Measurement Task Answers
For each case, identify the kind of measurement scale implied — either nominal, ordinal, interval, or ratio.
Works categorized as either ragtime, stride bass, big band, bebop, Dixieland, free jazz or other.
Nominal: These are named categories.
The age of audience members.
Ratio: Zero is meaningful. A doubling of age (from 20 to 40) is a true doubling.
Year of birth for audience members.
Interval: The year “0” has no special meaning; The year 1000 A.D. is not half as old as 2000 A.D.
The participant’s sex, coded as male or female.
Nominal: These are named categories.
Interval size in semitones.
Ratio: Zero has meaning, namely a unison distance. Twelve semitones is twice six semitones.
Year of composition.
Interval: The year “0” has no special meaning; The year 1000 A.D. is not half as old as 2000 A.D.
Either: medieval, renaissance, baroque, classical, romantic, or modern.
Ordinal: There is a rank ordering in terms of history, but the distances between successive items is not the same.
Dynamic level, according to the scale: ppp, pp, p, mp, mf, f, ff, or fff.
Ordinal: There is a rank order, but the distances between successive items is not necessarily the same.
The skin temperature of listeners in Fahrenheit.
Interval: Recall that zero degrees has no special meaning. One hundred degrees is not twice as warm as fifty degrees.
Watts of power produced by an amplifier.
Ratio: Zero watts means there is no power at all.
A list of instruments.
Nominal: These are named categories.
A list of instruments from brightest to darkest timbres.
Ordinal: There is a rank order from brightest to darkest, but the distance between neighboring instruments on the list is not constant.
MIDI key numbers (e.g., middle C = 60).
Interval: notice that MIDI key “0” has no special meaning and that MIDI key “60” (C4) is not “twice as much or twice as high” as MIDI key “30” (F#2).
Coded S, A, T or B.
Ordinal: There is a rank order in terms of pitch height. However, the distance in tessitura is not necessarily the same. For example, the distance between the bass and the tenor might well be larger than the distance between the soprano and the alto.
Number of hours of practice.
Ratio: Zero has meaning (no practice at all); 2 hours of practice is twice as much as 4 hours of practice.
IQ.
Interval: Zero has no special meaning. Instead “100” has a special meaning, namely the average intelligence. A person who has an IQ of “200” is not twice as smart as the average person.
Number of instruments.
Ratio: Zero has a special meaning. Four instruments is half of eight instruments.
Reaction times in milliseconds.
Ratio: Zero has a special meaning; 50 milliseconds is half 100 milliseconds.
Three categories: (1) Obviously major, (2) obviously minor, or (3) not obviously major or minor.
Nominal: These are named categories.
The amount of money a busker makes per hour.
Ratio: Zero has meaning; $6/hr is twice as much as $3/hr.
Length of hairpin markings in centimeters.
Ratio: Zero means no distance at all. Six centimeters is twice the distance of three centimeters.
The notated key of a passage.
Nominal: These are named categories, like F major or B-flat minor.
The loudness of each instrument, measured in decibels.
Interval: This is really a trick question that requires special knowledge. Most people don’t know that zero decibels doesn’t mean the absence of sound. It means a sound of 0.0002 dynes per square centimeter, which is considered the quietest sound that a normal person can just hear. The total absence of sound is undefined in the decibel scale, making the scale an interval scale rather than a ratio scale.
The number of sharps (positive) or flats (negative) in a key signature. (E.g., F# & C# = +2; Bb = -1.)
Ratio or interval: A difficult question. If one is thinking purely in terms of the notational symbols, then zero has a special meaning — i.e., no sharp or flat symbols. This would make the scale a ratio scale. However, it is likely that the researcher is thinking in terms of the circle of fifths. One might argue that there is nothing special about C major/A minor compared with other keys. D major might have twice the number of sharps as G major, but does G major have infinitely more sharps than C major? If the researcher is thinking in terms of the circle of fifths, then no sharps or flats is not special, and therefore the measurement would be considered an interval scale.
Responses: never, rarely, sometimes, frequently, always.
Ordinal: We can’t say that the distance between never and rarely is the same as the distance between sometimes and frequently.
Musical preference on a 7-point scale:
like ◉ ◉ ◉ ◉ ◉ dislike Interval: respondents tend to treat the points as positions along a hypothetical line; although there is no meaningful “zero” position, one can interpret the distances between successvie points as meaningful.