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# Measurement pt. 2

## on Sep 29, 2010

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## Measurement pt. 2Presentation Transcript

• More Measurement
• Andrew Martin
• PS 372
• 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.
• Varying levels of measurement allow political scientists to make varying claims.
• In particular, the relationship between the variables and the numbers is key.
• Levels of Measurement
• Ratio
• Interval
• Ordinal
• Nominal
Nominal Ordinal Interval Ratio
• Nominal Level Nachmias-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 Level Nachmias-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 Level Nachmias-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. Asymmetry
• If a > b , then b > a
• 3. Transitivity
• If a > b and b > c , then a > c
• Ordinal Level
• Ordinal Level
• Ordinal Level
• 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.”
• Interval Level Nachmias-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 Level Nachmias-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 measures 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 .
• Properties of interval measures 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
• Ratio Level Nachmias-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
• Levels of Measurement
• Measurement Indexes
• A summation index is a method of accumulating scores on individual items to form a composite measure of a complex phenomenon.
•
• Factor Analysis
• Factor analysis a statistical technique useful in the construction of multi-item scales to measure abstract concepts.