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S01.1 · Data types and measurement

A free, illustrated module of 4 lessons and one interactive in S01 Exploratory Data Analysis: Rows, columns and what one row is; Categorical variables: nominal and ordinal; Numerical variables: counts, measurements and scales; Measurement: what a number stands for.

S01.1 L1 · Core 4 lessons · about 100 min Live · in review

Part of S01 Exploratory Data Analysis in the Statistics and Data Analysis track.

Before any summary, know what each number in a table stands for. These four lessons read the course’s table of nine flats as units, variables and values, sort its columns into names, ordered names, counts and measurements, climb the ladder of scales from nominal to ratio to see which statements each column allows, and ask how close a recorded number is to the quantity it stands for: rounding, random scatter, systematic offset and whether the column measures the right thing.

What you need first. Reading sum notation and working with fractions (M01.1, M01.7), and a little Python and pandas: lists, dictionaries and a first DataFrame (P01.6, P02.4). No statistics is assumed.

Lessons

Rows, columns and what one row is S01.1.1 25 min

Before any average, decide what one row of a table stands for. Read the flats table as units, variables and values, keep the identifier apart, write a data dictionary, and see why a row per district hides the data.
Categorical variables: nominal and ordinal S01.1.2 25 min

District names groups with no order; an energy rating has an order but no distances. Count both, find their modes, take a median only of the rating, and read every encoding of a category as a claim about its scale.
Numerical variables: counts, measurements and scales S01.1.3 25 min

Counts jump, measurements flow. Years built sit on an interval scale and rents on a ratio scale, and the difference decides which statements survive a change of unit. Derive why, climb the ladder of scales, and see why a dtype is not a scale.
Measurement: what a number stands for S01.1.4 25 min

A recorded value is a true value plus error: rounding, random scatter and a systematic offset. Separate the offset from the scatter by hand, see by simulation that averaging shrinks only the scatter, and ask whether a column measures what the question is about.

The interactive

S01.1-X1 · Scale ladder. Choose a column of the flats table and a change to its values: rename them, stretch them while keeping their order, shift the zero or change the unit. Watch which statements about two flats and which summaries keep their truth, and see each scale as the set of changes it survives. It lives in Numerical variables: counts, measurements and scales.