Week 11 · Applied Statistics · HEG Genève

Nine survey questions, one satisfaction score?

Beyond the textbook. Two things a working analyst meets in the first month: data that break the assumptions of the tests you have learned (small, skewed, ordinal), and too many variables to look at one at a time. This week is the non-parametric toolkit and a first meeting with principal component analysis — hands-on in DataTab, no formulas by hand.

🏫 In class: 3 h · lesson ~1 h, then exercises ~2 h 📖 DataTab · beyond Saylor ▶ The Lecture button shows the slide outline

By the end of Week 11 you will be able to

Recognise when a parametric test's assumptions fail and name the non-parametric counterpart (Mann–Whitney, Wilcoxon, Kruskal–Wallis, Spearman).
Run and interpret one of them in DataTab.
Explain the idea of principal component analysis: variance, components, loadings.
Run a PCA on a customer survey in DataTab and read the first two components.
Understand what "machine learning" adds to — and borrows from — the statistics of this course.

Resources

✓DataTab — online statistics calculator (free, browser-based) ↗

✓DataTab tutorial — Mann-Whitney U test ↗

✓DataTab tutorial — Principal component analysis ↗

Homework for this week is written with the week itself, on the Week 1–2 pattern: a fresh dataset, hints and worked solutions.

← Course page

Section 11.1 · The hook

The customer survey

Planned · Hook

Nine questions on a 1–5 scale — what would you do with them?

A survey of 60 customers, nine items. Estimate: how many underlying things is it really measuring?

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 11.2 · When assumptions fail

Ordinal, skewed, small

Planned · Non-parametric

Non-parametric counterparts

Classify (6 rows): the parametric test → its non-parametric twin — t test ↔ Mann–Whitney, paired t ↔ Wilcoxon, ANOVA ↔ Kruskal–Wallis, Pearson ↔ Spearman.
Widget: ranks instead of values — watch an outlier lose its power.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 11.3 · In DataTab

Run a Mann–Whitney

Planned · Hands-on

The pizzeria survey, lake vs station

Step-by-step: paste the data, choose the test, read the output. Screenshots of what DataTab shows and what each number means.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 11.4 · PCA — the idea

Directions of variance

Planned · PCA

Components, loadings, the scree plot

Widget: a 2-D cloud of two survey items; rotate the axis and watch the variance along it; the first component is the direction that captures most of it.
Then nine dimensions: what "the first two components explain 71%" means, and how to name a component from its loadings.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 11.5 · PCA in DataTab

Nine items → two scores

Planned · Hands-on

Run it, read it, name the components

Step-by-step on the survey; the loadings table; naming "food quality" and "service" from what loads where.
A closing card: how this connects to machine learning — models that predict, evaluation on held-out data, the same estimation logic underneath.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 11.6 · Checkpoint

Prove it to yourself

Planned · Quiz

Self-check quiz & where this goes next

Eight questions: which non-parametric test, why ranks, what a component is, reading a loadings table, the scree plot, and one machine-learning vocabulary item.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 11.7 · Workshop

The pizzeria file · instalment eleven

Planned · Exercise

Workbook fields

w11_survey — the survey you would run on your customers: five items, and the analysis you would do.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Course page →

Part 2 · Exercises

8 exercises, worked together

Planned · ~119 min

The second half of the session

When this week is written, each exercise below becomes a form on this page and a slide in the deck, generated from one array so the two can never disagree — and its solution opens when the instructor reveals it in class. Same engine as Weeks 1–2 (exercises.js).

Exercise 1 · Which non-parametric twin? 12 min
six parametric tests → their counterparts
Exercise 2 · Ranks by hand 12 min
rank the data, and watch the outlier lose its power
Exercise 3 · Mann–Whitney in DataTab 20 min
lake vs station: run it, read it
Exercise 4 · Wilcoxon on the paired data 15 min
Week 8's before-and-after, without the normality assumption
Exercise 5 · Spearman vs Pearson 15 min
the price–rating data both ways — and when they disagree
Exercise 6 · Read a loadings table 15 min
nine survey items, two components
Exercise 7 · PCA in DataTab 20 min
run it on the survey, then name the components
Exercise 8 · What would you report? 10 min
one paragraph for a non-technical partner

Status → outline only. Nothing here is interactive or counted yet.

Course page →