scales & indices. measurement overview using multiple indicators to create variables using...

Scales & Scales & IndicesIndices

MeasurementMeasurementOverviewOverview

Using multiple indicators to create variablesUsing multiple indicators to create variables Two-step process:Two-step process:

1. Which items go together to measure which 1. Which items go together to measure which variablesvariables Factor AnalysisFactor Analysis

2. Evaluating the reliability of multi-item scales2. Evaluating the reliability of multi-item scales Cronbach’s AlphaCronbach’s Alpha

Factor AnalysisFactor Analysis

Starts with a group of similar indicators Starts with a group of similar indicators (survey items)(survey items) Sorts items based on patterns of inter-item Sorts items based on patterns of inter-item

similaritiessimilarities I.e., which items are correlated (which ones group I.e., which items are correlated (which ones group

together)together) Items that group together share some underlying Items that group together share some underlying

common underlying factorcommon underlying factor

Procedure is based on inter-item correlationsProcedure is based on inter-item correlations Correlation:Correlation:

Measure of similarity between two variablesMeasure of similarity between two variables Varies between 1 and -1Varies between 1 and -1

Stages in Factor Stages in Factor AnalysisAnalysis

ExtractionExtraction How the computer searches for patternsHow the computer searches for patterns

RotationRotation Mathematical manipulation of patternsMathematical manipulation of patterns Whether the computer produces correlated or Whether the computer produces correlated or

uncorrelated factorsuncorrelated factors

Concept measurement Concept measurement example:example:

Research on effects of TV news coverage Research on effects of TV news coverage of social protestof social protest Subjects shown one of three TV news Subjects shown one of three TV news

stories about an anarchist protest:stories about an anarchist protest: 1. Extremely critical1. Extremely critical 2. Highly critical2. Highly critical 3. Moderately critical3. Moderately critical

Respond to questionnaireRespond to questionnaire Examined differences between exposure Examined differences between exposure

groupsgroups

Example of Factor Example of Factor AnalysisAnalysis

Started with 28 items measuring Started with 28 items measuring attitudesattitudes Factor analysis reduces to underlying Factor analysis reduces to underlying

factors…factors…

Rotated Component Matrixa

-.470 .178 .327 -.263

.811

-.374 .131 .653 .280 -.122

.553 -.160 -.220 .442

.690

-.106 .846 .182

.257 -.102 .732

.865 .117

.570 -.232 -.234 .399

.743 -.102 -.250 .161

.481 -.166 -.285 .134 -.180

-.440 .126 .685 .110

-.136 .809

-.801 -.139

.836 .185 -.159

-.104 .276 .158 .692 -.101

.187 .838

Protesters actionswere justified

Felt sorry for the police

Police were out of line

Protesters were out ofline

Protesters inititiatedthe conflict

Police used excessiveforce

Protesters were violent

Police were violent

Protesters weretrouble-makers

Protesters weredisrespectful

Protest ineffective onpoliticians

Protesters offer newinsights

Protesters have a rightto protest

Not be allowed toprotest in public places

Protesters have a rightto be heard

Important to listen tothese protesters

Protesters broughtissues to my attention

1 2 3 4 5

Component

Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization.

Rotation converged in 7 iterations.a.

Remove


.111 -.428 .355 .189 -.238

-.104 .817

.128 -.369 .296 .653 -.128

.716

-.100 .187 .846

.261 .753

.120 .867

-.235 .553 -.264 .404

-.102 .736 -.285 .175

-.163 .498 .116 -.281 -.163

-.403 .703 .129 .125

.817 -.117

-.797 -.137 .107

.835 .188 -.158

.268 .693 .155 -.112

.838 .187







Police were violent

Protesters weretrouble-makers









1 2 3 4 5

Component



Remove


.115 .368 .170 -.450 -.271

.835

.131 .303 .651 -.362 -.131

.739 .123

.187 .849

-.111 .229 .752

.119 .871

-.114 -.305 .713 .183

-.166 .106 -.271 .517 -.143

.712 .125 -.394 .117

.819 -.106

-.798 -.131 .114

.838 .190 -.153

.272 .696 .166

.838 .182







Police were violent









1 2 3 4 5

Component



Remove


-.101 .831

.135 .658 .305 -.345 -.133

.755 .147

.850 .184

-.110 .229 .764

.872 .114

-.117 -.326 .712 .201

-.167 -.274 .523 -.133

.138 .718 -.372 .113

.824

-.796 -.129 .118

.836 .195 -.162

.269 .164 .705 -.110

.187 .840






Police were violent









1 2 3 4 5

Component



Five FactorsFive Factors

1. Protest rights1. Protest rights

2. Police hostility2. Police hostility

3. Protest utility3. Protest utility

4. Blame the protesters4. Blame the protesters

5. Anti-violence5. Anti-violence


-.101 .831

.135 .658 .305 -.345 -.133

.755 .147

.850 .184

-.110 .229 .764

.872 .114

-.117 -.326 .712 .201

-.167 -.274 .523 -.133

.138 .718 -.372 .113

.824

-.796 -.129 .118

.836 .195 -.162

.269 .164 .705 -.110

.187 .840






Police were violent









1 2 3 4 5

Component



1. Support for Protest 1. Support for Protest RightsRights

A. Protesters have a right to protestA. Protesters have a right to protest B. Protesters should not be allowed to B. Protesters should not be allowed to

protest in public places (reverse coded)protest in public places (reverse coded) C. Protesters have a right to be heardC. Protesters have a right to be heard

Correlations

1 -.478** .600**

. .000 .000

212 212 212

-.478** 1 -.581**

.000 . .000

212 212 212

.600** -.581** 1

.000 .000 .

212 212 212

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N




Protestershave a rightto protest

Not beallowed toprotest in

public places

Protestershave a rightto be heard

Correlation is significant at the 0.01 level (2-tailed).**.

2. Hostility the Police2. Hostility the Police

A. Police were out of lineA. Police were out of line

B. Police used excessive forceB. Police used excessive force

C. Police were violentC. Police were violent

Correlations

1 .564** .508**

. .000 .000

212 212 212

.564** 1 .636**

.000 . .000

212 212 212

.508** .636** 1

.000 .000 .

212 212 212

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N


Police usedexcessive force

Police were violent

Police wereout of line

Police usedexcessive

forcePolice were

violent


3. Utility of Protest3. Utility of Protest

A. Protesters offer new insightsA. Protesters offer new insights

B. It’s important to listen to protestersB. It’s important to listen to protesters

C. Protesters brought issues to my C. Protesters brought issues to my attentionattention

Correlations

1 .416** .510**

. .000 .000

212 212 212

.416** 1 .453**

.000 . .000

212 212 212

.510** .453** 1

.000 .000 .

212 212 212

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N




Protestersoffer newinsights

Important tolisten to these

protesters

Protestersbrought

issues to myattention


4. Blame the 4. Blame the ProtestersProtesters

A. Protesters initiated the conflictA. Protesters initiated the conflict

B. The protesters were disrespectfulB. The protesters were disrespectful

C. Protest was ineffective on politiciansC. Protest was ineffective on politiciansCorrelations

1 .446** .108

. .000 .118

211 211 211

.446** 1 .221**

.000 . .001

211 212 212

.108 .221** 1

.118 .001 .

211 212 212

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N



Protest ineffectiveon politicians

Protestersinititiated the

conflict

Protesterswere

disrespectful

Protestineffective on

politicians


5. Opposition to Protest 5. Opposition to Protest ViolenceViolence

A. I feel sorry for the police because of A. I feel sorry for the police because of the way they were treated by the the way they were treated by the protestersprotesters

B. The protesters were violentB. The protesters were violent

Correlations

1 .370**

. .000

212 212

.370** 1

.000 .

212 212

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N



Felt sorry forthe police

Protesterswere violent


Combining items into a Combining items into a scalescale

Summative scaleSummative scale

Factor scoresFactor scores

Summative scalesSummative scales

Adding items or taking the meanAdding items or taking the mean E.g.,:E.g.,:

Compute scale = sum.1(var1,var2,var3)Compute scale = sum.1(var1,var2,var3) Compute scale = mean.1(var1,var2,var3)Compute scale = mean.1(var1,var2,var3)

Weights each item equallyWeights each item equally

Factor scoresFactor scores

Uses factor loadings from the factor matrix to weight Uses factor loadings from the factor matrix to weight the itemsthe items

Heavier weighting to items that are more central Heavier weighting to items that are more central to the factorto the factor

Use save command when running factor analysis Use save command when running factor analysis (under “scores”: “save as variables”(under “scores”: “save as variables”

New variables with values for each case saved in New variables with values for each case saved in data file for each factordata file for each factor

Cronbach’s AlphaCronbach’s Alpha

Assessing reliability of a multi-item scaleAssessing reliability of a multi-item scale Based on the average inter-item correlationBased on the average inter-item correlation

Weighted by the number of items in the scaleWeighted by the number of items in the scale

Measures internal consistency Measures internal consistency (unidimensionality)(unidimensionality) Are all the items measuring the same thing?Are all the items measuring the same thing? If so, they should all be highly inter-correlatedIf so, they should all be highly inter-correlated

Cronbach’s Alpha Cronbach’s Alpha Formula:Formula:

A = A = N * rN * r

[1+ (N –1)r][1+ (N –1)r]

N = number of items in the scaleN = number of items in the scale

r = average inter-item correlationr = average inter-item correlation

Acceptable alpha for a Acceptable alpha for a scalescale

Ideally, alpha > .80Ideally, alpha > .80

Some journals accept > .70Some journals accept > .70

Low alpha means either:Low alpha means either: 1. Scale is not reliable (items have lots of error)1. Scale is not reliable (items have lots of error) 2. Items could measure two different things2. Items could measure two different things

Alpha if item deleted can help identify a Alpha if item deleted can help identify a bad itembad item More than one bad item could be an indicator More than one bad item could be an indicator

that there are items that measure a different that there are items that measure a different conceptconcept

scales & indices. measurement overview using multiple indicators to create variables using...

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number of items

violentcombining items

reliable items

items tha

multiitem scalebased

anarchist protest

protest rightsa

protest rights2