Research Design & Analysis 2: Class 22 Announcement: Honours conference, Saturday 8:30-12:15 BAC 132...

Research Design & Analysis 2: Class 22

• Announcement: Honours conference, Saturday 8:30-12:15 BAC 132

• Multiple regression SPSS output – (optional lab assignment)

• Other Multivariate Designs– text book: Chapter 14

• Developmental Designs– text book: Chapter: 6 171-180 – (ch 9: 262-271 in 4th Edition)

psyc 2023 class #22 (c) Peter McLeod

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SPSS Multiple Regression Assignment Output: EnterVariables Entered/Removedb

EMPATEND,CONTROL,EFFICACY,SYMPATHY,ANGER

a

. Enter

Model1

VariablesEntered

VariablesRemoved Method

All requested variables entered.a.

Dependent Variable: ZHELPb.

Model Summary

.626a .392 .352 1.0085Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Predictors: (Constant), EMPATEND, CONTROL,EFFICACY, SYMPATHY, ANGER

a.

1

)1( 222

.

pN

RpRRadj

p=#IvsN=sample


3

ANOVAb

49.272 5 9.854 9.689 .000a

76.281 75 1.017

125.553 80

Regression

Residual

Total

Model1

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), EMPATEND, CONTROL, EFFICACY, SYMPATHY, ANGERa.

Dependent Variable: ZHELPb.

Coefficientsa

-4.407 .790 -5.580 .000

-1.12E-03 .076 -.001 -.015 .988

.456 .107 .416 4.276 .000

.288 .090 .315 3.186 .002

.431 .133 .297 3.228 .002

1.089E-02 .009 .119 1.255 .214

(Constant)

CONTROL

SYMPATHY

ANGER

EFFICACY

EMPATEND

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: ZHELPa.

SPSS Multiple Regression Assignment Output: Enter

t =B/Std. Error


4

Variables Entered/Removeda

SYMPATHY .Stepwise (Criteria:Probability-of-F-to-enter <= .050,Probability-of-F-to-remove >= .100).

ANGER .Stepwise (Criteria:Probability-of-F-to-enter <= .050,Probability-of-F-to-remove >= .100).

EFFICACY .Stepwise (Criteria:Probability-of-F-to-enter <= .050,Probability-of-F-to-remove >= .100).

Model1

2

3

VariablesEntered

VariablesRemoved Method

Dependent Variable: ZHELPa. Model Summary

.455a .207 .197 1.1225

.548b .300 .282 1.0612

.616c .380 .355 1.0058

Model1

2

3

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Predictors: (Constant), SYMPATHYa.

Predictors: (Constant), SYMPATHY, ANGERb.

Predictors: (Constant), SYMPATHY, ANGER, EFFICACYc.

SPSS Multiple Regression Assignment Output: Stepwise

alpha

R2 increases with additional variables


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ANOVAd

26.008 1 26.008 20.641 .000a

99.544 79 1.260

125.553 80

37.715 2 18.858 16.746 .000b

87.837 78 1.126

125.553 80

47.654 3 15.885 15.701 .000c

77.899 77 1.012

125.553 80

Regression

Residual

Total

Regression

Residual

Total

Regression

Residual

Total

Model1

2

3

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), SYMPATHYa.

Predictors: (Constant), SYMPATHY, ANGERb.

Predictors: (Constant), SYMPATHY, ANGER, EFFICACYc.

Dependent Variable: ZHELPd.



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Coefficientsa

-1.892 .510 -3.713 .000

.498 .110 .455 4.543 .000

-2.660 .537 -4.950 .000

.539 .104 .492 5.159 .000

.281 .087 .308 3.224 .002

-4.308 .732 -5.885 .000

.494 .100 .451 4.938 .000

.284 .083 .310 3.429 .001

.412 .132 .284 3.134 .002

(Constant)

SYMPATHY

(Constant)

SYMPATHY

ANGER

(Constant)

SYMPATHY

ANGER

EFFICACY

Model1

2

3

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: ZHELPa.



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Excluded Variablesd

.157a 1.549 .125 .173 .966

.308a 3.224 .002 .343 .985

.282a 2.911 .005 .313 .979

.073a .702 .485 .079 .922

.042b .394 .694 .045 .819

.284b 3.134 .002 .336 .979

.086b .869 .387 .099 .920

.013c .128 .898 .015 .812

.119c 1.269 .208 .144 .909

CONTROL

ANGER

EFFICACY

EMPATEND

CONTROL

EFFICACY

EMPATEND

CONTROL

EMPATEND

Model1

2

3

Beta In t Sig.Partial

Correlation Tolerance

CollinearityStatistics

Predictors in the Model: (Constant), SYMPATHYa.

Predictors in the Model: (Constant), SYMPATHY, ANGERb.

Predictors in the Model: (Constant), SYMPATHY, ANGER, EFFICACYc.

Dependent Variable: ZHELPd.


Tolerance=1-R2

IVs

if high, (near 1), collinearity is not a problem


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Correlations

1.000 -.184 .403** .053 .067 .023

. .100 .000 .640 .550 .837

81 81 81 81 81 81

-.184 1.000 -.120 .145 .455** .280*

.100 . .284 .195 .000 .011

81 81 81 81 81 81

.403** -.120 1.000 -.026 .248* -.071

.000 .284 . .818 .025 .530

81 81 81 81 81 81

.053 .145 -.026 1.000 .342** -.061

.640 .195 .818 . .002 .586

81 81 81 81 81 81

.067 .455** .248* .342** 1.000 .195

.550 .000 .025 .002 . .081

81 81 81 81 81 81

.023 .280* -.071 -.061 .195 1.000

.837 .011 .530 .586 .081 .

81 81 81 81 81 81

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

CONTROL

SYMPATHY

ANGER

EFFICACY

ZHELP

EMPATEND

CONTROL SYMPATHY ANGER EFFICACY ZHELP EMPATEND

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

Correlation is significant at the 0.05 level (2-tailed).*.

SPSS Multiple Regression: Correlations


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Multivariate Designs and Analyses

• Multiple Regression: goal is to explain as much of the variance in the criterion variable (Y - the DV) based on a set of predictor variables (Xs).

• Discriminant Analysis: basically Multiple regression, with a categorical dependent variable.


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Activism Among Black South Africans:C. Motjuwadi M.Sc.


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Activism Among Black South Africans:C. Motjuwadi M.Sc.


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Motjuwadi’s Discriminant Analyses

Predicting Protest Participation• gender, friend support, personal

power, perceptions of injustice, & area

Predicting political Membership• participation, genderPredicting Detention• participants, gender, area


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• Canonical Correlation: looks at the relationship between a set of predictor variables and a set of dependent variables by creating one new predictor variable and one new dependent variable and relates these canonical variates.


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• Multivariate Analysis of Variance (MANOVA). Used when you have more than one independent variable and more than one dependent variable that you believe are related (i.e., not independent). – Controls for type I error– Considering relations among DVs may be

more powerful • Log-linear analysis. This non-parametric statistic

is basically a multivariate Chi-squared.


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Log-Linear Example


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• Path Analysis. Uses multiple regression methods to examine hypothesized causal relationships among variables with only correlational data. See how well your theoretically derived model describes relationships among variables. Can also compare competing theories about the relationships among variables.


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Possible Causal Relationships

A B

A

B

C

A

B

C


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Possible Causal Relationships: Fig 14-9

PE SM SAT

PE SM WH SAT


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A

C

B

D


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A C

B D

E


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Path Diagram: Table 14-7

A C

B D

E

0.21

0.390.12

0.72

0.680.12

Decomposition of Model

PathDirectEffect

IndirectEffect

B E None 0.32A E None 0.15B C 0.12 0.27A C 0.21 None

B E = (.39*.12)+(.12*.72)+(.39*.68*.72)=.32


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Causal Antecedents of Attachment

23psyc 2023 class #22 (c) Peter McLeod

Stewart, Taylor, Jang, Cox, Watt, Fedoroff, & Borger (in press)

causal modeling of relations among

learning history, anxiety sensitivity, and panic attacks


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Cross-correlation in Developmental Research


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• Factor analysis is a multivariate form of data reduction. Factor analysis is typically use to extract a relatively small number of underlying dimensions or factors that can account for relationships among measures (see example from text)


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Multivariate Designs and Analyses are all very powerful and some are easy statistics to use, and misuse.

To use these the techniques appropriately depends upon careful research design and thought.

Remember...


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Data Collections Methods in Developmental Psychology

Naturalistic Observations

Interviews• structured

– questionnaires– surveys

• unstructured– clinical

Case StudiesExperimental:• lab• fieldQuasi-

experimental• correlational• ex post facto


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Experimental Designs in Developmental Psychology

• Longitudinal Designs • Cross-sectional Designs • Cohort-Sequential (Cross-sequential,

time-sequential) Designs


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Longitudinal Designs

Examine developmental changes in one cohort followed over time

Within-Subjects Quasi-analytic designAdvantages: Process of development can be

followed with individuals Disadvantages: • Large investment of time and money is

required (especially if large age span) • Subject attrition can be a problem • Carryover effects (e.g., learning) • Differences among cohorts are not addressed


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Cross-sectional Designs

Examine two (or more) ages (or cohorts) at one time

Between-Subjects Quasi-analytic designAdvantages: • Fast and cheap • No subject attrition Disadvantages: • Confounds age and cohort effects • Unable to examine the process of

development within individuals


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Cohort-Sequential Designs Combination of cross-sectional & longitudinal

designs• two (or more) cohorts, each studied at two (or

more) ages. (Sometimes with additional groups tested once to "fill in" the design.)

Mixed Quasi-analytic designAdvantages & Disadvantages • This is a compromise solution with some of the

advantages and disadvantages of cross-sectional & longitudinal designs

• depends on length of the within cohort component and the number of cohorts.


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Age, Education and I.Q.


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Age, Education and I.Q.

Research Design & Analysis 2: Class 22 Announcement: Honours conference, Saturday 8:30-12:15 BAC 132...

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