2. Module 3.Scales of Measurement

Measurement

The assignment of numerals to objects or events according to rules, transforming observations into data.

Data

Recorded observations that are analyzed and interpreted using statistics.

Levels of Measurement

Different ways to assign numbers to objects or events, including nominal, ordinal, interval, and ratio.

Nominal Level of Measurement

A scale used for categorical data where numbers are assigned arbitrarily with no numerical meaning.

Ordinal Level of Measurement

A scale that ranks variables in order but does not have equal intervals between values.

Interval Level of Measurement

A scale with equal intervals between values but no true zero point, allowing for the computation of differences.

Ratio Level of Measurement

The most advanced scale that includes equal intervals and a true zero point, allowing for meaningful comparisons using ratios.

Nominal Data

Data that classify observations into groups or categories without implying order or rank.

Ordinal Data

Data that can be ranked but where the exact differences between ranks are unknown.

Interval Data

Data that have equal intervals but lack a true zero point, allowing for the measurement of differences.

Ratio Data

Data that have equal intervals and a true zero point, allowing for the computation of differences, multiplication, and division.

Instrumental Measures

Measurements obtained using electronic instrumentation for physical variables, such as airflow.

Observer Measures

Measurements of behavior variables, such as language or speech variables.

Examples of Nominal Measurement

Gender, hair color, and favorite fruit, where categories are distinct but do not have numerical value.

Examples of Ordinal Measurement

Satisfaction levels, rankings in a race, and education levels, where order matters but differences are not equal.

Examples of Interval Measurement

Temperature, IQ scores, and dates on a calendar, where intervals are equal but there is no true zero.

Examples of Ratio Measurement

Length, weight, height, and time, where there are equal intervals and a true zero point.

Statistical Operations

Mathematical operations applicable to measurements made with each type of scale, varying by the level of measurement.

Yoga Study Example

Using different levels of measurement to categorize participants based on yoga practice and assess their well-being.