measurement levels

Levels of MeasurementLevels of Measurement

The Levels of MeasurementThe Levels of Measurement

� NominalNominal� OrdinalOrdinal� IntervalInterval� RatioRatio

Some DefinitionsSome Definitions

VariableVariableVariableVariable



AttributeAttributeAttributeAttribute AttributeAttributeAttributeAttribute


GenderGenderGenderGenderVariableVariableVariableVariable



GenderGenderGenderGender

FemaleFemaleFemaleFemale MaleMaleMaleMale



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


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


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

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ValuesValuesValuesValues


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

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AttributesAttributesAttributesAttributes RepublicanRepublican IndependentIndependent DemocratDemocrat


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

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AttributesAttributesAttributesAttributes


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.



� The name does The name does notnot imply any imply any ordering of the cases.ordering of the cases.



� 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.



� 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……


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..



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



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…


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


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


� Has an Has an absolute zero absolute zero that is meaningfulthat is meaningful� Can construct a meaningful Can construct a meaningful ratioratio

(fraction)(fraction)



(fraction), for example, number of (fraction), for example, number of clients in past six monthsclients in past six months



(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


NominalNominalNominalNominal Attributes are only named; weakest



OrdinalOrdinalOrdinalOrdinal



Attributes can be orderedOrdinalOrdinalOrdinalOrdinal



IntervalIntervalIntervalInterval

Attributes are only named; weakest

Attributes can be orderedOrdinalOrdinalOrdinalOrdinal





Attributes can be ordered

Distance is meaningful





RatioRatioRatioRatio








RatioRatioRatioRatio




Absolute zero


measurement levels

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