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measurements and level of meaurments
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Levels of MeasurementLevels of Measurement
The Levels of MeasurementThe Levels of Measurement
� NominalNominal� OrdinalOrdinal� IntervalInterval� RatioRatio
Some DefinitionsSome Definitions
VariableVariableVariableVariable
Some DefinitionsSome Definitions
VariableVariableVariableVariable
AttributeAttributeAttributeAttribute AttributeAttributeAttributeAttribute
Some DefinitionsSome Definitions
GenderGenderGenderGenderVariableVariableVariableVariable
AttributeAttributeAttributeAttribute AttributeAttributeAttributeAttribute
Some DefinitionsSome Definitions
GenderGenderGenderGender
FemaleFemaleFemaleFemale MaleMaleMaleMale
VariableVariableVariableVariable
AttributeAttributeAttributeAttribute AttributeAttributeAttributeAttribute
Qualities of VariablesQualities of Variables
� ExhaustiveExhaustive -- Should include all -- Should include all possible answerable responses.possible answerable responses.
� Mutually exclusive Mutually exclusive -- No respondent -- No respondent should be able to have two attributes should be able to have two attributes simultaneously (for example, employed simultaneously (for example, employed vs. unemployed -- it is possible to be vs. unemployed -- it is possible to be both if looking for a second job while both if looking for a second job while employed).employed).
What Is Level of Measurement?What Is Level of Measurement?
The relationship of the values that are The relationship of the values that are assigned to the attributes for a variableassigned to the attributes for a variable
What Is Level of Measurement?What Is Level of Measurement?
The The relationshiprelationship of the values that are of the values that are assigned to the attributes for a variableassigned to the attributes for a variable
RelationshipRelationshipRelationshipRelationship
What Is Level of Measurement?What Is Level of Measurement?
The relationship The relationship of the values of the values that are that are assigned to the attributes for a variableassigned to the attributes for a variable
11 22 33
RelationshipRelationshipRelationshipRelationship
ValuesValuesValuesValues
What Is Level of Measurement?What Is Level of Measurement?
The relationship of the values The relationship of the values that are that are assigned to the attributes assigned to the attributes for a variablefor a variable
11 22 33
RelationshipRelationshipRelationshipRelationship
ValuesValuesValuesValues
AttributesAttributesAttributesAttributes RepublicanRepublican IndependentIndependent DemocratDemocrat
What Is Level of Measurement?What Is Level of Measurement?
The relationship of the values that are The relationship of the values that are assigned to the attributes assigned to the attributes for a variablefor a variable
11 22 33
RelationshipRelationshipRelationshipRelationship
ValuesValuesValuesValues
AttributesAttributesAttributesAttributes
VariableVariableVariableVariable
RepublicanRepublican IndependentIndependent DemocratDemocrat
Party AffiliationParty Affiliation
Why Is Level of Measurement Why Is Level of Measurement Important?Important?
� Helps you decide what Helps you decide what statistical statistical analysis analysis is appropriate on the values is appropriate on the values that were assignedthat were assigned
� Helps you decide how to Helps you decide how to interpretinterpret the the data from that variabledata from that variable
Nominal MeasurementNominal Measurement
� The values “The values “namename” the attribute ” the attribute uniquely.uniquely.
Nominal MeasurementNominal Measurement
� The values “The values “namename” the attribute ” the attribute uniquely.uniquely.
� The name does The name does notnot imply any imply any ordering of the cases.ordering of the cases.
Nominal MeasurementNominal Measurement
� The values “The values “namename” the attribute ” the attribute uniquely.uniquely.
� The value does The value does notnot imply any imply any ordering of the cases, for example, ordering of the cases, for example, jersey numbers in football.jersey numbers in football.
Nominal MeasurementNominal Measurement
� The values “The values “namename” the attribute ” the attribute uniquely.uniquely.
� The value does The value does notnot imply any imply any ordering of the cases, for example, ordering of the cases, for example, jersey numbers in football.jersey numbers in football.
� Even though player 32 has Even though player 32 has higher higher number number than player 19, you can’t say than player 19, you can’t say from the data that he’s from the data that he’s greatergreater than or than or moremore than the other. than the other.
Ordinal MeasurementOrdinal Measurement
When attributes can be When attributes can be rank-orderedrank-ordered……
Ordinal MeasurementOrdinal Measurement
When attributes can be When attributes can be rank-orderedrank-ordered……� Distances between attributes Distances between attributes do not do not
have any meaninghave any meaning..
Ordinal MeasurementOrdinal Measurement
When attributes can be When attributes can be rank-orderedrank-ordered……� Distances between attributes Distances between attributes do not do not
have any meaninghave any meaning,for example, code ,for example, code Educational Attainment as 0=less Educational Attainment as 0=less than H.S.; 1=some H.S.; 2=H.S. than H.S.; 1=some H.S.; 2=H.S. degree; 3=some college; 4=college degree; 3=some college; 4=college degree; 5=post collegedegree; 5=post college
Ordinal MeasurementOrdinal Measurement
When attributes can be When attributes can be rank-orderedrank-ordered……� Distances between attributes Distances between attributes do not do not
have any meaninghave any meaning,for example, code ,for example, code Educational Attainment as 0=less Educational Attainment as 0=less than H.S.; 1=some H.S.; 2=H.S. than H.S.; 1=some H.S.; 2=H.S. degree; 3=some college; 4=college degree; 3=some college; 4=college degree; 5=post collegedegree; 5=post college
Is the distance from 0 to 1 the same as Is the distance from 0 to 1 the same as 3 to 4?3 to 4?
Interval MeasurementInterval Measurement
When When distancedistance between attributes has between attributes has meaning…meaning…
Interval MeasurementInterval Measurement
When When distancedistance between attributes has between attributes has meaning, for example, temperature (in meaning, for example, temperature (in Fahrenheit) -- distance from 30-40 is Fahrenheit) -- distance from 30-40 is same as distance from 70-80same as distance from 70-80
Interval MeasurementInterval Measurement
When When distancedistance between attributes has between attributes has meaning, for example, temperature (in meaning, for example, temperature (in Fahrenheit) -- distance from 30-40 is Fahrenheit) -- distance from 30-40 is same as distance from 70-80same as distance from 70-80
� Note that Note that ratios don’t make any sense -ratios don’t make any sense -- - 80 degrees is not 80 degrees is not twicetwice as hot as 40 as hot as 40 degrees (although the attribute values degrees (although the attribute values are).are).
Ratio MeasurementRatio Measurement
� Has an Has an absolute zero absolute zero that is meaningfulthat is meaningful
Ratio MeasurementRatio Measurement
� Has an Has an absolute zero absolute zero that is meaningfulthat is meaningful� Can construct a meaningful Can construct a meaningful ratioratio
(fraction)(fraction)
Ratio MeasurementRatio Measurement
� Has an Has an absolute zero absolute zero that is meaningfulthat is meaningful� Can construct a meaningful Can construct a meaningful ratioratio
(fraction), for example, number of (fraction), for example, number of clients in past six monthsclients in past six months
Ratio MeasurementRatio Measurement
� Has an Has an absolute zero absolute zero that is meaningfulthat is meaningful� Can construct a meaningful Can construct a meaningful ratioratio
(fraction), for example, number of (fraction), for example, number of clients in past six monthsclients in past six months
� It is meaningful to say that “...we had It is meaningful to say that “...we had twicetwice as many clients in this period as as many clients in this period as we did in the previous six months.we did in the previous six months.
The Hierarchy of LevelsThe Hierarchy of Levels
NominalNominalNominalNominal
The Hierarchy of LevelsThe Hierarchy of Levels
NominalNominalNominalNominal Attributes are only named; weakest
The Hierarchy of LevelsThe Hierarchy of Levels
NominalNominalNominalNominal Attributes are only named; weakest
OrdinalOrdinalOrdinalOrdinal
The Hierarchy of LevelsThe Hierarchy of Levels
NominalNominalNominalNominal Attributes are only named; weakest
Attributes can be orderedOrdinalOrdinalOrdinalOrdinal
The Hierarchy of LevelsThe Hierarchy of Levels
NominalNominalNominalNominal
IntervalIntervalIntervalInterval
Attributes are only named; weakest
Attributes can be orderedOrdinalOrdinalOrdinalOrdinal
The Hierarchy of LevelsThe Hierarchy of Levels
NominalNominalNominalNominal
IntervalIntervalIntervalInterval
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
OrdinalOrdinalOrdinalOrdinal
The Hierarchy of LevelsThe Hierarchy of Levels
NominalNominalNominalNominal
IntervalIntervalIntervalInterval
RatioRatioRatioRatio
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
OrdinalOrdinalOrdinalOrdinal
The Hierarchy of LevelsThe Hierarchy of Levels
NominalNominalNominalNominal
IntervalIntervalIntervalInterval
RatioRatioRatioRatio
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
Absolute zero
OrdinalOrdinalOrdinalOrdinal