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# Measurement pt. 2

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### Measurement pt. 2

1. 1. More Measurement <ul><li>Andrew Martin </li></ul><ul><li>PS 372 </li></ul>
2. 2. Level of Measurement <ul><li>Level of measurement is the extent or degree to which the values of variables can be compared and mathematically manipulated. </li></ul>
3. 3. Level of Measurement <ul><li>The level of measurement depends on the type of information the measurement contains. </li></ul><ul><li>Varying levels of measurement allow political scientists to make varying claims. </li></ul><ul><li>In particular, the relationship between the variables and the numbers is key. </li></ul>
4. 4. Levels of Measurement <ul><li>Ratio </li></ul><ul><li>Interval </li></ul><ul><li>Ordinal </li></ul><ul><li>Nominal </li></ul>Nominal Ordinal Interval Ratio
5. 5. Nominal Level Nachmias-Nachmias (2000)‏ <ul><li>The nominal level of measurement refers to the most basic level of measurement. </li></ul><ul><li>At the nominal level , numbers or symbols are used to classify objects or events into categories that are names or classes of other characteristics. </li></ul><ul><li>There is no mathematical relationship between categories. Each category has an equivalent relationship. </li></ul>
6. 6. Nominal Level <ul><li>or </li></ul>
7. 7. Ordinal Level Nachmias-Nachmias (2000)‏ <ul><li>Ordinal level measurement allows for a complete ranking of all observations, though the distance between observations cannot be precisely measured. </li></ul><ul><li>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. </li></ul>
8. 8. Ordinal Level Nachmias-Nachmias (2000) <ul><li>Has three important logical properties: </li></ul><ul><li>1. Irreflexive </li></ul><ul><li>For any value of a , a > a </li></ul><ul><li>For any a, it is not true that a > a </li></ul><ul><li>2. Asymmetry </li></ul><ul><li>If a > b , then b > a </li></ul><ul><li>3. Transitivity </li></ul><ul><li>If a > b and b > c , then a > c </li></ul>
9. 9. Ordinal Level
10. 10. Ordinal Level
11. 11. Ordinal Level
12. 12. Ordinal Level Nachmias-Nachmias (2000) <ul><li>Surveys use ordinal scales. </li></ul><ul><li>Ex: Political efficacy question: Do you agree with the following statement? “People like me have a lot of influence on gov't decisions.” </li></ul>
13. 13. Interval Level Nachmias-Nachmias (2000) <ul><li>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. </li></ul>
14. 14. Interval Level Nachmias-Nachmias (2000) <ul><li>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. </li></ul>
15. 15. Properties of interval measures Nachmias-Nachmias (2000) <ul><li>1. Uniqueness : If a and b stand for real numbers, then a + b and a * b represent only one real number. </li></ul><ul><li>2. Symmetry : If a = b , then b = a </li></ul><ul><li>3. Commutation: If a and b denote real numbers, then a + b = b + a . </li></ul>
16. 16. Properties of interval measures Nachmias-Nachmias (2000) <ul><li>4. Substitution: If a = b and a + c = d , then b + c = d ; and if a = b and ac = d , then bc = d </li></ul><ul><li>5. Association: If a , b and c stand for real numbers, then ( a + b ) + c = a + ( b + c ), and ( ab ) c = a ( bc )‏ </li></ul><ul><li>Examples: Income, SAT scores, years </li></ul>
17. 17. Ratio Level Nachmias-Nachmias (2000) <ul><li>The ratio level of measurement has the same properties as the interval level with one exception: the absolute zero point. </li></ul><ul><li>In other words, we apply the arithmetic operations and numbers to the total amount measured from the absolute zero point, not some arbitrary point. </li></ul><ul><li>Examples: Weight, age, unemployment rate, % vote </li></ul>
18. 18. Levels of Measurement
19. 19. Measurement Indexes <ul><li>A summation index is a method of accumulating scores on individual items to form a composite measure of a complex phenomenon. </li></ul>
20. 21. Factor Analysis <ul><li>Factor analysis a statistical technique useful in the construction of multi-item scales to measure abstract concepts. </li></ul>