Variables and Measurement Scales

Variable

An attribute that takes on different values across persons or items (e.g., GPA, IQ, reaction time). In the textbook, a variable is defined as the concrete data object resulting from applying a measure to a theoretical construct in the world. (Slide 2; Transcript 00:00:27; Textbook p. 15)

Nominal Scale

Responses grouped into qualitative, mutually exclusive categories with no inherent rank order, where arithmetic operations cannot be performed. The professor emphasized that categories cannot be ordered from higher to lower or better to worse (e.g., marital status categorized into 5 groups: never married, married/partner, widowed, divorced, separated; sex; pet type; high school attended). The textbook notes that nominal variables only indicate that categories are different. (Slide 5, 11; Transcript 00:21:05, 00:35:06; Textbook p. 16)

Ordinal Scale

Responses grouped into categories with a natural, meaningful rank order, but where categories are not equidistant and arithmetic operations remain impossible. The professor illustrated this with academic degrees (Bachelor, Master, Ph.D.), letter grades (A, B, C, D, F), home value trends (increase, same, decrease), and Olympic medals, noting that the knowledge difference between a B and a C is not equal to that between an A and a B. The textbook notes that while responses can be ranked (e.g., finishing position in a race), the intervals are unknown and averaging them produces meaningless results. (Slide 5, 6, 12; Transcript 00:29:28, 00:34:50; Textbook pp. 16–18)

Interval Scale

A numerical scale where the difference/interval between measurements is meaningful and equal across the scale (equal distance), allowing addition and subtraction, but lacking a clear/true definition of zero (0 does not mean absence of the attribute). The professor highlighted Fahrenheit and Celsius temperature scales as classic examples (where 10° vs. 20° is the same 10° difference as 80° vs. 90°, but 0° does not mean "no heat" and 10° is not twice 5°). The textbook adds starting year in university as an interval scale, where multiplication or division is meaningless. (Slide 7, 8; Transcript 00:01:59, 00:02:52, 00:04:39; Textbook p. 18)

Ratio Scale

A numerical scale possessing all properties of an interval scale plus a clear, non-arbitrary definition of zero, where 0 indicates complete absence of the variable. This clear zero enables meaningful ratio calculations (e.g., "twice as long"). The professor provided examples including height, age, weight, exam length (a 50-question final is twice as long as a 25-question midterm), and number of items on a questionnaire (0 items means no questionnaire). The textbook adds response time (RT) in seconds. (Slide 8; Transcript 00:03:34, 00:13:45, 00:58:35; Textbook p. 18)

Continuous Variable

A variable where, for any two given values, it is always logically possible to have another value in between. The professor noted that continuous variables allow infinite decimal precision depending on how data is recorded (e.g., age measured as 2.5321 years, reaction time in seconds, or exact liquid volume). The textbook reinforces this using response time and temperature as examples. (Slide 9, 10; Transcript 00:14:27, 00:15:01, 00:25:15; Textbook pp. 18–19)

Discrete Variable

A variable with separate, distinct values where intermediate values do not logically exist. The professor emphasized that all categorical variables (nominal and ordinal) are discrete (e.g., cat vs. dog, clothing sizes), alongside certain numerical variables like college year, number of pets owned, or questionnaire item counts (e.g., one cannot own 1.5 pets). The textbook confirms that nominal and ordinal scales are always discrete, while interval and ratio scales can be discrete (e.g., calendar year, correct answer count) or continuous. (Slide 10; Transcript 00:15:17, 00:17:12, 00:18:05; Textbook pp. 18–20)

Quasi-Interval Scale (Likert Scale)

Rating scale items (e.g., 4- or 5-point Likert scales ranging from 1 = "never" to 5 = "always") that are technically ordinal because equal numerical distance cannot be proven, but are treated by researchers as "fake" or quasi-interval variables to allow numerical data analysis. The professor explained that analyzing Likert scales as categorical data requires complex methods like logistic regression, so statisticians compromise by assuming equal distances. The textbook notes that while Likert scales lack a natural zero or proven equal intervals, participants act as if intervals are equal, so researchers treat them as quasi-interval. (Slide 13; Transcript 00:44:50, 00:45:20, 00:50:40; Textbook pp. 20–21)

Theoretical Construct

The underlying, unobservable, or abstract idea, concept, or attribute that a researcher seeks to measure (e.g., age, gender, or opinion). (Textbook p. 15)

Measure

The specific tool, method, or instrument used to make empirical observations or collect data (e.g., a survey question, behavioral observation, or brain scan). (Textbook p. 15)

Operationalisation

The formal process of taking a vague or abstract theoretical construct and turning it into a precise, concrete measurement with defined allowable values and procedures. (Textbook pp. 13–15)

Reliability

The consistency or precision of a measurement tool; indicates how consistently a measure yields the same result under identical conditions. (Textbook p. 22)

Test-retest Reliability

The consistency of a measure over time; evaluated by administering the same test to the same individuals at a later date and comparing the scores. (Textbook p. 22)

Inter-rater Reliability

The consistency of a measure across different human observers or raters; evaluated by checking the level of agreement between independent raters assessing the same phenomenon. (Textbook p. 22)

Parallel Forms Reliability

The consistency of results across two theoretically equivalent forms or versions of the same measurement tool. (Textbook p. 22)

```