Bell RingerBell Ringer

Using female = 0 and male = 1, Using female = 0 and male = 1, calculate the average maleness in calculate the average maleness in this classroom. this classroom.

Levels of Levels of MeasurementMeasurement

NOIR and your Survey NOIR and your Survey QuestionsQuestions

NominalNominal

Nominal Level of Measurement  Nominal Level of Measurement  At the At the nominalnominal level level of measurement, numbers or other symbols are of measurement, numbers or other symbols are assigned to a set of categories for the purpose of assigned to a set of categories for the purpose of naming, labeling, or classifying the observations. naming, labeling, or classifying the observations.

GenderGender is an example of a nominal level variable. is an example of a nominal level variable. Using the numbers 0 and 1, for instance, we can Using the numbers 0 and 1, for instance, we can classify our observations into the categories classify our observations into the categories "females" and "males," with 0 representing "females" and "males," with 0 representing females and 1 representing males. We do not females and 1 representing males. We do not imply anything about the magnitude or imply anything about the magnitude or quantitative difference between the categories. quantitative difference between the categories.

We cannot manipulate these quantities, i.e. what is We cannot manipulate these quantities, i.e. what is average maleness of this class? average maleness of this class?

Nominal-ExampleNominal-Example

GenderGender is an example of a nominal level is an example of a nominal level variable. Using the numbers 0 and 1, for variable. Using the numbers 0 and 1, for instance, we can classify our observations instance, we can classify our observations into the categories "females" and "males," into the categories "females" and "males," with 0 representing females and 1 with 0 representing females and 1 representing males. We do not imply representing males. We do not imply anything about the magnitude or anything about the magnitude or quantitative difference between the quantitative difference between the categories. categories.

We cannot manipulate these quantities, i.e. We cannot manipulate these quantities, i.e. what is average maleness of this class? what is average maleness of this class?

OrdinalOrdinal

Whenever we assign numbers to rank-Whenever we assign numbers to rank-ordered categories ranging from low ordered categories ranging from low to high, we have an to high, we have an ordinal ordinal level level variable. variable.

Ordinal = orderOrdinal = order

Ordinal- ExampleOrdinal- Example

Social classSocial class is an example of an ordinal is an example of an ordinal variable. We might classify individuals with variable. We might classify individuals with respect to their social class status as respect to their social class status as "upper class", "middle class", or "working "upper class", "middle class", or "working class".class".

"upper class" has a higher class position "upper class" has a higher class position than a person in a "middle class" categorythan a person in a "middle class" category

do not know the magnitude of the do not know the magnitude of the differences between the categories; that differences between the categories; that is, we don't know how much higher "upper is, we don't know how much higher "upper class" is compared to "middle class". class" is compared to "middle class".

Interval/RatioInterval/Ratio

If the categories (or values) of a If the categories (or values) of a variable can be rank-ordered, and if variable can be rank-ordered, and if the measurements for all the cases the measurements for all the cases are expressed in the same units, are expressed in the same units, then an then an interval-ratiointerval-ratio level of level of measurement has been achieved.measurement has been achieved.

Interval-ExampleInterval-Example

Examples of variables measured at the Examples of variables measured at the interval-ratio level are interval-ratio level are ageage,, income income, , and and SAT scoresSAT scores. With all these . With all these variables we can compare values not variables we can compare values not only in terms of which is larger or only in terms of which is larger or smaller, but also in terms of how smaller, but also in terms of how much larger or smaller one is much larger or smaller one is compared with another. compared with another.

Interval – Ratio DistinctionInterval – Ratio Distinction

In some discussions of levels of measurement In some discussions of levels of measurement you will see a distinction made between you will see a distinction made between interval-ratio variables that have a natural interval-ratio variables that have a natural zero point (where zero means the absence zero point (where zero means the absence of the property) and those variables that of the property) and those variables that have zero as an arbitrary point. have zero as an arbitrary point.

Weight and length have a natural zero point, Weight and length have a natural zero point, whereas temperature has an arbitrary zero whereas temperature has an arbitrary zero point (C vs. K). Variables with a natural zero point (C vs. K). Variables with a natural zero point are also calledpoint are also called ratio variables ratio variables. .

NOIRNOIR

Scales (levels) of Scales (levels) of Measurement Measurement

To determine level of To determine level of measurementmeasurement

Step #1 Identify the Step #1 Identify the Unit of ObservationUnit of Observation (obs unit) (obs unit) (sampling unit) (sampling unit) – (one of something)(one of something)

What you are interested on studying? What you are interested on studying? -individual-individual (participant) for psychologists (participant) for psychologists- Other possible Observational units:- Other possible Observational units:

– A rat A rat – A Group/teamA Group/team– A HouseholdA Household– A CityA City– A CountryA Country– A College student A College student

Scales (Levels) of Scales (Levels) of MeasurementMeasurement

To determine level of To determine level of measurement measurement Step #2 Ask: “Step #2 Ask: “What am going to do What am going to do

with the Obs unit?”with the Obs unit?”– Two options:Two options:

Option A:Option A: Assign the Obs unit to a category Assign the Obs unit to a category (quality) (quality)

– E.g. gender, race, social security number (unique) E.g. gender, race, social security number (unique)

Option B:Option B: Measure the Obs unit on some Measure the Obs unit on some attribute or behaviorattribute or behavior

– Intelligence, age, motivational level, number of Intelligence, age, motivational level, number of hotdogs eatenhotdogs eaten

If Yes to Option AIf Yes to Option A

– If “Yes” to If “Yes” to Option AOption A Ask: are the categories ranked on some Ask: are the categories ranked on some

quality?quality?– E.g. job class (clerical I, II, III)E.g. job class (clerical I, II, III)– E.g. class standing (rank in class)E.g. class standing (rank in class)

If “NO”, not ranked, then level of If “NO”, not ranked, then level of measurement is measurement is NOMINALNOMINAL

If “Yes”, categories ranked, level of measure If “Yes”, categories ranked, level of measure is is ORDINALORDINAL

If Option B: Measure If Option B: Measure Obs Obs UnitUnit on some attribute or on some attribute or

behavior behavior Step #3 Identify Step #3 Identify Unit of MeasureUnit of Measure

(Measurement Unit)(Measurement Unit)– One of something (attribute or behavior)One of something (attribute or behavior)

E.g. item on a test, inventory E.g. item on a test, inventory

– Ask: Ask: “Does the measure have a true zero?“Does the measure have a true zero? UsuallyUsually:: Physical and behavioral ones Physical and behavioral ones dodo

– E.g height, weight, number of cases soldE.g height, weight, number of cases sold

Psychological attributes Psychological attributes do notdo not– IQ, need for approval, depression level, attitude IQ, need for approval, depression level, attitude

toward boss toward boss

Scales (Levels) of Scales (Levels) of MeasurementMeasurement

To determine level of To determine level of measurement measurement If answer to “Does the measure have If answer to “Does the measure have

a true zero?”a true zero?”– Is “YES”, level is Is “YES”, level is RatioRatio– Is “No”, level is Is “No”, level is IntervalInterval

Try out a few:Try out a few:

What Level Measurement?What Level Measurement?Students Fail v. Pass Students Fail v. Pass

Observational unit? Observational unit? – One studentOne student

Place student in category?Place student in category?– Yes: fail or passYes: fail or pass

Are the categories ranked on some Are the categories ranked on some quality?quality?– Yes (underlying continuous variable…success Yes (underlying continuous variable…success

in learning)in learning) Level of measurement?Level of measurement?

– Ordinal Ordinal

Now PracticeNow Practice

Go to computer lab, log on to my wiki Go to computer lab, log on to my wiki and click on link for today’s class and click on link for today’s class 2/11. Complete exercises 1-10 and 2/11. Complete exercises 1-10 and follow up question, record your follow up question, record your answer on worksheet then check answer on worksheet then check your answers. your answers.