Statistic Level of Measurement

Level of Measurement

Debra Wallace

Level of Measurement

Level of measurement is the extent or degree to which the values of variables can be compared and mathematically manipulated.

Level of Measurement

The level of measurement depends on the type of information the measurement contains.

The relationship between the variables and the numbers is key.

Levels of Measurement

Ratio

Interval

Ordinal

NominalNominal

Ordinal

Interval

Ratio

Nominal LevelNachmias-Nachmias (2000)

The nominal level of measurement refers to the most basic level of measurement.

At the nominal level, numbers or symbols are used to classify objects or events into categories that are names or classes of other characteristics.

There is no mathematical relationship between categories. Each category has an equivalent relationship.

Nominal Level

or

Ordinal LevelNachmias-Nachmias (2000)

Ordinal level measurement allows for a complete ranking of all observations, though the distance between observations cannot be precisely measured.

Rank values indicate rank but do not indicate that the intervals or size of the difference between the ranks are equal, nor do they indicate absolute quantities.

Ordinal LevelNachmias-Nachmias (2000)

Has three important logical properties:

1. Irreflexive For any value of a, a > a

For any a, it is not true that a > a

2. AsymmetryIf a > b, then b > a

3. TransitivityIf a > b and b > c, then a > c

Ordinal Level

Ordinal Level

Ordinal Level

Ordinal LevelNachmias-Nachmias (2000)

● Surveys use ordinal scales.

● Ex: Political efficacy question: Do you agree with the following statement? “People like me have a lot of influence on gov't decisions.”

Interval LevelNachmias-Nachmias (2000)

Interval level measurements are characterized by a common and constant, fixed and equal unit of measurement that assigns a real number to all the objects in the ordered set.

Interval LevelNachmias-Nachmias (2000)

Interval level measurements are isomorphic, meaning there is similarity or identity in structure between the properties of a variable and the properties of the instrument used to measure it.

Properties of interval measuresNachmias-Nachmias (2000)

1. Uniqueness: If a and b stand for real numbers, then a + b and a * b represent only one real number.

2. Symmetry: If a = b, then b = a

3. Commutation: If a and b denote real numbers, then a + b = b + a.

Properties of interval measuresNachmias-Nachmias (2000)

4. Substitution: If a = b and a + c = d, then b + c = d; and if a = b and ac = d, then bc = d

5. Association: If a, b and c stand for real numbers, then (a + b) + c = a + (b + c), and (ab)c = a(bc)

Examples: Income, SAT scores, years

Ratio LevelNachmias-Nachmias (2000)

The ratio level of measurement has the same properties as the interval level with one exception: the absolute zero point.

In other words, we apply the arithmetic operations and numbers to the total amount measured from the absolute zero point, not some arbitrary point.

Examples: Weight, age, unemployment rate, % vote