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Statistic Level of Measurement
Level of measurement refers to the degree to which variables can be compared and mathematically manipulated. There are four levels of measurement: nominal, ordinal, interval, and ratio. Nominal measurement involves categorizing variables without mathematical relationships between categories. Ordinal measurement allows ranking but not precise measurement of distances between ranks. Interval measurement assigns real numbers with equal units of measurement and mathematical properties. Ratio measurement has all interval properties plus an absolute zero point.
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Statistic Level of Measurement
- 1. Level of Measurement DebraWallace
- 2. Level of Measurement Levelof measurement is the extent or degree to which the values of variables can be compared and mathematically manipulated.
- 3. Level of Measurement Thelevel of measurement depends on the type of information the measurement contains. The relationship between the variables and the numbers is key.
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- 5. Nominal Level Nachmias-Nachmias (2000) Thenominal 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.
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- 7. Ordinal Level Nachmias-Nachmias (2000) Ordinallevel 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.
- 8. Ordinal Level Nachmias-Nachmias (2000) Hasthree important logical properties: 1. Irreflexive For any value of a, a > a For any a, it is not true that a > a 2. Asymmetry If a > b, then b > a 3. Transitivity If a > b and b > c, then a > c
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- 12. Ordinal Level Nachmias-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.”
- 13. Interval Level Nachmias-Nachmias (2000) Intervallevel 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.
- 14. Interval Level Nachmias-Nachmias (2000) Intervallevel 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.
- 15. Properties of intervalmeasures Nachmias-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.
- 16. Properties of intervalmeasures Nachmias-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
- 17. Ratio Level Nachmias-Nachmias (2000) Theratio 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