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

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Presentation transcript:

Levels of Measurement

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

Some Definitions VariableVariable

VariableVariable AttributeAttributeAttributeAttribute

GenderGenderVariableVariable AttributeAttributeAttributeAttribute

GenderGender FemaleFemaleMaleMale VariableVariable AttributeAttributeAttributeAttribute

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).

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

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

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

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

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

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

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

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

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.

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.

Ordinal Measurement When attributes can be rank-ordered…

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

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

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?

Interval Measurement When distance between attributes has meaning…

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

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

Ratio Measurement l Has an absolute zero that is meaningful

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

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

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.

The Hierarchy of Levels Nominal

Nominal Attributes are only named; weakest

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

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

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

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

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

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