Unit 1.2 — Data Types and Measurement Scales: Deep Context

Who published “On the Theory of Scales of Measurement” in 1946?

Stevens

Complete Stevens’ definition of measurement: the assignment of ___ to objects or events according to rules.

Numerals

In what year did the British Association committee on measurement issue the report that prompted Stevens’ paper?

1940

What mnemonic gives Stevens’ four scales in ascending order?

NOIR

What property of a scale’s permissible transformations decides which statistics are meaningful?

Invariance

Stevens called applying means to ordinal data “___ statisticizing”.

Illegal

Which scale is invariant under any one-to-one substitution of its values?

Nominal

What mathematical group does Stevens assign the nominal scale?

Permutation group

Which transformations leave an ordinal scale invariant?

Monotonic increasing

What mathematical group does Stevens assign the ordinal scale?

Isotonic group

Complete the interval scale’s permissible transformation: x′ = ___.

ax + b

What mathematical group does Stevens assign the interval scale?

General linear group

Complete the ratio scale’s permissible transformation: x′ = ___.

ax

What mathematical group does Stevens assign the ratio scale?

Similarity group

Which scale has equal intervals but a zero point fixed by convention?

Interval

Which scale is defined by having an absolute zero?

Ratio

Stevens’ own example of an ordinal scale was the hardness of what?

Minerals

Temperature in Celsius sits on which of Stevens’ scales?

Interval

Temperature in Kelvin sits on which of Stevens’ scales?

Ratio

Which measure of central tendency does Stevens permit at the nominal scale?

Mode

Which measure of central tendency does Stevens permit at the ordinal scale?

Median

At which scale does Stevens first permit the mean and standard deviation?

Interval

Which statistic appears first at the ratio scale in Stevens’ table?

Coefficient of variation

Who wrote the 1993 paper “Nominal, Ordinal, Interval, and Ratio Typologies Are Misleading”?

Velleman and Wilkinson

Which 1953 note used footballers’ jersey numbers to attack scale-type restrictions?

Lord’s football numbers

Velleman and Wilkinson argue scale type is a property of the question asked, not of the ___.

Data

Which pair proposed names, grades, ranks, counted fractions, counts, amounts and balances instead?

Mosteller and Tukey

In the Mosteller–Tukey scheme, what is a quantity bounded by 0 and 1 called?

Counted fractions

In the Mosteller–Tukey scheme, what is an unbounded quantity that may go negative called?

Balances

Who extended Stevens’ four levels to ten for cartography in 1998?

Chrisman

A compass bearing of 359° is nearer 1° than 180°. Do Stevens’ four scales accommodate this?

No

Who introduced the summated attitude rating technique in 1932?

Likert

What is a single ordered-response question called, as distinct from the summated total?

A Likert item

A single Likert item sits on which of Stevens’ scales?

Ordinal

Is the distance from “agree” to “strongly agree” known to equal that from “neutral” to “agree”?

No

Whose 2010 paper argued parametric statistics are robust enough for Likert data?

Norman

Which numeric variable type takes only isolated, countable values?

Discrete

Support tickets logged per day is which numeric variable type?

Discrete

Which numeric variable type can take any value within an interval?

Continuous

What is a categorical variable with exactly two levels called?

Binary

Is “categorical” a synonym for “nominal”?

No

What term describes data carrying its own schema through embedded tags or keys?

Semi-structured

JSON and XML fall into which structural category?

Semi-structured

Which structural category has no predefined data model?

Unstructured

The claim that 80% of enterprise data is unstructured is usually traced to which 1998 source?

Merrill Lynch

Is that 80% figure backed by an identifiable published study?

No

Who wrote “Tidy Data” in the Journal of Statistical Software in 2014?

Wickham

Tidy rule one: each variable forms a ___.

Column

Tidy rule two: each observation forms a ___.

Row

Tidy rule three: each type of observational unit forms a ___.

Table

In Wickham’s terms, what holds all values measuring the same underlying attribute?

A variable

Tidy data is equivalent to which database normal form?

Third normal form

A table with columns headed 2023, 2024 and 2025 holding revenue is untidy because the headers are ___, not variable names.

Values

What did Wickham call the operation that turns columns into key–value pairs?

Melting

In R for Data Science 2e, the third tidy rule states that each value is a ___.

Cell

What is the layout called when one unit’s repeated measures occupy several columns?

Wide

What is the layout called when one unit’s repeated measures occupy several rows?

Long

Does the Tidy Data paper endorse “wide” and “long” as precise terms?

No