user friendly demonstration pca

8/12/2019 User Friendly Demonstration PCA

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A User-Friendly

Demonstration of PrincipalComponents Analysis as a

Data Reduction Method

R. Michael Haynes, PhD Keith Lamb, MBAAssistant Vice President Associate Vice President

Student Life Studies Student Affairs

Tarleton State University Midwestern State University


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What is Principal Components

Analysis (PCA)?

A member of the general linear model (GLM) where all

analyses are correlational

Term often used interchangeably with factor analysis,

however, there are slight differences

A method of reducing large data sets into more

manageable factors or components

A method of identifying the most usefulvariables in a

dataset

A method of identifying and classifying variables across

common themes, or constructs that they represent


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Before we get started, aGLOSSARYofterms well be using today:

Bartlettss Test of Sphericity

Communality coefficients

Construct

Correlation matrix

Cronbachs alpha coefficient

Effect sizes (variance accounted for) Eigenvalues

Extraction

Factor or component

Kaiser criterion for retaining factors

Kaiser-Meyer-Olkin Measure of Sampling Adequacy

Latent

Reliability

Rotation

Scree plot

Split-half reliability

Structure coefficients


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Desired outcomes from

todays session

Understand the terminology associated with principalcomponents analysis (PCA)

Understand when using PCA is appropriate

Understand how to conduct PCA using SPSS 17.0 Understand how to interpret a correlation matrix

Understand how to interpret a communality matrix

Understand how to interpret a components matrix andthe methods used in determining how many componentsto retain

Understand how to analyze a component to determinewhich variables to include and why

Understand the concept of reliability and why it is

important in survey research


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LETS GET STARTED!!


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When is using PCA appropriate?

When your data is interval or ratio level

When you have at least 5 observations per variable and

at least 100 observations (ie20 variables>100

observations)

When trying to reduce the number of variables to be

used in another GLM technique (ie.regression,

MANOVA, etc...)

When attempting to identify latent constructs that are

being measured by observed variables in the absence of

a priori theory.


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HUERISTIC DATA

Responses to the Developing Purpose Inventory (DPI)collected at a large, metropolitan university between2004-2006 (IRB approval received)

45 questions related to Chickeringsdeveloping purposestage

Responses on 5 interval scale; 1=always true to5=never true

Sample size = 998 participants

SUGGESTION: always visually inspect data for missing

cases and potential outliers! (APA Task Force onStatistical Inference, 1999).

Multiple ways of dealing with missing data, but thats foranother day!


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SPSS 17.0

Make sure your set-up in Variable View is complete toaccommodate your data

Names, labels, possible values of the data, and type of measure


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Analyze>Dimension Reduction>Factor

SPSS 17.0


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SPSS 17.0 SYNTAXOrangeindicates sections specific to your analysis!

DATASET ACTIVATE DataSet1.

FACTOR

/VARIABLES question1 question2 question3 question4 question5 question6 question7 question8question9 question10 question11 question12 question13 question14 question15 question16question17 question18 question19 question20 question21 question22 question23 question24question25 question26 question27 question28 question29 question30 question31 question32question33 question34 question35 question36 question37 question38 question39 question40question41 question42 question43 question44 question45

/MISSING LISTWISE/ANALYSIS question1 question2 question3 question4 question5 question6 question7 question8

question9 question10 question11 question12 question13 question14 question15 question16question17 question18 question19 question20 question21 question22 question23 question24question25 question26 question27 question28 question29 question30 question31 question32question33 question34 question35 question36 question37 question38 question39 question40question41 question42 question43 question44 question45

/PRINT INITIAL CORRELATION SIG KMO EXTRACTION ROTATION FSCORE

/FORMAT SORT BLANK(.000)/PLOT EIGEN

/CRITERIA MINEIGEN(1) ITERATE(25)

/EXTRACTION PC

/CRITERIA ITERATE(25)

/ROTATION VARIMAX

/SAVE AR(ALL)

/METHOD=CORRELATION.


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OUTPUT COMPONENTS

Correlation Matrix Pearson R between the individual variables

Variables range from -1.0 to +1.0; strong, modest, weak; positive,

negative

Correlations of 1.00 on the diagonal; every variable is perfectly and

positively correlated with itself!

It is this information that is the basis for PCA! In other words, if you

have only a correlation matrix, you can conduct PCA!

Question 1 - ARI Question 2 - VI Question 3 - SL Question 4 - ARI Question 5 - VI

Question 1 - ARI 1.000 .157 .077 .165 .069

Question 2 - VI .157 1.000 .261 .109 .211

Question 3 - SL .077 .261 1.000 .157 .017

Question 4 - ARI .165 .109 .157 1.000 .098

Question 5 - VI .069 .211 .017 .098 1.000


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KMO Measure of Sampling Adequacy and Bartletts

Test of Sphericity

KMO values closer to 1.0 are better

Kaiser (1970 & 1975; as cited by Meyers, Gamst, & Guarino, 2006)

states that a value of .70 is considered adequate. Bartletts Test: you want a statistically significant value

Reject the null hypothesis of a lack of sufficient correlation between the

variables.

Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .861

Bartlett's Test of

Sphericity

Approx. Chi-Square 9193.879

df 990

Sig. .000

OUTPUT COMPONENTS


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Communality Coefficients amount of variance in the

variable accounted for

by the components

higher coefficients

=stronger variables

lower coefficients

=weaker variables

Initial Extraction

Question 1 - ARI 1.000 .560

Question 2 - VI 1.000 .446

Question 3 - SL 1.000 .773


Question 5 - VI 1.000 .539

Question 6 - SL 1.000 .439


Question 8 - VI 1.000 .527

Question 9 - SL 1.000 .537

Question 10 - ARI 1.000 .775

Question 11 - VI 1.000 .635

Question 12 - SL 1.000 .476

Question 13 - ARI 1.000 .542

Question 14 - VI 1.000 .435

Question 15 - SL 1.000 .426

OUTPUT COMPONENTS


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Total Variance Explained Table Lists the individual components (remember, you have as

many components as you have variables) by eigenvalue andvariance accounted for

How do we determine how many components to retain?

Component

Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings

Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative %

1 7.216 16.035 16.035 7.216 16.035 16.035 3.666 8.147 8.147

2 3.107 6.904 22.938 3.107 6.904 22.938 2.649 5.887 14.034

3 2.455 5.456 28.395 2.455 5.456 28.395 2.597 5.771 19.806

4 1.846 4.103 32.498 1.846 4.103 32.498 2.555 5.677 25.482

5 1.690 3.755 36.253 1.690 3.755 36.253 2.243 4.984 30.466

6 1.458 3.239 39.493 1.458 3.239 39.493 2.189 4.865 35.331

7 1.307 2.906 42.398 1.307 2.906 42.398 1.746 3.880 39.212

8 1.180 2.623 45.021 1.180 2.623 45.021 1.578 3.507 42.719

9 1.107 2.461 47.482 1.107 2.461 47.482 1.555 3.455 46.174

10 1.064 2.364 49.846 1.064 2.364 49.846 1.314 2.919 49.093

11 1.024 2.275 52.121 1.024 2.275 52.121 1.221 2.712 51.805

12 1.014 2.253 54.374 1.014 2.253 54.374 1.156 2.569 54.374

13 .976 2.170 56.544

OUTPUT COMPONENTS


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Component



1 7.216 16.035 16.035 7.216 16.035 16.035 3.666 8.147 8.147

2 3.107 6.904 22.938 3.107 6.904 22.938 2.649 5.887 14.034

3 2.455 5.456 28.395 2.455 5.456 28.395 2.597 5.771 19.806

4 1.846 4.103 32.498 1.846 4.103 32.498 2.555 5.677 25.482

5 1.690 3.755 36.253 1.690 3.755 36.253 2.243 4.984 30.466

6 1.458 3.239 39.493 1.458 3.239 39.493 2.189 4.865 35.331

7 1.307 2.906 42.398 1.307 2.906 42.398 1.746 3.880 39.212

8 1.180 2.623 45.021 1.180 2.623 45.021 1.578 3.507 42.719

9 1.107 2.461 47.482 1.107 2.461 47.482 1.555 3.455 46.174

10 1.064 2.364 49.846 1.064 2.364 49.846 1.314 2.919 49.093

11 1.024 2.275 52.121 1.024 2.275 52.121 1.221 2.712 51.805

12 1.014 2.253 54.374 1.014 2.253 54.374 1.156 2.569 54.374

13 .976 2.170 56.544

OUTPUT COMPONENTS

Total Variance Explained Table

Kaiser Criterion (K1 Rule): retain only those components with

an eigenvalue of greater than 1; can lead to retaining more

components than necessary


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OUTPUT COMPONENTS

Component



1 7.216 16.035 16.035 7.216 16.035 16.035 3.666 8.147 8.147

2 3.107 6.904 22.938 3.107 6.904 22.938 2.649 5.887 14.034

3 2.455 5.456 28.395 2.455 5.456 28.395 2.597 5.771 19.806

4 1.846 4.103 32.498 1.846 4.103 32.498 2.555 5.677 25.482

5 1.690 3.755 36.253 1.690 3.755 36.253 2.243 4.984 30.466

6 1.458 3.239 39.493 1.458 3.239 39.493 2.189 4.865 35.331

7 1.307 2.906 42.398 1.307 2.906 42.398 1.746 3.880 39.212

8 1.180 2.623 45.021 1.180 2.623 45.021 1.578 3.507 42.719

9 1.107 2.461 47.482 1.107 2.461 47.482 1.555 3.455 46.174

10 1.064 2.364 49.846 1.064 2.364 49.846 1.314 2.919 49.093

11 1.024 2.275 52.121 1.024 2.275 52.121 1.221 2.712 51.805

12 1.014 2.253 54.374 1.014 2.253 54.374 1.156 2.569 54.374

13 .976 2.170 56.544

Total Variance Explained Table

Retain as many factors as will account for a pre-determined

amount of variance, say 70%; can lead to retention of

components that are variable specific (Stevens, 2002)


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Scree Plot

Plots eigenvalues on Y axis and component number onX

axis

Recommendation is toretain all components

in the descent before

the first one on the line

where it levels off

(Cattell, 1966; as cited

by Stevens, 2002).

OUTPUT COMPONENTS


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Other Retention Methods

Velicers Minimum Average Partial (MAP) test

Seeks to determine what components are common

Does not seek cut-off point, but rather to find a more

comprehensive solution Components that have high number of highly correlated

variables are retained

However, variable based decisions can result inunderestimating the number of components to retain

(Ledesma & Valero-Mora, 2007)


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Other Retention Methods

Horns Parallel Analysis (PA)

Compares observed eigenvalues with simulatedeigenvalues

Retain all components with an eigenvalue greater than themean of the simulated eigenvalues

Considered highly accurate and exempt from extraneousfactors

(Ledesma & Valero-Mora, 2007)


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OUTPUT COMPONENTS

Component Matrix

Column values are structure coefficients, or thecorrelation between the test question and the syntheticcomponent; REMEMBER: squared structure

coefficients inform us of how well the item canreproduce the effect in the component!


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Rotated Component Matrixa

Component

1 2 3 4 5 6 7 8 9 10 11 12

Question 42 - SL .781 -.060 .000 .117 .034 .071 .055 -.062 .093 -.002 .032 .025

Question 39 - SL .778 -.132 .107 .109 .008 .024 -.025 .018 .044 -.010 .022 -.025

Question 33 - SL .765 -.042 .115 .098 .034 .090 -.035 -.035 .011 .013 -.012 .020

Question 9 - SL .672 -.103 .127 .092 .050 .126 .005 -.119 -.002 -.063 -.034 -.114

Question 37 - ARI .462 -.173 .193 -.103 .075 .197 .345 -.018 .024 .232 .009 .119

Question 15 - SL .406 -.002 .340 .038 .050 .091 .120 -.007 .067 -.152 -.127 -.273

Question 36 - SL .395 -.067 .212 -.104 .225 .125 .365 -.089 .110 .168 -.037 .221

Question 44 - VI .375 -.033 .360 .128 .175 .091 .221 -.023 .177 -.035 -.027 -.001

Question 26 - VI -.022 .660 -.113 .009 .021 -.063 -.096 .089 .044 .034 -.060 .174

Question 27 - SL -.158 .652 -.088 .032 .069 -.091 .040 .193 -.032 -.150 -.019 .003

Question 38 - VI -.058 .501 -.109 -.171 .032 -.276 -.051 .078 -.042 .255 -.016 -.097

Question 20 - VI -.240 .489 .016 .076 .036 -.092 -.052 .434 -.102 .071 -.079 .056

Question 32 - VI -.101 .488 -.134 .084 -.074 -.415 -.010 .046 .025 -.057 -.050 .020

Question 45 - SL -.144 .443 -.049 -.097 -.105 -.026 -.097 .078 -.031 .057 .421 -.013

Question 29 - VI -.006 .439 .154 -.114 .007 .231 .238 -.196 .145 -.098 .089 -.138

Question 41 - VI -.019 .421 -.087 -.210 .006 -.107 .333 -.005 .125 .091 .300 -.082

Question 24 - SL .129 -.067 .720 .101 .147 .119 -.003 .011 .005 .011 -.012 .203

Question 21 - SL .125 -.164 .676 -.056 .161 .047 .160 -.044 -.012 .137 -.006 .029

Question 23 - VI .313 -.164 .537 .286 .063 .007 .076 -.094 .119 .049 .123 .031

Question 17 - VI .076 -.050 .459 .187 .040 .136 .314 .048 .120 -.212 .083 -.140

Question 30 - SL .120 .114 .420 .287 -.081 .309 -.109 -.165 .061 .328 -.107 .161

Question 22 - ARI .042 .075 .364 .045 .087 -.081 -.135 -.353 .324 .216 .016 -.188

Question 34 - ARI .187 .042 .067 .791 -.002 .075 -.031 -.019 .012 .063 -.050 -.036

Question 1 - ARI -.002 -.062 .082 .722 .055 -.018 .008 -.014 .039 .132 .015 -.075

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.


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Rotated Component Matrixa , continuedComponent

Question 35 - VI .113 .077 .015 .569 .030 .439 -.053 -.140 .067 -.089 .095 .105

Question 40 - ARI .194 -.161 .176 .553 .033 .057 -.041 .016 .186 -.086 .216 .147

Question 10 - ARI .029 .016 .144 .033 .860 .036 .010 -.074 .032 .063 -.010 .006

Question 3 - SL .069 -.015 .197 .050 .848 -.029 .025 -.011 .067 -.026 -.003 .004

Question 12 - SL .297 .069 .072 .000 .488 .137 .282 .024 .033 .091 .082 .158

Question 13 - ARI -.046 .058 -.118 .045 .447 -.102 .321 .069 .128 .368 -.222 -.033

Question 11 - VI .151 -.021 .024 .361 .115 .663 .000 -.006 -.124 -.028 .021 .104

Question 5 - VI .154 -.134 .201 .042 -.057 .652 .020 .028 -.019 .124 .039 -.092

Question 8 - VI -.090 .250 -.017 .010 .000 -.623 -.034 .115 -.105 .141 .120 .088

Question 18 - SL .034 .003 .095 -.055 .092 -.039 .686 -.026 .015 .006 -.024 .036

Question 14 - VI .241 -.157 .289 -.007 .132 .221 .418 .061 -.057 -.006 .122 -.080

Question 28 - ARI -.232 .248 .051 .181 -.128 -.237 .357 -.112 .043 .074 -.144 .240

Question 16 - ARI -.069 .213 -.008 .062 -.006 -.075 .033 .678 -.051 -.101 -.103 .023

Question 19 - ARI .001 .054 -.042 -.241 -.033 -.010 -.112 .630 .147 -.010 .127 .036

Question 43 - ARI .138 -.011 .067 .255 .017 .045 -.091 .086 .756 .024 -.074 .075

Question 31 - ARI .062 .045 .069 -.048 .122 -.040 .186 -.053 .721 .140 -.077 .033

Question 4 - ARI .023 -.057 .119 .100 .132 .007 .034 -.131 .184 .643 .020 -.088

Question 6 - SL -.186 .177 -.039 .065 -.051 -.066 .087 .372 -.059 .390 .230 -.080

Question 7 - ARI .024 -.059 .047 .149 .010 .005 .016 -.017 -.133 .008 .736 .126

Question 2 - VI .234 -.198 .246 .175 .233 .094 .203 .086 .179 -.161 .254 -.162

Question 25 - ARI -.048 .063 .119 .021 .073 -.049 .064 .085 .078 -.123 .108 .767




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Component Matrix

Column values are structure coefficients, or thecorrelation between the test question and the syntheticcomponent; REMEMBER: squared structure

coefficients inform us of how well the item canreproduce the effect in the component!

Rule of thumb, include all items with structurecoefficients with an absolute value of .300 or greater

OUTPUT COMPONENTS


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Component

1 2 3 4 5 6 7 8 9 10 11 12

Question 42 - SL .781 -.060 .000 .117 .034 .071 .055 -.062 .093 -.002 .032 .025

Question 39 - SL .778 -.132 .107 .109 .008 .024 -.025 .018 .044 -.010 .022 -.025

Question 33 - SL .765 -.042 .115 .098 .034 .090 -.035 -.035 .011 .013 -.012 .020

Question 9 - SL .672 -.103 .127 .092 .050 .126 .005 -.119 -.002 -.063 -.034 -.114

Question 37 - ARI .462 -.173 .193 -.103 .075 .197 .345 -.018 .024 .232 .009 .119

Question 15 - SL .406 -.002 .340 .038 .050 .091 .120 -.007 .067 -.152 -.127 -.273

Question 36 - SL .395 -.067 .212 -.104 .225 .125 .365 -.089 .110 .168 -.037 .221

Question 44 - VI .375 -.033 .360 .128 .175 .091 .221 -.023 .177 -.035 -.027 -.001

Question 26 - VI -.022 .660 -.113 .009 .021 -.063 -.096 .089 .044 .034 -.060 .174

Question 27 - SL -.158 .652 -.088 .032 .069 -.091 .040 .193 -.032 -.150 -.019 .003

Question 38 - VI -.058 .501 -.109 -.171 .032 -.276 -.051 .078 -.042 .255 -.016 -.097

Question 20 - VI -.240 .489 .016 .076 .036 -.092 -.052 .434 -.102 .071 -.079 .056

Question 32 - VI -.101 .488 -.134 .084 -.074 -.415 -.010 .046 .025 -.057 -.050 .020

Question 45 - SL -.144 .443 -.049 -.097 -.105 -.026 -.097 .078 -.031 .057 .421 -.013

Question 29 - VI -.006 .439 .154 -.114 .007 .231 .238 -.196 .145 -.098 .089 -.138

Question 41 - VI -.019 .421 -.087 -.210 .006 -.107 .333 -.005 .125 .091 .300 -.082

Question 24 - SL .129 -.067 .720 .101 .147 .119 -.003 .011 .005 .011 -.012 .203

Question 21 - SL .125 -.164 .676 -.056 .161 .047 .160 -.044 -.012 .137 -.006 .029

Question 23 - VI .313 -.164 .537 .286 .063 .007 .076 -.094 .119 .049 .123 .031

Question 17 - VI .076 -.050 .459 .187 .040 .136 .314 .048 .120 -.212 .083 -.140

Question 30 - SL .120 .114 .420 .287 -.081 .309 -.109 -.165 .061 .328 -.107 .161

Question 22 - ARI .042 .075 .364 .045 .087 -.081 -.135 -.353 .324 .216 .016 -.188

Question 34 - ARI .187 .042 .067 .791 -.002 .075 -.031 -.019 .012 .063 -.050 -.036

Question 1 - ARI -.002 -.062 .082 .722 .055 -.018 .008 -.014 .039 .132 .015 -.075




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Question 35 - VI .113 .077 .015 .569 .030 .439 -.053 -.140 .067 -.089 .095 .105

Question 40 - ARI .194 -.161 .176 .553 .033 .057 -.041 .016 .186 -.086 .216 .147

Question 10 - ARI .029 .016 .144 .033 .860 .036 .010 -.074 .032 .063 -.010 .006

Question 3 - SL .069 -.015 .197 .050 .848 -.029 .025 -.011 .067 -.026 -.003 .004

Question 12 - SL .297 .069 .072 .000 .488 .137 .282 .024 .033 .091 .082 .158

Question 13 - ARI -.046 .058 -.118 .045 .447 -.102 .321 .069 .128 .368 -.222 -.033

Question 11 - VI .151 -.021 .024 .361 .115 .663 .000 -.006 -.124 -.028 .021 .104

Question 5 - VI .154 -.134 .201 .042 -.057 .652 .020 .028 -.019 .124 .039 -.092

Question 8 - VI -.090 .250 -.017 .010 .000 -.623 -.034 .115 -.105 .141 .120 .088

Question 18 - SL .034 .003 .095 -.055 .092 -.039 .686 -.026 .015 .006 -.024 .036

Question 14 - VI .241 -.157 .289 -.007 .132 .221 .418 .061 -.057 -.006 .122 -.080

Question 28 - ARI -.232 .248 .051 .181 -.128 -.237 .357 -.112 .043 .074 -.144 .240

Question 16 - ARI -.069 .213 -.008 .062 -.006 -.075 .033 .678 -.051 -.101 -.103 .023

Question 19 - ARI .001 .054 -.042 -.241 -.033 -.010 -.112 .630 .147 -.010 .127 .036

Question 43 - ARI .138 -.011 .067 .255 .017 .045 -.091 .086 .756 .024 -.074 .075

Question 31 - ARI .062 .045 .069 -.048 .122 -.040 .186 -.053 .721 .140 -.077 .033

Question 4 - ARI .023 -.057 .119 .100 .132 .007 .034 -.131 .184 .643 .020 -.088

Question 6 - SL -.186 .177 -.039 .065 -.051 -.066 .087 .372 -.059 .390 .230 -.080

Question 7 - ARI .024 -.059 .047 .149 .010 .005 .016 -.017 -.133 .008 .736 .126

Question 2 - VI .234 -.198 .246 .175 .233 .094 .203 .086 .179 -.161 .254 -.162

Question 25 - ARI -.048 .063 .119 .021 .073 -.049 .064 .085 .078 -.123 .108 .767




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Component Matrix

For heuristic purposes, were retaining the first Xcomponents; what variables should we include in thecomponents?

Column values are structure coefficients, or thecorrelation between the test question and the syntheticcomponent; REMEMBER: squared structurecoefficients inform us of how well the item canreproduce the effect in the component!

Rule of thumb, include all items with structurecoefficients with an absolute value of .300 or greater

Stevens recommends a better way!

OUTPUT COMPONENTS


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Critical Values for a Correlation Coefficient at =

.01 for a Two-Tailed Test

n CV n CV n CV

50 .361 180 .192 400 .129

80 .286 200 .182 600 .105

100 .256 250 .163 800 .091

140 .217 300 .149 1000 .081

(Stevens, 2002, pp. 394)

Test the structure coefficient for statistical significance against a

two-tailed table based on sample size and a critical value (CV); for

our sample size of 998, the CV would be |.081| doubled (two-tailed),

or |.162|.


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Component

1 2 3 4 5 6 7 8 9 10 11 12

Question 42 - SL .781 -.060 .000 .117 .034 .071 .055 -.062 .093 -.002 .032 .025

Question 39 - SL .778 -.132 .107 .109 .008 .024 -.025 .018 .044 -.010 .022 -.025

Question 33 - SL .765 -.042 .115 .098 .034 .090 -.035 -.035 .011 .013 -.012 .020

Question 9 - SL .672 -.103 .127 .092 .050 .126 .005 -.119 -.002 -.063 -.034 -.114

Question 37 - ARI .462 -.173 .193 -.103 .075 .197 .345 -.018 .024 .232 .009 .119

Question 15 - SL .406 -.002 .340 .038 .050 .091 .120 -.007 .067 -.152 -.127 -.273

Question 36 - SL .395 -.067 .212 -.104 .225 .125 .365 -.089 .110 .168 -.037 .221

Question 44 - VI .375 -.033 .360 .128 .175 .091 .221 -.023 .177 -.035 -.027 -.001

Question 26 - VI -.022 .660 -.113 .009 .021 -.063 -.096 .089 .044 .034 -.060 .174

Question 27 - SL -.158 .652 -.088 .032 .069 -.091 .040 .193 -.032 -.150 -.019 .003

Question 38 - VI -.058 .501 -.109 -.171 .032 -.276 -.051 .078 -.042 .255 -.016 -.097

Question 20 - VI -.240 .489 .016 .076 .036 -.092 -.052 .434 -.102 .071 -.079 .056

Question 32 - VI -.101 .488 -.134 .084 -.074 -.415 -.010 .046 .025 -.057 -.050 .020

Question 45 - SL -.144 .443 -.049 -.097 -.105 -.026 -.097 .078 -.031 .057 .421 -.013

Question 29 - VI -.006 .439 .154 -.114 .007 .231 .238 -.196 .145 -.098 .089 -.138

Question 41 - VI -.019 .421 -.087 -.210 .006 -.107 .333 -.005 .125 .091 .300 -.082

Question 24 - SL .129 -.067 .720 .101 .147 .119 -.003 .011 .005 .011 -.012 .203

Question 21 - SL .125 -.164 .676 -.056 .161 .047 .160 -.044 -.012 .137 -.006 .029

Question 23 - VI .313 -.164 .537 .286 .063 .007 .076 -.094 .119 .049 .123 .031

Question 17 - VI .076 -.050 .459 .187 .040 .136 .314 .048 .120 -.212 .083 -.140

Question 30 - SL .120 .114 .420 .287 -.081 .309 -.109 -.165 .061 .328 -.107 .161

Question 22 - ARI .042 .075 .364 .045 .087 -.081 -.135 -.353 .324 .216 .016 -.188

Question 34 - ARI .187 .042 .067 .791 -.002 .075 -.031 -.019 .012 .063 -.050 -.036

Question 1 - ARI -.002 -.062 .082 .722 .055 -.018 .008 -.014 .039 .132 .015 -.075




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Question 35 - VI .113 .077 .015 .569 .030 .439 -.053 -.140 .067 -.089 .095 .105

Question 40 - ARI .194 -.161 .176 .553 .033 .057 -.041 .016 .186 -.086 .216 .147

Question 10 - ARI .029 .016 .144 .033 .860 .036 .010 -.074 .032 .063 -.010 .006

Question 3 - SL .069 -.015 .197 .050 .848 -.029 .025 -.011 .067 -.026 -.003 .004

Question 12 - SL .297 .069 .072 .000 .488 .137 .282 .024 .033 .091 .082 .158

Question 13 - ARI -.046 .058 -.118 .045 .447 -.102 .321 .069 .128 .368 -.222 -.033

Question 11 - VI .151 -.021 .024 .361 .115 .663 .000 -.006 -.124 -.028 .021 .104

Question 5 - VI .154 -.134 .201 .042 -.057 .652 .020 .028 -.019 .124 .039 -.092

Question 8 - VI -.090 .250 -.017 .010 .000 -.623 -.034 .115 -.105 .141 .120 .088

Question 18 - SL .034 .003 .095 -.055 .092 -.039 .686 -.026 .015 .006 -.024 .036

Question 14 - VI .241 -.157 .289 -.007 .132 .221 .418 .061 -.057 -.006 .122 -.080

Question 28 - ARI -.232 .248 .051 .181 -.128 -.237 .357 -.112 .043 .074 -.144 .240

Question 16 - ARI -.069 .213 -.008 .062 -.006 -.075 .033 .678 -.051 -.101 -.103 .023

Question 19 - ARI .001 .054 -.042 -.241 -.033 -.010 -.112 .630 .147 -.010 .127 .036

Question 43 - ARI .138 -.011 .067 .255 .017 .045 -.091 .086 .756 .024 -.074 .075

Question 31 - ARI .062 .045 .069 -.048 .122 -.040 .186 -.053 .721 .140 -.077 .033

Question 4 - ARI .023 -.057 .119 .100 .132 .007 .034 -.131 .184 .643 .020 -.088

Question 6 - SL -.186 .177 -.039 .065 -.051 -.066 .087 .372 -.059 .390 .230 -.080

Question 7 - ARI .024 -.059 .047 .149 .010 .005 .016 -.017 -.133 .008 .736 .126

Question 2 - VI .234 -.198 .246 .175 .233 .094 .203 .086 .179 -.161 .254 -.162

Question 25 - ARI -.048 .063 .119 .021 .073 -.049 .064 .085 .078 -.123 .108 .767




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Sum the interval values for the responses of all questions

included in the retained component

Obtain mean values for the responses of all questions

included in the retained componenthintyoull get thesame R, R, , and structure coefficients as with the sums!

Use SPSS to obtain factor scores for the component

Choose Scores button when setting up your PCA

Options include calculating scores based on regression, Bartlett, orAndersonRubin methodologiesbe sure and check Save asVariables

Factor scores will appear in your data set and can be used asvariables in other GLM analyses

Obtaining Continuous Component Values

for Use in Further Analysis


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RELIABILITY

The extent to which scores on a test are consistent

across multiple administrations of the test; the amount of

measurement error in the scores yielded by a test (Gall,

Gall, & Borg, 2003).

While validity is important in ensuring our tests are really

measuring what we intended to measure; You wouldnt

administer an English literature test to assess math

competency, would you?

Can be measured several ways using SPSS 17.0


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A Visual Explanation of

Reliability and Validity
http://rds.yahoo.com/_ylt=A0S020psNm9LtGkA9pOjzbkF/SIG=12q8fameb/EXP=1265666028/**http%3a/blog.questionmark.com/wp-content/uploads/2009/04/newchartwp.jpg


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RELIABILITY


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RELIABILITY


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Cronbachs Alpha CoefficientRELIABILITY

/VARIABLES=question1 question2 question3 question4 question5 question6 question7 question8

question9 question10 question11 question12 question13 question14 question15 question16 question17



question36 question37 question38 question39 question40 question41 question42 question43 question44question45

/SCALE('ALL VARIABLES') ALL

/MODEL=ALPHA.

Split-Half CoefficientRELIABILITY

/VARIABLES=question1 question2 question3 question4 question5 question6 question7 question8question9 question10 question11 question12 question13 question14 question15 question16 question17




question45

/SCALE('ALL VARIABLES') ALL

/MODEL=SPLIT.

RELIABILITY


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Cronbachs Alpha Coefficient

Reliability Statistics

Cronbach's Alpha N of Items

.749 45

RELIABILITY

Benchmarks for Alpha

.9 & up = very good

.8 to .9 = good

.7 to .8 = acceptable

.7 & below = suspect.

dont refer to the

test as reliable, but

scores from this

administration of the

test yielded reliable

results.Kyle Roberts
http://smu.edu/education/teachereducation/faculty/images/KyleRoberts.jpg


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Split-Half Coefficient Reliability StatisticsCronbach's Alpha Part 1 Value .620

N of Items 23a

Part 2 Value .623

N of Items 22b

Total N of Items 45

Correlation Between

Forms

.518

Spearman-Brown

Coefficient

Equal Length .683

Unequal Length .683

Guttman Split-Half

Coefficient

.683

a. The items are: Question 1 - ARI, Question 2 - VI, Question 3 - SL, Question 4

- ARI, Question 5 - VI, Question 6 - SL, Question 7 - ARI, Question 8 - VI,Question 9 - SL, Question 10 - ARI, Question 11 - VI, Question 12 - SL,

Question 13 - ARI, Question 14 - VI, Question 15 - SL, Question 16 - ARI,

Question 17 - VI, Question 18 - SL, Question 19 - ARI, Question 20 - VI,

Question 21 - SL, Question 22 - ARI, Question 23 - VI.

b. The items are: Question 23 - VI, Question 24 - SL, Question 25 - ARI,

Question 26 - VI, Question 27 - SL, Question 28 - ARI, Question 29 - VI,Question 30 - SL, Question 31 - ARI, Question 32 - VI, Question 33 - SL,

Question 34 - ARI, Question 35 - VI, Question 36 - SL, Question 37 - ARI,

Question 38 - VI, Question 39 - SL, Question 40 - ARI, Question 41 - VI,Question 42 - SL, Question 43 - ARI, Question 44 - VI, Questiton 45 - SL.

RELIABILITY


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http://faculty.chass.ncsu.edu/garson/PA765/factor.ht

m

http://www.uic.edu/classes/epsy/epsy546/Lecture%2

04%20---

%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYS

IS1.pdf

http://www.ats.ucla.edu/stat/Spss/output/factor1.htm

http://www.statsoft.com/textbook/principal-components-factor-analysis/

RELATED LINKS
http://faculty.chass.ncsu.edu/garson/PA765/factor.htmhttp://faculty.chass.ncsu.edu/garson/PA765/factor.htmhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.ats.ucla.edu/stat/Spss/output/factor1.htmhttp://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.statsoft.com/textbook/principal-components-factor-analysis/http://www.ats.ucla.edu/stat/Spss/output/factor1.htmhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://faculty.chass.ncsu.edu/garson/PA765/factor.htmhttp://faculty.chass.ncsu.edu/garson/PA765/factor.htm


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Gall, M.D., Gall, J.P., & Borg, W.R. (2003). Educational research: An introduction7th

ed.). Boson: Allyn and Bacon.

Ledesma, R.D., & Valero-Mora, P. (2007). Determining the number of factors to

retain in EFA: an easy-to-use computer program for carrying out parallel analysis.

Practical Assessment, Research, & Evaluation,12(2).

Meyers, L.S., Gamst, G., & Guarino, A.J. (2006).Applied multivariate research:

Design and interpretation. Thousand Oaks, CA: Sage.

Stevens, J. P. (2002).Applied multivariate statistics for the social sciences(4thed.).

Mahwaw, NJ: Lawrence Erlbaum Associates.

University of California at Los Angeles Academic Technology Services (2009).

Annotated SPSS output: Factor analysis. Retrieved January 11, 2010 from

http://www.ats.ucla.edu/stat/Spss/output/factor1.htm

University of Illinois at Chicago (2009). Principal components analysis and factor

analysis. Retrieved January 11, 2010 fromhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---

%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20F

ACTOR%20ANALYSIS1.pdf

Wilkinson, L. & Task Force on Statistical Inference. (1999). Statistical methods in

psychology journals: Guidelines and explanation.American Psychologist, 54, 594-

604

REFERENCES
http://www.ats.ucla.edu/stat/Spss/output/factor1.htmhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.uic.edu/classes/epsy/epsy546/Lecture%204%20---%20notes%20on%20PRINCIPAL%20COMPONENTS%20ANALYSIS%20AND%20FACTOR%20ANALYSIS1.pdfhttp://www.ats.ucla.edu/stat/Spss/output/factor1.htm

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