M e a s u r e m e n t

Hard: concrete concepts Soft : abstract concepts (construct) What is Measurement? DATA: Hard: concrete concepts Soft : abstract concepts (construct)

Alternative definition Measurement is the process of linking abstract concepts to empirical indicants. Zellar & Carmines

Concepts Indicants Weight Distance Depression Test anxiety Marital satisfaction Pounds/grams/tons meters, kilometers ?????

Some Definitions Variable

Some Definitions Variable Attribute

Some Definitions Variable Gender Attribute

Some Definitions Variable Gender Attribute Female Male

Qualities of Variables exhaustive - should include all possible answerable responses mutually exclusive - no respondent should be able to have two attributes simultaneously (e.g., employed vs. unemployed - it is possible to be both if looking for a second job while employed)

Levels of Measurement

The Levels of Measurement Nominal Ordinal Interval Ratio

Nominal Measurement the values just “name” the attribute uniquely

Nominal Measurement the values just “name” the attribute uniquely does not imply any ordering of the cases

Nominal Measurement the values just “name” the attribute uniquely does not imply any ordering of the cases for example, jersey numbers in football

Nominal Measurement the values just “name” the attribute uniquely does not imply any ordering of the cases for example, jersey numbers in football even though player 10 has higher number than player 5, you can’t say from the data that he’s greater than or more than the other

Ordinal Measurement when attributes can be rank-ordered distances between attributes do not have any meaning for example, code Educational Attainment as 0=less than H.S. 1=H.S. degree 3=M.S. degree 4=Phd degree is distance from 0 to 1 same as 3 to 4?

Interval Measurement when distance between attributes has meaning

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

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

Ratio Measurement has an absolute zero that is meaningful

Ratio Measurement has an absolute zero that is meaningful can construct a meaningful ratio (fraction)

Ratio Measurement has an absolute zero that is meaningful can construct a meaningful ratio (fraction) for example,number of clients in past six months

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

Why is Level of Measurement Important? helps you decide what statistical analysis is appropriate on the values that were assigned helps you decide how to interpet the data from that variable

The Hierarchy of Levels Nominal

The Hierarchy of Levels Nominal Attributes are only named; weakest

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

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

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

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

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

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

Scales and Scaling

General Issues in Scaling

What is a scale? the assignment...

What is a scale? the assignment... ...of objects... Are you willing to permit immigrants to live in your country? Are you willing to permit immigrants to live in your neighborhood? Would you let your child marry an immigrant?

What is a scale? the assignment... ...of objects... ...to numbers... Are you willing to permit immigrants to live in your country? Are you willing to permit immigrants to live in your neighborhood? Would you let your child marry an immigrant?

What is a scale? the assignment... ...of objects... ...to numbers... Are you willing to permit immigrants to live in your country? Are you willing to permit immigrants to live in your neighborhood? Would you let your child marry an immigrant? ...according to a rule...

What is a scale? the assignment... ...of objects... ...to numbers... Are you willing to permit immigrants to live in your country? Are you willing to permit immigrants to live in your neighborhood? Would you let your child marry an immigrant? cumulative ...according to a rule...

Scale versus Response Scale

Scale versus Response Scale results from a process

Scale versus Response Scale is used to collect the response for an item results from a process

Scale versus Response Scale is used to collect the response for an item results from a process each item on scale has a scale value

Scale versus Response Scale is used to collect the response for an item results from a process each item on scale has a scale value item not associated with a scale value

Scale versus Response Scale is used to collect the response for an item results from a process each item on scale has a scale value item not associated with a scale value refers to a set of items

Scale versus Response Scale is used to collect the response for an item results from a process each item on scale has a scale value item not associated with a scale value refers to a set of items used for a single item

Purposes of Scaling hypothesis testing is the construct or concept a single dimensional one? what dimensions underlie some ratings? for assigning values to responses exploration scoring

Dimensionality One-dimensional Constructs

Dimensionality One-dimensional Constructs height

Dimensionality One-dimensional Constructs height shorter taller

Dimensionality One-dimensional Constructs height shorter taller thirst

Dimensionality One-dimensional Constructs height thirst shorter taller less thirsty more thirsty

Dimensionality One-dimensional Constructs height thirst self esteem shorter taller thirst less thirsty more thirsty self esteem

Dimensionality One-dimensional Constructs height thirst self esteem shorter taller thirst less thirsty more thirsty self esteem less more

Dimensionality Two-dimensional Construct

Dimensionality Two-dimensional Construct academic ability

Dimensionality Two-dimensional Construct academic ability verbal

Dimensionality Two-dimensional Construct academic ability verbal worse better

Dimensionality quantitative Two-dimensional Construct academic ability verbal worse better

Dimensionality quantitative Two-dimensional Construct academic ability better academic ability verbal worse better worse

Dimensionality Three-dimensional Construct

Dimensionality Three-dimensional Construct

Dimensionality semantic differential (meaning) Three-dimensional Construct

Dimensionality semantic differential (meaning) Three-dimensional Construct evaluation

Dimensionality semantic differential (meaning) Three-dimensional Construct evaluation unfavorable favorable

Dimensionality semantic differential (meaning) Three-dimensional Construct potency evaluation unfavorable favorable

Dimensionality semantic differential (meaning) Three-dimensional Construct potency powerful evaluation powerless unfavorable favorable

Dimensionality semantic differential (meaning) Three-dimensional Construct activity potency powerful evaluation powerless unfavorable favorable

Dimensionality semantic differential Three-dimensional Construct active activity potency powerful evaluation passive powerless unfavorable favorable

Types of Scales Unidimensional Multidimensional easier to understand usefule for understanding multidimensional many concepts may be unidimensional reflect multiple properties simultaneously Multidimensional

The Major Unidimensional Scale Types Thurstone Likert Guttman