Chapter 8: Principles of Measurement

Define measurement

The process of assigning numerals to variables to represent quantities of characteristics according to specific rules.

What is the primary purpose of measurement?

To provide a basis for choosing between two courses of action.

What defines a 'variable' in the context of clinical measurement?

A property that can differentiate individuals or objects by having more than one possible value.

A variable represents an attribute that can have values denoting what?

An attribute that can have more than one value, either a quantity (e.g., height) or a/an attribute (e.g., sex)

In measurement theory, how is a 'numeral' distinguished from a 'number'?

A numeral is used as a label without quantitative meaning, whereas a number represents a known quantity.

What is the term for a measure that only allows for two possible values, such as 'Yes' or 'No'?

Dichotomous

What is the term for a measure where multiple values are possible?

Polytomous

Define continuous Variable

A variable that can theoretically take on any value along a continuum within a defined range.

What factor generally limits the precision of continuous variable measurements?

The precision of the measuring instrument.

Define discrete variable

A variable described only in whole integer units

What is an example of a discrete variable

Heart rate in bpm

What is precision

The exactness of a measure

In measurement, how is 'precision' statistically reflected?

By the number of decimal places (or digits of precision) in the value.

Measurement values are sensitive to what two primary factors

The variable itself
Measurement tool's sensitivity

Why is Range of Motion (ROM) measured in degrees considered a 'direct' measure?

It involves the direct observation of a physical property.

How is an 'indirect measure' defined?

A measure of a proxy used to represent the actual property

What does a recording of Electromyography (EMG) serve as an indirect measure of?

Muscle activation

Define construct

An abstract variable that is not unidimensional or absolute, such as pain or confidence.

Because constructs have no absolute measures, they must define what

How we choose measure a “latent trait”

Why are criteria (rules) needed when assigning units and values for a measure

So the levels of the measure can be objectively differentiated or equated

List the four levels of measurement in the hierarchy from lowest to highest.

Nominal, Ordinal, Interval, and Ratio.

What is the primary classificatory purpose of the nominal scale?

To assign subjects into mutually exclusive and exhaustive categories.

In a nominal scale, categories must be exhaustive … why?

Such that all subjects can be assigned to one.

Which two statistical methods are typically used to assess nominal data?

Frequency counts and group proportions.

Handedness and sex are examples of which level of measurement?

Nominal scale

What is the defining characteristic of an 'ordinal scale'?

Numbers indicate a rank order with a 'greater than/less than' relationship.

Why are arithmetic operations (e.g., addition, division) prohibited for ordinal data?

The intervals between ranks are inconsistent or unknown.

Manual Muscle Test (MMT) grading and Likert scales (Strongly Agree to Strongly Disagree) are examples of which measurement level?

Ordinal scale

How does an interval scale differ from an ordinal scale?

It demonstrates known and equal intervals between consecutive values in addition to rank order.

What is the status of the 'zero point' in an interval scale?

It is an artificial zero that does not indicate the total absence of the variable.

Fahrenheit and Celsius temperature scales are examples of which measurement level

Interval scale

What arithmetic limitation exists for interval scale data due to the lack of a true zero?

Ratios cannot be developed (e.g., 20∘C is not 'twice' as hot as 10∘C).

Define ratio scale

The highest level of measurement, possessing equal intervals and an absolute zero representing the absence of the attribute.

Why are negative numbers not possible on a ratio scale?

The scale starts at an absolute zero that represents the total absence of the trait.

Force, height, and weight are examples of which level of measurement?

Ratio scale

What types of arithmetic and statistical operations are permitted for ratio level data?

All statistical and arithmetic operations are permissible.

If a researcher ranks step lengths from shortest to longest, what level of measurement is being used?

Ordinal scale

If a researcher uses a cut-point to label step lengths as 'Long' or 'Short', what level of measurement is being used?

Nominal scale

If step length is measured precisely in centimeters with a tape measure, what level of measurement is being used?

Ratio scale

Parametric statistics require data from which two levels of measurement?

Interval or Ratio.

Nonparametric statistics are specifically designed for which two levels of measurement?

Nominal and Ordinal.

A measurement of 50.3∘ compared to 50∘ is an example of increased _____.

Precision

In measurement hierarchy, which level is considered the 'lowest'?

Nominal

Which level of measurement allows for the determination of relative difference and equivalence but lacks a true zero?

Interval scale

What type of variable is 'Number of athletes on a team'?

Discrete variable

What type of variable is 'Distance'?

Continuous variable

Is it possible to operationally re-define a ratio-level variable at a nominal level?

Yes, it is always possible to re-define a variable at a lower level.

What level of measurement is used when coding subjective data from '1' (Strongly Disagree) to '5' (Strongly Agree)?

Ordinal (using numerals as labels for rank).

Why is 'Pain' classified as a construct?

It is an abstract variable without a single, absolute unidimensional measure.

What is the requirement for nominal categories to be 'mutually exclusive'?

A subject can only belong to one category.

Which level of measurement is characterized by 'Relative Order' but lacks known intervals?

Ordinal scale

True or False: Measurement is the process of assigning numerals to variables according to random selection.

False (it must be according to certain rules).

What statistical operation is permissible for Nominal data but NOT for Ratio data to compare groups?

None (Ratio data allows all operations allowed by Nominal data).

Temperature measured in Celsius is which level of measurement?

Interval scale

The use of a proxy, like height of mercury for temperature, is necessary for _ measures.

Indirect