1. Levels of Measurement

2. The Levels of Measurement l Nominal l Ordinal l Interval l Ratio

3. Some Definitions VariableVariable

4. VariableVariable AttributeAttributeAttributeAttribute

5. GenderGenderVariableVariable AttributeAttributeAttributeAttribute

6. GenderGender FemaleFemaleMaleMale VariableVariable AttributeAttributeAttributeAttribute

7. Qualities of Variables l Exhaustive -- Should include all possible answerable responses. l Mutually exclusive -- No respondent should be able to have two attributes simultaneously (for example, employed vs. unemployed -- it is possible to be both if looking for a second job while employed).

8. What Is Level of Measurement? The relationship of the values that are assigned to the attributes for a variable

9. What Is Level of Measurement? The relationship of the values that are assigned to the attributes for a variable Relationship

10. What Is Level of Measurement? The relationship of the values that are assigned to the attributes for a variable 123 Relationship Values

11. What Is Level of Measurement? The relationship of the values that are assigned to the attributes for a variable 123 Relationship Values Attributes RepublicanIndependentDemocrat

12. What Is Level of Measurement? The relationship of the values that are assigned to the attributes for a variable 123 Relationship Values Attributes Variable RepublicanIndependentDemocrat Party Affiliation

13. Why Is Level of Measurement Important? l Helps you decide what statistical analysis is appropriate on the values that were assigned l Helps you decide how to interpret the data from that variable

14. Nominal Measurement l The values “name” the attribute uniquely.

15. Nominal Measurement l The values “name” the attribute uniquely. l The name does not imply any ordering of the cases.

16. Nominal Measurement l The values “name” the attribute uniquely. l The value does not imply any ordering of the cases, for example, jersey numbers in football.

17. Nominal Measurement l The values “name” the attribute uniquely. l The value does not imply any ordering of the cases, for example, jersey numbers in football. l Even though player 32 has higher number than player 19, you can’t say from the data that he’s greater than or more than the other.

18. Ordinal Measurement When attributes can be rank-ordered…

19. Ordinal Measurement When attributes can be rank-ordered… l Distances between attributes do not have any meaning.

20. Ordinal Measurement When attributes can be rank-ordered… l Distances between attributes do not have any meaning,for example, code Educational Attainment as 0=less than H.S.; 1=some H.S.; 2=H.S. degree; 3=some college; 4=college degree; 5=post college

21. Ordinal Measurement When attributes can be rank-ordered… l Distances between attributes do not have any meaning,for example, code Educational Attainment as 0=less than H.S.; 1=some H.S.; 2=H.S. degree; 3=some college; 4=college degree; 5=post college Is the distance from 0 to 1 the same as 3 to 4?

22. Interval Measurement When distance between attributes has meaning…

23. Interval Measurement When distance between attributes has meaning, for example, temperature (in Fahrenheit) -- distance from 30-40 is same as distance from 70-80

24. Interval Measurement When distance between attributes has meaning, for example, temperature (in Fahrenheit) -- distance from 30-40 is same as distance from 70-80 l Note that ratios don’t make any sense -- 80 degrees is not twice as hot as 40 degrees (although the attribute values are).

25. Ratio Measurement l Has an absolute zero that is meaningful

26. Ratio Measurement l Has an absolute zero that is meaningful l Can construct a meaningful ratio (fraction)

27. Ratio Measurement l Has an absolute zero that is meaningful l Can construct a meaningful ratio (fraction), for example, number of clients in past six months

28. Ratio Measurement l Has an absolute zero that is meaningful l Can construct a meaningful ratio (fraction), for example, number of clients in past six months l It is meaningful to say that “...we had twice as many clients in this period as we did in the previous six months.

29. The Hierarchy of Levels Nominal

30. Nominal Attributes are only named; weakest

31. The Hierarchy of Levels Nominal Attributes are only named; weakest Ordinal

32. The Hierarchy of Levels Nominal Attributes are only named; weakest Attributes can be ordered Ordinal

33. The Hierarchy of Levels Nominal Interval Attributes are only named; weakest Attributes can be ordered Ordinal

34. The Hierarchy of Levels Nominal Interval Attributes are only named; weakest Attributes can be ordered Distance is meaningful Ordinal

35. The Hierarchy of Levels Nominal Interval Ratio Attributes are only named; weakest Attributes can be ordered Distance is meaningful Ordinal

36. The Hierarchy of Levels Nominal Interval Ratio Attributes are only named; weakest Attributes can be ordered Distance is meaningful Absolute zero Ordinal