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Statistics LabMAST20005 · 2020

Statistics Lab / Showcase

A guided tour

Three short recordings of the main workflows, each step captioned on screen, then screenshots of every feature. A scripted browser made them against this site, with fixed seeds, so anyone with the repository can re-record them and see the same numbers.

3
captioned walkthroughs
19
screenshots, light, dark and mobile
0
AI keys entered to record them

Workflow walkthroughs

Watch the main journeys

The videos are silent. Each step is captioned on screen, the player also offers the captions as a text track, and the numbered steps beside each video are its transcript, with the time each step starts.

Walkthrough 1 · 0:58

Estimators

Compare the method of moments with maximum likelihood for a uniform endpoint by simulation, then see the paired midrange-against-mean comparison.

Open Ch. 1 Estimators

Steps and transcript

  1. 10:00Unif(0, θ) with θ = 3: method of moments 2X̄ against maximum likelihood max(Xᵢ), 2,000 samples of n = 10, seed 20005.
  2. 20:05The MoM is unbiased but wide; the MLE is tight but always below θ. Each MSE carries its Monte Carlo standard error.
  3. 30:09Drag n to 1, as in part (a): the MLE is X itself, biased down by half, and in theory the two MSEs tie at 3.
  4. 40:19Drag n to 40: the MLE's MSE falls like 1/n², the MoM's only like 1/n, so the gap grows about seven-fold.
  5. 50:29Rescaling the MLE by (n + 2)/(n + 1) removes the bias and about halves its MSE. The table sets simulation beside theory.
  6. 60:38A new seed redraws all 2,000 samples; the ranking holds. Reset returns to seed 20005.
  7. 70:50Midrange or mean (A1 Q4): seed 2529 replays the 2020 R draws, and a paired bootstrap puts the variance ratio at 2.29 (1.76 to 3.05).

Walkthrough 2 · 1:10

Intervals

Run the coverage simulator: watch 95% intervals miss about one time in twenty, then change the level, the sample size and the interval.

Open Ch. 3 Intervals

Steps and transcript

  1. 10:00100 t intervals for a normal mean, each from a fresh sample of n = 10. Seed 1 gives 99 hits, as R's own t.test() loop does.
  2. 20:05Observed coverage is itself an estimate, so it carries a Wilson 95% interval: 94.6% to 99.8%.
  3. 30:09Draw new samples: the misses, marked ×, come and go at about five in every hundred.
  4. 40:24Lower the confidence level to 80%: the intervals shorten and about one in five misses μ.
  5. 50:33Back to 95% with n = 3: t₂ has heavy tails, so the intervals are very wide, yet coverage stays near 95%.
  6. 60:47Switch to the z interval, which uses the true σ = 3, and draw 200 intervals at once.
  7. 71:01Optional AI: explain a result with your own key. Without one nothing is sent, and the site works fully.

Walkthrough 3 · 1:23

Tests & regression

Trade Type I against Type II error and read the power curves, then fit a regression and inspect its intervals and diagnostics.

Open Ch. 4 Tests Open Ch. 5 Regression

Steps and transcript

  1. 10:00One exponential observation tests H₀: θ = 2 against H₁: θ = 5, rejecting when X > 4: α = 0.135 and power 0.449, as in 2020.
  2. 20:06Drag the cut-off k: moving it right shrinks α, the red area under H₀, and grows β, the blue area under H₁.
  3. 30:17Size α = 0.05 puts k at 5.991. The power curve gives P(reject) at every θ and passes through α at θ₀.
  4. 40:25The likelihood ratio test for a rate: raise n and the power curve steepens on both sides of λ₀ = 1.
  5. 50:41Simple linear regression on 20 simulated coffee-shop days, with 95% confidence and prediction bands.
  6. 60:46Drag x₀: the mean and new-day intervals share a centre, but the prediction interval stays much wider.
  7. 71:02R's summary(lm()) printout, recreated with R's own formatting rules, then the four plot(lm) diagnostics.
  8. 81:12New synthetic data: the fit, the bands and every diagnostic panel update together.

Screenshots

Every feature at a glance

Desktop shots are 1440 × 900. Select one to open a larger view; the arrow keys move between them.

On a phone (390 px)

How these were made

  • A Playwright script drives Google Chrome through each journey at a human pace, adds the caption banner and a visible cursor, and records the screen at 1280 × 800. The same script is an end-to-end test: it checks the numbers on screen as it goes (99 of 100 intervals at seed 1, α = 0.1353 and power 0.4493 at k = 4, a regression slope of 6.3378).
  • Every seed is the site’s default or typed in by the script, so a re-recording shows the same results. The recordings are trimmed and converted with ffmpeg, and the captions above come from the same step list.
  • No AI key was entered and no AI provider was called. The AI settings dialog is shown empty. The audit-log screenshot shows one mocked record written straight into the browser’s storage, labelled on screen as a mocked AI response for illustration.