INVESTIGATIONS / MEASUREMENT & FRAMING

Constructed example

What the dashboard leaves out

One set of outcomes. Two different stories.

YOUR TASK / CONSTRUCTED EXAMPLE

Decide what the dashboard should answer

You’re reviewing a fictional programme’s completion dashboard. Name the question you need answered, then inspect people who completed, stopped, or never started.

A first judgment.
An evidence trail.
Your decision.

Begin with a provisional judgment

Loading the supplied example…

Which question are you trying to answer?How many starters completed?How many invitees completed?I need both questions kept distinct

Keep a private first thought (optional)

Your first reasoning

Private writing stays out of links and default downloads. A reopened link does not restore it.

This records a provisional judgment and the starting configuration. It does not change a mathematical setting or save automatically.

Who is being counted?

A percentage carries a boundary. Before we trust the number, we need to know who sits inside it.

Invited: 140
Started: 100
Completed: 80

Record an initial thought

Which population did you first imagine?Optional. Included only if you save this experiment.

80 of 100 starters

80%

Among people who started.One dot = one person

80 of 140 invitees

57.1%

Among everyone invited.One dot = one person

Select a group to follow the same people across both frames.

Both rates are correct.

They answer different questions.

Open the instrument →

Save this experiment

MODEL & LIMITS

What the number cannot tell us

A single percentage does not show how people were selected, what completion means, or why some never started. These counts are constructed to reveal the arithmetic.

PopulationWho is in the denominator?
DefinitionWhat counts as completion?
OutcomeWhat does the number answer?

Denominator →Selection & missing data ↓Full workings ↓

Selection, missing data and time

The example supplies three nested counts. “Did not start” is a recorded category here, not an assumed reason or a missing record. We do not know the invitation rule, reasons for non-participation, assessment window or quality of completion.

Before comparing real rates, align the population, definition and time window. Keep unknown records distinct from observed non-completions. This demonstration cannot establish causes or judge programme quality.

Inspect the calculation and definitions

Every term, in the open.

Completion rates · denominator-v1 · constructed counts
Definition	Completed	Population	Rate
Among starters	80	100	80%
Among invitees	80	140	57.1%

Rate = completed ÷ population × 100. Display rounded to one decimal; calculations and exports retain the unrounded result. A population of zero has no defined completion rate.

Definition IDs: completion-among-starters; completion-among-invitees.

Source and evidence status

Evidence: constructed teaching example, authored for Epistemologium. There is no external participant dataset. Model: denominator-v1.

OpenStax, Prealgebra, Chapter 4: Key Terms supports the elementary fraction terminology. It is not the source of these invented counts.

Method, validation and version policy →