictly between 0 and 1, at the cost of coefficients that no longer read directly as probability changes. Chapter 09 · Dummy Dependent-Variable Models: LPM, Logit & Probit

What's the key difference between ridge and LASSO?

Both add a penalty on the size of the coefficients to control overfitting, but ridge (L2) shrinks every coefficient toward zero without eliminating any, while LASSO (L1) can drive some coefficients exactly to zero, so LASSO doubles as a variable-selection method. The penalty strength λ is tuned by cross-validation in both. Chapter 10 · Cross-Validation, Ridge & LASSO Regression

How do I read the Durbin-Watson statistic quickly?

Use ρ̂ ≈ 1 − DW/2. A DW near 2 means ρ̂ near 0 (no autocorrelation), a DW well below 2 means positive autocorrelation (ρ̂ > 0), and a DW well above 2 means negative autocorrelation. Confirm borderline cases with the Breusch-Godfrey test, which gives a clean p-value. Chapter 11 · Regression with Time-Series Data & Autocorrelation

Why can't I use the normal t-table for the Dickey-Fuller test?

Under a unit root the usual t-distribution theory breaks down, so the ADF statistic follows a non-standard distribution. Dickey and Fuller tabulated special critical values (more negative than the ordinary t-values), and you must compare your statistic against those — using a t-table would wrongly reject the unit root too often. Chapter 12 · Stationarity, Spurious Regression & the Dickey-Fuller Test

How to study for the exam

Treat ECON20003 as a decision-making subject, not a memorisation subject: the formula sheet is given, so your edge comes from picking the right test and reading the R output fast and correctly.

(1) Build the which-test decision tree until it is automatic — for any prompt, classify the data and the goal (estimate, test one mean/variance/proportion, compare two groups, ANOVA across several, model with regression, or analyse a time series), then check assumptions (normality via Q-Q/Shapiro-Wilk, equal variance via the F-test) to land on parametric vs nonparametric.

(2) Drill the five-step ritual on every test — H₀/H₁ → statistic & its distribution → decision rule → statistical decision → contextual conclusion — because partial marks attach to each line. (3) Learn to read R printouts cold: know where the Estimate, Std.

Error, t value, Pr(>|t|), residual std error, Multiple/Adjusted R², F-statistic and the diagnostic blocks (BP, White, DW, BG, VIF, Shapiro-Wilk, Wilcoxon, Kruskal-Wallis) sit, and what a small p means for each. (4) Map the provided formula sheet so exam time goes to setup, not searching.

(5) Because the exam is a 50% hurdle, treat it as the priority artefact — keep up weekly with the tutorial homework that rehearses exactly these moves, and use the assignments and mid-semester test as dress rehearsals for reading R output under pressure.

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