PS 366

Levels of Measurement

• How we classify / observe things

• Affects how they are described

• Affects what statistics we use to test hypotheses about relationships between things

Levels of Measurement

• Nominal– Things classified or categorized– No rank order– No scale

Race, gender, hair color,

Levels of Measurement

• Ordinal– Things classified, categorized– Things ordered, ranked– No set distance between categories– More of, less than

Satisfaction with democracy; prejudice; academic rank; party identification

Levels of Measurement

• Interval / ratio– Things measured on a continuous scale– Equal distance between units on scale– (if ratio) zero means zero

Age (years); GPA; income; education (years)

IQ; Celsius scale [zero = ??]

Levels of Measurement

• Some things (variables) can be measured at each level

• Example, Pain– Nominal– Ordinal– Numeric (interval)

Levels of Measurement

• Some things not clear cut

– Poverty– Freedom– Unemployment– Alienation

Levels of Measurement• Exercise: Create measures

of Education(how much)

– Nominal– Ordinal– Numeric (interval)

– As a question that can be asked on a survey

• Exercise: Create measures of Happiness

(how much)

– Nominal– Ordinal– Numeric

– As a question that can be asked on a survey

Levels of Measurement

• Why it matters?– If nominal, ordinal, interval:

– How do we describe• Central tendency?

• Variation?

• What graphics?

Nominal Data

• Simple percentages, proportions– Yes 45%, No 55%

• Most frequent occurrence (Mode)

• What is the meaning of the mean of gender?– 200 observations: M = 1, F = 2; mean = 1.5 ?

Example: General Social Survey

• Sex before marriage ok? permarsx

• Frequency distribution– Analyze -> Descriptive Stats ->frequency

– GSS Sex before marriage 1) always wrong, 2) almost always wrong, 3) sometimes wrong, 4) not at all wrong

Ordinal data frequency distribution

Ordinal Data

• How describe graphically?

• Bar charts (categories, but not range of variation)

Frequency of responses

Ordinal Data

– Very satisfied (1)12

– Satisfied (2)15

– Neither satisfied nor dissatisfied (3) 5

– Dissatisfied (4) 5

– Very dissatisfied (5) 3

• total40

Ordinal data

• Does it ‘behave’ like interval?

• Center: Mode

Interval Data

• Mean, median, mode – What is most representative observation

• Frequency distributions can be ‘normal’

Example: General Social Survey

• Analyze -> descriptives -> frequency

– Range 18 – 89 plus:

– What’s the distribution going to look like?

This is where Powerpoint crashed

Interval Data

• Standard deviation– how is what we observe

distributed around the central point

• Frequency distributions

Measuring Concepts

• But what is a variable?

• Something that varies– Influences something else; influenced by

something else

• Not a constant– Does not vary [Death, gravity, speed of

light ]

Measuring Concepts

• Measuring a variable =

• Quantifying a concept– turning a concept into something we can measure• Nominal, ordinal, interval

Measuring Concepts

• Variable = religion

• Type?

• Frequency?

• Intensity?

Measuring Concepts

• Religion:

– Type: Catholic, Baptist, None, Christian [self-identified]

– Frequency: How often attend religious services

– Intensity: Is Bible literally word of God? Do you believe Jesus is / is not son of God?

Measuring Concepts

• Religion:

– Type: nominal

– Frequency: Ordinal

– Intensity: Interval??? [religiosity?]

Measuring Concepts

• Candidate support

– Vote intention– Reported vote– “Feelings” [interval, intensity?]

Measuring Concepts• Candidate support

– Thermometer scores• Romney 50.4 (23%)• Pawlenty 48.4

(67)• Huntsman 47.9 (84)• Paul 46.3 (34)• Bachman 45.6 (55)• Santorum 43.9 (63)• Newt 42.7 (17)

value in parentheses = % unable to rank

• On a scale of 0-100, with 0 being cold, 50 being neutral, and 100 being warm, how would you rate your feelings rate the following candidates

• June 15, 2012

Reliability and Validity

• Reliability– Does the method of measuring produce the same

results when used by others

– Consider religion measures• Response to questions:

– what is your religion? __________________– how religious are you? _________________vs:– Check the label that applies to you [P, C, J, etc. ]– Closed response options [very, sort of, not, not at all]

Reliability and Validity

• Reliability– Does the method of measuring produce the same

results when used by others

– Consider Intelligence• Subjective judgment• Written narrative• IQ test

Reliability and Validity

• Validity– Construct Validity: does the measure really

measure the concept? [Religion & faith]

– Predictive Validity: does the measure predict what it should? [PID & voting]

– Content Validity: does the measure include things closely related to the concept?

Reliability and Validity

• Validity

– Face Validity: Does the measure correlate well with things related to the concept?

Reliability and Validity

• Validity

– IQ test measure; SAT score, GRE score

• What do they really measure?

• What do they predict?

• What should they predict if valid measures of ______

Reliability and Validity

• Validity?– Party Identification• Strong D• D• Ind, leans D• Ind• Ind, leans R• R• Strong R