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Measurement pt. 2
 

Measurement pt. 2

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    Measurement pt. 2 Measurement pt. 2 Presentation 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.