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Faculty of Education, University of Malaya,
50603 Kuala Lumpur, Malaysia.
Tel: 603-79675046 (Off)
603-79675010 (Fax)
Email: [email protected],
PROF. DR. ANANDA KUMAR PALANIAPPAN, Ph.D
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Outline
Brief overview of SPSS Part I workshop
Instrument Validity and Reliability
Factor Analyses and InterpretationMultiple Regression
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Types of Research
Research
Quantitative
ExperimentalEthnography
Qualitative
Non-experimental
Action
Research
Case Study
Grounded
Theory
Historical
Descriptive
Causal
Comparative
Correlational
Phenomenology
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Steps in Educational Research 1) Identify the problem area / the need for investigation
2) Write the statement of the problem in either (a) QuestionForm [e.g. Do children from kindergarten perform better at school
compared to children who have no kindergarten experience?]
(b) Hypothesis [e.g. There is no significant difference in academic
achievement between children with kindergarten experience and
children without kindergarten experience] 3) Decide which research design is most appropriate.
4) Review studies in the variables indicated in the research questions /
hypothesis (a) to form a conceptual framework for the research (b)
information required to design instruments
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Steps in Educational Research
(Contd.) 5) define the variables involved in operational terms [e.g.
Academic achievement are grades assigned by teachers; or
Intelligence is the score obtained in Cattle’s Culture Fair
Intelligence Test]
6) Design instruments to measure the variables involved
7) Pilot test the instruments to ascertain (I) whether it is
suitable for the sample under study (2) Internal
Reliabilities (Item Analyses), Test Reliablities and Test
Validities.
8)Administer the instruments and score based on a
predetermined score sheet.
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Steps in Educational Research
(Contd.) 9) Analyse the data using SPSS
10) Interpret the analyses and answer the research question
or reject/accept the hypotheses
11) State any assumptions or limitations in the study.
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Pilot Study- Reliability and
Validation of Instrument Ascertain Reliability:
(A) INTERNAL CONSISTENCY: (1) Item Analysis -Index of discriminability (2) Split-half reliability (3)Kuder-Richardson reliability (for dichotomous data) (4)Cronbach Alpha (for ordinal data) SPSS- Data Editor-Statistics-Scale-Reliability Analysis - Model (Alpha, Split-
half, Guttman, Parallel) (B) STABILITY: (1)Test-retest reliability (2) Alternate
Forms reliability - use SPSS-Data Editor-Statistics-Compare Means-Paired-Samples t-test .
Ascertain Validity: (1) Content Validity - (use Expert
testimony) (2) Construct Validity – SPSS – Data Editor – Analyze – Data Reduction (3) Criterion-related Validity/Concurrent Validity- Use correlation (4) PredictiveValidity – Use correlation
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Validity
Content Validity - if the instrument tests all aspects thatshould be tested (Ascertained using Expert testimony)
Construct Validity - if the test measures what it is
supposed to measure (Ascertained using Factor Analysis)
Criterion-related Validity/ concurrent validity - if thetest scores are closely related to another test which
measures similar construct (Ascertained using Pearson
Correlation)
Predictive Validity - if the instrument can predictcorrectly a particular outcome (Ascertained using Pearson
Correlation)
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METHODS OF ESTIMATING RELIABILITY
Type of
Reliability Measure Procedure
Test-retest method Measure of stability Give the same twice to the samegroup with any time interval
between tests from several
minutes to several years
Equivalent-Forms Measure of equivalence Give two forms of the test to
Method the same group in closesuccession
Test-retest with Measure of stability Give two forms of the test to the
equivalence forms and equivalence same group with increased time
interval between forms
Split-half method Measure of internal Give test once. Score two equivalent
consistency halves test (e.g. odd items and even time)
Kuder-Richardson Measure of internal Give test once. Score total test and
method consistency apply Kuder-Richardson formula
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DESIGNING INSTRUMENTS
Should be suitable for the population under study
Should sample the universe of data pertaining to
the variable measured Should be reliable
Should be reliably scored
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Outline of SPSS Part 1
Types of Data
How to enter data and examine data
How to explore data for normality
What analyses / statistics to use
How to run these analysesHow to COMPUTE and RECODE
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Start your SPSS for Windows now. You will get the
Data Editor Window. Study the menu bar and the
options available in each menu.
Then,
1. Open the data file call ‘PRACTICE’.
2. Run some simple frequency analyses on thefollowing variables:
a) sex
b) race
c) regiond) happy
3. From the results in your Output Navigator
describe the respondents in this study
Exercise 1
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Types of Measurement Scales and their
Statistical Analyses
MeasurementScale
Characteristics Type of Data StatisticalTests
NominalSimple Classification in
Categories without any order
e.g Boy / Girl
Happy / Not HappyMuslim / Buddhist / Hindu
Non-
parametricChi-square
Ordinal Has order or rank ordering
e.g. Strongly agree, agree,
undecided, disagree, strongly
disagree
(LIKERT SCALE)
Non-
parametric
Spearman’s rho
Mann-Whitney
Wilcoxon
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Types of Measurement Scales and their
Statistical Analyses
MeasurementScale
Characteristics Type of Data StatisticalTests
IntervalDo not have true 0 points. Has
order as well as equal distance
or interval between judgements
(Social Sciences) e.g. IQ scoreof 95 is better than IQ 85 by 10
IQ points
Parametric COMPARISON:
t-tests
ANOVA
RELATIONSHIP:Pearson r
Ratio Have true 0 points. Has high
order, equal distance between
judgements, a true zero value
(Physical Sciences) e.g.age, no.of children, 9 ohm is 3 times 3
ohm and 6 ohm is 3 times 2
ohm But IQ 120 is more
comparable to IQ 100 than to IQ
144, although ratio
IQ 120 /100 = 144 /120 = 1.2
ParametricCOMPARISON:
t-tests
ANOVARELATIONSHIP:
Pearson r
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Types of Measurement Scales and their
Statistical Analyses
Higher order of measurement --> lower
order e.g. Interval ---> ordinal, nominal
But not ordinal, nominal ----> interval
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Refer to the handout provided.
Exercise 1
Indicate in the spaces provided in
Table 1 the level of measurement of thecorresponding variables
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Data Collection
Identify the population to be studied
Choose sample randomly or by stratified
random sampling
The accuracy of the findings of a research
depends greatly on (1) how the sample is
chosen (2) whether the correctinstruments are used (3) the reliability
and validity of the instruments
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Entering & Editing Data
Open SPSS by double clicking at the SPSS icon or
‘START’ - ‘PROGRAM’ - ‘SPSS’
Define variable
Enter data
Adding labels for variables and value labels Inserting new cases
Inserting new variables
Adding Missing Value codes Examining Data by running ‘FREQUENCY’
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Refer to the handout provided.
Exercise 2:
Enter data given in the handout
then answer the questions
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Exploring Data Graphically
To check normality graphically and decide onits appropriate analyses
1) By displaying data
Histogram
Boxplot
Stem-and-leaf Plot
2) By Statistical Analyses
Descriptive StatisticsM - Estimators
Kolmogorov-Sminov Test
Shapiro-Wilk
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Histogram
CHILD REARING PRACTICES
25.022.520.017.515.012.510.0
Histogram
F r e q u e n c y
14
12
10
8
6
4
2
0
Std. Dev = 3.89
Mean = 18.0
N= 41.00
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Checking Normality -
SkewnessSkewness measures the symmetry of the
sample distribution
Skewness = StatisticStandard Error
If Skewness < -2 or > +2, reject normalityIf -2 < Skewness < 2 ---> Normal
distribution
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Negatively Skewed
If Ratio is negativeIf Mean < Median
2213N =
SEX
FEMALEMALE
C R A
22
20
18
16
14
12
10
8
6
35
Boxplot
Negatively skewed
MeanMedia
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Checking Normality - Kurtosis
Kurtosis measures the spread of the data
Kurtosis = Statistic
Standard Error
If Kurtosis < -2 or > +2 reject normalityIf -2 < Kurtosis < 2 ---> Normal
distribution
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Kurtosis
Negative value of Kurtosis indicates shorter
tails (Box like distribution)
Normal Graf
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2941N=
CHILDREARINGPRACTI
30
20
10
0
Slightly positively
skewed
Largest observed value that isn’t
outlier
Smallest observed value that isn’t
outlier
Median
75th Percentile
25th Percentile
Boxplot Values more than 1.5
box-lengths from 75th
percentile (outliers)
Values more than 3 box-lengths from 75th
percentile
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Fig.1. Boxplot comparisons of the creativity scores of
Malaysian and American students
Elaboration > Fluency > Flexibility > Originality
Descriptive Statistics
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Example: Boxplots for more than one variable / time series
http://upload.wikimedia.org/wikipedia/commons/f/fa/Michelsonmorley-boxplot.svghttp://upload.wikimedia.org/wikipedia/commons/f/fa/Michelsonmorley-boxplot.svg
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Stem - and - Leaf Plot
CHILD R
Fre
1
St
Eac
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Testing Normality of data
collected All data must be tested for normality before analyzing
them statistically.
Normality - if the data samples the populationrepresentatively, it will be normally distributed - where the
mean and median are approximately equal Type of analysis depends on the normality of data and the
level of measurement of data
- Normally distributed data - use Parametric Tests like t -
tests, ANOVA, Pearson r .- Non-normally distributed data - use Non-parametricTests like Chi-square, Spearman’s rho, Mann-Whitney,Wilcoxon
To show Normality of Data
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To show Normality of Data
I
I
I
I
i
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Not sig. at p < .01.
Data is normally distributed
Data Editor - Analyze - Descriptive Statistics - Explore
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BoxPlot for Male and Female parents
2213N =
SEX
FEMALEMALE
CRA
22
20
18
16
14
12
10
8
6
35
Slightly Negatively
Skewed
Slightly Positively
Skewed
Detrended Normal Q-Q Plot
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Detrended Normal Q-Q Plot of CRA
For SEX= MALE
Observed Value
2220181614121086
Devfrom
Normal
.4
.2
-.0
-.2
-.4
-.6
Normal Q-Q Plot of CRA
For SEX= FEMALE
Observed Value
2220181614121086
ExpectedNormal
2.0
1.5
1.0
.5
0.0
-.5
-1.0
-1.5
-2.0
Normal Q-Q Plot of CRA
Detrended Normal Q-Q Plot of CRA
For SEX= FEMALE
Observed Value
2220181614121086
Devfrom
Normal
.2
.1
0.0
-.1
-.2
-.3
-.4
Normal Q-Q Plot of CRA
For SEX= MALE
Observed Value
2220181614121086
ExpectedNormal
1.5
1.0
.5
0.0
-.5
-1.0
-1.5
Detrended Normal Q Q Plot
of CRA
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Exercise
Open the data file “PRACTICE’ and check the normality of
the ‘Age’ data of the respondents using
a) Histogram
b) Boxplotc) Stem-and-leaf
d) E-estimators
e) Kolmogorov-Sminov & Shapiro Wilk
f) Normal Q-Q Plot
g) Detrended Normal Q-Q Plot
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Testing equali ty of var iance
Levernes Test (SPSS-DataEditor-Analize-Explore-Plots(Leverne)
If Leverne Statistic is highly significant (p < .001), the groups do not
have equal variance
If Leverne Statistic is not significant (p > .001), the groups have
equality of variance and t-tests analyses can be undertaken
Not
Sig.
Mothers
Fathers
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Compute Data
Please try exercise 3.
SPSS data editor - Transform - Compute -
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RECODE SPSS Data Editor - Transform - Recode - into different variable
/ into same variable
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Recode (contd)
Please try exercise 4
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Select cases SPSS Data Editor - Data - Select cases-
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To Analyze & Report Demographic Data
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To Analyze & Report Demographic Data
ANALYSE DESCRIPTIVE STATISTICS EXPLORE
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Source: Palaniappan, A. K. (2009). Penyelidikan Pendidikan dan SPSS .
Kuala Lumpur, Malaysia: Pearson.
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Source:American Psychological Association. (2010). Publication Manual
of the American Psychological Association (6th ed.). Washington, DC: Author.
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Source:
American Psychological Association. (2010). Publication Manual of the American Psychological Association (6th ed.). Washington, DC: Author.
Sample APA Reporting of Demographic
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Sample APA Reporting of Demographic
I nformation for 4 Subsamples
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Parametric Statistical Analyses
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Parametric Statistical Analyses
(Degree of Association/ Relationship)
SPSS Data Editor - Statistics - Correlate - Bivariate -
Parametric Statistical Analyses
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Parametric Statistical Analyses
(Degree of Association/ Relationship)Pearson Product-moment Correlation
*
P ti C l ti T bl
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Presenting Correlation Table
Table 1 Pearson Product Moment Correlations between SAM,
WKOPAY and CRA Scores
CRA SAM WKOPAY
SAM .20 1.00 .38*
WKOPAY .29 .38* 1.00
N of Cases: 165 1- tailed Signif: * - .01 ** - .001
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Effect size for correlation
55
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Reporting Product Moment Correlations
Table 1 presents the inter-correlations among Creative Child Rearing Practices
(CRA), Something About Myself (SAM) and What Kind of Person Are You?
(WKOPAY) scores. The correlation coefficient between CRA and SAM scores
is .20 which is not significant at p < .05 and with small effect size. This
indicates that parents who perceive themselves as creative based on their past
creative performances do not engage in creative child rearing practices.
The correlation coefficent between CRA and WKOPAY scores is also not
significant (r = .29, p > .05) with small effect size. This indicates that parents
who perceive themselves as creative based on their personality characteristics,
also do not engage in creative child rearing practices.
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Report
There is a significant correlation between SAMand WKOPAY (r = .375, p < .05) with smalleffect size. The correlation is positive, indicating
that an increase in SAM scores will result in anincrease in WKOPAY scores. Results also showthat 14% (r squared) of the variance of SAMscores is explained by WKOPAY scores. About
86% of the variance in SAM is unaccounted for.
S l f C l ti R t
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Sample of Correlation Report
Creed, P. A. & Lehmann, K. (2009). The relationship between core self-evaluations, employment commitment and
well-being in the unemployed. Personality and Individual Differences, 47 , 310 – 315.
S l f C l ti T bl
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Sample of Correlation Table
Creed, P. A. & Lehmann, K. (2009). The relationship between core self-evaluations, employment commitment and
well-being in the unemployed. Personality and Individual Differences, 47 , 310 – 315.
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Source:
American Psychological Association. (2010). Publication Manual of the American Psychological Association (6th ed.). Washington, DC: Author.
Means and SDs
for the Upper
Group
Means and SDs
for the Lower
Group
An example of a Scatter Plot (Palaniappan, 2007)
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10080604020
Individualism
0.51
0.48
0.45
0.42
0.39
Ov
erallExpressivity
Endorsement
ZimbabweUSA
Turkey
Switzerland
South Korea
Russia
Portugal
PolandPeople's Republic of China
New Zealand
NetherlandsMexico
Malaysia
Lebanon
Japan
ItalyIsrael
Indonesia
India Hungary
Hong Kong
Germany
Denmark
Croatia
Canada
Brazil
Belgium
Australia
Graphical Representation of the Relationship Between Individualismand Overall Expressivity Endorsement
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t - tests
Paired t-tests
Grouped t-tests
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Assumptions of t -tests
1) Data must be interval or ratio
2) Data must be obtained via random
sampling from population3) Data must be normally distributed
Parametric Statistical Analyses
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( comparisons - t -tests )
SPSS Data Editor - Compare means - Independent Sample t test
Parametric Statistical Analyses
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Parametric Statistical Analyses
( comparisons - t -tests )
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Presentation of t -test results
Table 2
T-tests comparisons of CRA scores by gender
Father Mother
Mean
SD
15.06 14.36
4.05 3.63
t -value p < .05
5.38 NS
(n =13) (n =12)EffectSize
.18
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Effect Size
221
___
21
__
s s
X X
EffectSize
X1 = 15.08 s1 = 4.05
X2 = 14.36 s2 = 3.63
1875.84.3
72.0
2
63.305.4
36.1408.15
EffectSize
Example:
Result: Effect Size (Cohen’s d ) = .1875 (Small effect size)
Note: Effect size ~ .5 (medium); ~ .8 (high)
Eff t Si d b C h ’ d
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.
Effect size (Cohen’s d), Eta Squared and Interpretation
---------------------------------------------------------------------------------------------------
Effect Size (Cohen’s d ) Eta Squared, η2 Interpretation
----------------------------------------------------------------------------------------------------
0.2
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Report
The mean CRA scores of fathers and mothers are15.08 and 14.36 and the standard deviations are 4.05and 3.63 respectively. These scores are subjected tot -test analysis. The Levene’s Test for equality of
variance indicates that the variances are similar. Thet -value obtained is .54 which is not significant at p <.05. The effect is .18.
These results indicate that fathers and mothers do
not differ in their child rearing practices. The effectsize indicates that parents’ gender has only a smalleffect on their creative child-rearing practices.
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Palaniappan, A K. (2000). Sex differences in Creative Perceptions of Malaysian
Students, Perceptual and Motor Skills, 91, 970 - 972.
See handout for a clearer page (article page # 971)
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Paired t -test
Assumptions
1) Normality of the population difference ofscores – this is ascertained by ensuring the
normality of each variable separately.
2) the other assumptions similar to group t – test
a) Data must be interval or ratio
b) Data must be obtained via randomsampling from population
c) Data must be normally distributed
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Exercise
1) Is there a significant difference in the
highest year of education between the
respondent’s mother and father?2) Is there a significant difference in the
highest year of education of respondent and
his/her spouse?
Parametric Statistical Analyses
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y
( comparisons - Oneway ANOVA )
SPSS Data Editor - Compare Means - One-way ANOVA -
Parametric Statistical Analyses
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( comparisons - Oneway ANOVA )
Understanding the ANOVA table
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Understanding the ANOVA table
Variations among the sample means
F = -------------------------------------------
Variance within the samples
Between groups sum of squares / df 1 Between mean square
F = --------------------------------------------- = --------------------------
Within groups sum of squares / df 2 Within mean square
Between mean square is computed by subtracting the mean of the observations (the overall
mean) from the mean of each group, squaring each difference, multiplying each square by the
number of cases in its group, and adding the results for each group together. The total is called
between-group sum of squares
Within-group sum of squares is computed by multiplying each group variance by the numberof cases in the group minus 1 and add the results for all groups.
Mean square column reports sum of squares divided by its respective degree of freedom.
F ratio is the ratio of the two mean squares.
Presentation of One
way ANOVA results
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Presentation of One-way ANOVA resultsTable 3
One-way ANOVA for CRA scores by WKOPAY groups
Source df Sum of Mean of F F
Squares Squares Ratio Probability
Between Gps 2 31.145 15.573 .632 .537
Within Grps 38 936.660 24.649
Total 40 967.805
Multiple Range Test
Scheffe Procedure
No groups are significantly different at the .05 level
i
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Interpreting F
If the F value is significant, then the groups
are significantly different
To ascertain which groups are significantlydifferent, perform the Scheffe test.
F (Groups -1, No. of Participants – Groups) = F Value
Report
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Report
Results show that the three groups do notdiffer significantly on CRA scores
( F (2, 38) = .632, p >.05). This represents aneffect size of 3.22% [{31 / (31 + 937)} x100] which indicates that only 3.22% of thevariance of CRA scores was accounted for
by the 3 groups. (do the same for SAM)
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Effect Size
Sum of Squares between GroupsEffect Size = ------------------------------------------- x 100
Total Sum of Squares
Is the degree to which the phenomena exists (Cohen, 1988)
B f i C i f
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Bonferonni Correction for
Multiple Comparisons
For multiple comparisons, Bonferonni
corrections must be made
If the overall level of significance is set at p< .05 and the number of comparisons
involved is 10, then the level of significance
for each comparison must be .05/10 whichis .005.
T bl f P t h C i
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Table for Post-hoc Comparisons
Power of a test
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Power of a statistical test is the probability of observing atreatment effect when it occurs.
It is the probability that it will correctly lead to therejection of a false null hypothesis (Green, 2000)
The statistical power is the ability of the test to detect aneffect if it actually exists (High, 2000)
The statistical power is denoted by 1 – β, where β is the
Type II error, the probability of failing to reject the nullhypothesis when it is false.
Conventionally, a test with a power greater than .8 level(or β = < .2) is considered statistically powerful.
α = is the probability of rejecting the true null hypothesis (Type I error)
β = is the probability of not rejecting the false null hypothesis (Type II error)
There are four components that
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f p
influence the power of a test:
1) Sample size, or the number of units (e.g., people)accessible to the study
2) Effect size, the difference between the means, divided
by the standard deviation (i.e. 'sensitivity') 3) Alpha level (significance level), or the probability that
the observed result is due to chance
4) Power, or the probability that you will observe atreatment effect when it occurs
Usually, experimenters can only change the sample size(population) of the study and/or the alpha value
Other ways to calculate Sample size and
Confidence Interval
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Confidence Interval
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T l l t S l Si
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To calculate Sample Size or
Power
http://www.stat.ubc.ca/~rollin/stats/ssize/n2.
html
http://www.downloadforge.com/Windows/Mathematics/Download/GPower-319.html
Sample size and Effect size Table
http://www.stat.ubc.ca/~rollin/stats/ssize/n2.htmlhttp://www.stat.ubc.ca/~rollin/stats/ssize/n2.htmlhttp://www.stat.ubc.ca/~rollin/stats/ssize/n2.htmlhttp://www.downloadforge.com/Windows/Mathematics/Download/GPower-319.htmlhttp://www.downloadforge.com/Windows/Mathematics/Download/GPower-319.htmlhttp://www.downloadforge.com/Windows/Mathematics/Download/GPower-319.htmlhttp://www.downloadforge.com/Windows/Mathematics/Download/GPower-319.htmlhttp://www.stat.ubc.ca/~rollin/stats/ssize/n2.html
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ANOVA (1-way)
To compare 3 groups or more on a
dependent variable.
Same assumptions as T-tests applyAnalyze Compare Means One-way
ANOVA
Do Exercise 10A, page 11.
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Sample APA Table for One-way ANOVA
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90Source: Palaniappan, A. K. (2009). Penyelidikan Pendidikan dan SPSS .
Kuala Lumpur, Malaysia: Pearson.
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2 – way ANOVA, 3 - way ANOVA
Do exercise on p.11
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ANCOVA
Try exercise on ANCOVA on page 10.
Presentation of Three
-
way ANOVA results
Table 4
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Table 4
Analysis of Variance using CRA scores as the dependent variable
Source of Variation Sum of DF Mean F Signif.
Squares Squares of F
Main Effects 14.916 3 4.972 .318 .812
Sex .192 1 .192 .012 .913
SAM grps 12.994 1 12.994 .830 .370
WK grp 3.346 1 3.346 .214 .648
2-way Interactions 32.025 3 10.675 .682 .571
Sex x SAM grps 8.403 1 8.403 .537 .470
Sex x WK grps 15.077 1 15.077 .963 .335
SAM grps x WK grps 13.149 1 13.149 .840 .367
3 – way Interactions 2.472 1 2.472 .158 .894Sex x SAM grps x WK
grps
Model 55.588 7 7.941 .507 ,821
Residual 422.583 27 15.651
Total 478.171 34 14.064
Reporting ANOVA
Simple
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Reporting ANOVA – Simple
Factorial As shown in Table 2, there is no significant differences between fathers
and mothers with respect to Child Rearing Practices ( F = .12, p > .05).
The results also show that WK groups ( F = .83, p > .05) and SAM
Groups ( F = .24, p > .05) also do not have significant effects on CRA
Scores. There are also no significant two-way interactions or three-way
Interactions between sex, WK groups and SAM groups.
The results indicate male parents do not differ from female parents
in their child rearing practices. Their creative perceptions also donot affect their child rearing practices.
Sample Report of an Experimental Research
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Dalton, J. J. & Glenwick, J. S. (2009). Effects of Expressive Writing
on Standardized Graduate Entrance Exam Performance and Physical
Health Functioning.The Journal of Psychology,143(3), 279 –
292
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Part II
Factor Analysis
Reliability – Item Analysis
Multiple Regression One-way Repeated Measures ANOVA
Multivariate ANOVA (MANOVA)
Discriminant Analysis
Testing for Moderating Effects of a Variable
FACTOR ANAYSIS
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C O N S S
Factor analysis is undertaken to ascertain howmay factors are measured by the items you haveconstructed. This is sometimes called DataReduction.
To do this, you need to enter the data item by item
in your datafile. Using Factor Analyses you will be able to tell which items are strongly correlatedand lump together to form a factor. By looking atthese items you will be able to give a collectivename to represent these items or Factor.
SPSS will be able to tell how many factors thereare and how many items fall in each factor.
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FACTOR ANALYSIS
Data are entered item by item in the datafile
In Factor Analyses you will be able to tell which
items are strongly correlated and lump together to
form a factor. By looking at these items you will
be able to give a collective name to represent these
items or Factor .
SPSS will indicate how many factors there are andhow many items fall in that factor.
Assumptions for Factor Analysis
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Assumptions for Factor Analysis
There must be at least [X variables (items) x 5]
respondents or more than 200 respondents to run FactorAnalysis reliably.
There must be linear relationship between the variables oritems
There should not be any outliers for each variable.
The correlations among the items must be more than .3 inorder to factorizable.
To be factorizable, the Bartlett’s test of sphericity must besignificant and large.
To be factorizable, the Kaiser-Meyer-Olkin (KMO)measure of Sampling Adequacy must be more than .6
To ensure sampling adequacy, the anti-image correlationmatrix is used. Variables with sampling adequacy below .5(see the diagonal of the anti-image correlation matrix)should be excluded from Factor Analysis.
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FACTOR ANAYSIS
Exercise 19
Using the datafile “Datafile for Item
Analysis and Factor Analysis” run a factoranalysis of all 20 items and determine how
many factors there are. By looking at the
items that fall within each factor, can yougive a common name to represent all the
items in each factor?
Factor Analysis Output
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y p
KMO and Bartlett's Test
.466
7478.285
3741
.000
Kaiser-Meyer-Olkin Measure of Sampling
Adequacy.
Approx. Chi-Square
df
Sig.
Bartlett 's Test of
Sphericity
The Kaiser-Meyer-Olkin Measure of Sampling Adequacy is less
than .6 (should be more than .6, the higher the better) so the
variables are marginally factorizable.
The Bartlett’s Test of Sphericity is significant p < .05. This indicates
that the variables are related and therefore factorizable.
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ITEM ANALYSIS
Item analysis is undertaken to ascertain to whatextend the items measuring a certain construct arecorrelated. Items that are closely correlatedindicate high internal consistency or reliability ofthe test. The measure of internal consistency orreliability is given by Cronbach Alpha.
If the items are ordinal (eg likert scale), SPSS willgive the Cronbach Alpha. But if the items are
dichotomous, you will need to use Kuder-Richardson 20 which also obtained by requestingCronbach Alpha.
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Item Analysis
Use the data file in your desktop icon called
SPSS WORKSHOP, use the data file called
“Datafile for Item Analysis and FactorAnalysis” run the Item Analysis and
ascertain the best Cronbach Alpha
Exercise 19
Sample Factor Analysis table
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Multiple Regression
Bivariate Multiple Regression
Aca Ach = Constant + b Motivation
Multivariate Multiple Regression
Aca Ach = Constant + b1 Motivation + b2 Creativity + b3 Self-confidence
Multiple Regression
-
Assumptions1) Ratio of cases to independent variables:
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20 times more cases than predictors
2) Variables must be normally distributed – check graphically or statistically(e.g. Box-plot, Histogram, skewness and kurtosis, Kolmogorov-Smirnof orShipiro Wilk)
3) IV must be linearly related to DV (Use Scatter-plot for BivariateRegression). For Multitivariate Use Residual Scatter Plot betweenStandarized residuals (Y-axis) and Standardized Predicted value (X-axis) – iflinearly related – points in scatter plot are evenly distributed on both sides of0 value of the Standardized Predicted value (X-axis).
4) No multicollinearity – IVs must not be significantly correlated (use Pearsoncorrelation Matrix to check / Tolerance = 1 – R 2 (must be more than .1) / VIF(Variance Inflation Factor) = 1/Tolerance (must be less than 10) [R is thecorrelation coefficient between the 2 IVs or predictors which should not bemore than .7. If more than .7, omit 1 of the IV or combine the IVs]
5) No multivariate outliers – use Mahalanobis Distance to ascertain this. UseChi-square value at p < .001 and df (= no of IVs) from Chi-square table todetermine which data is outlier in the MAHAL column produced in the
Datafile.
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Residuals are the differences between the predicted DVcalculated from the predictors and the obtained DV – obtained from the study.
Normality: These residuals must be normally distributed
about the predicted DV scores Linearity: These residuals should have a straight-line
relationship with the predicted DV scores
Homoscedasticity: The variance of the residuals about predicted DV scores should be the same for all predicted
scores Normality, Linearity and Homoscedasticity can be checked
using the residuals scatterplots generated by SPSS.
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Scatterplot
Dependent Variable: Highest Year of School Co
Regression Standardized Predicted Value
3210-1-2-3-4
4
3
2
1
0
-1
-2
-3
-4
Example of Scatterplot between Std Residual and Std Predicted Value
Collinearity Statistics
-
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Collinearity Statistics
Tolerance
Tolerance – is the statistic used to determine how
much the independent variables are linearly
related to one another (Multicollinear)
-Tolerance is the proportion of a variable's
variance not accounted for by other independent
variables in the model and is given by 1 – R 2,
where R is the correlation coefficient between the2 IVs or predictors.
Tolerance level must be more than .1
C lli i S i i
VIF
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Collinearity Statistics - VIF
VIF – Variance Inflation Factor
- is the reciprocal of the Tolerance
VIF should be less than 10
D bi
W
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Durbin-Watson
Gives a measure of autocorrelations in the
residuals (or errors) in the values or observations
in the multiple regression analyses
If the Durbin-Watson value is between 1.5 and
2.5, then the observations or values are
independent there are no systematic trend in
the errors of the observation of the values (thereshould not be a systematic trend in the errors)
Multivariate Outlier
–
an
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Multivariate Outlier an
example
It is usual to find a person who is 15 years old and willnot be a outlier when you plot a histogram for age(univariate)
It is also common to find a person earning a salary of
RM10,000 a month and this person may not be an outlierwhen you plot a histogram for salary (univariate)
However, if you combine both age and salary(multivariate) a person who is 15 years old earningRM10,000 may become an outlier called multivariate
outlier You need to get rid of multivariate outlier using
Mahalanobis Distance before you run your multipleregression
What havoc a multivariate outlier can do to your results?
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It can change your R from .08 to .88!
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Methods for Selecting Variables
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Forward Selection – starting from the constant
term, variable is added to the equation orregression model if it results in the largestsignificant (at p < .05 for e.g.) increase in multipleR 2 .
Backward Selection – all variables are put into
the equation or regression model. At each step, avariable is removed if this removal results in onlya small insignificant change in R 2.
Stepwise variable Selection – most commonly
used method for model building. Is a combinationof Forward Selection and Backward Selection.Variables already in the model can be removed ifthey are no longer significant predictors when newvariables are added to the regression model.
T f R i A l
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Types of Regression Analyses
Standard Multiple Regression
Sequential / Hierarchical Multiple
RegressionStatistical / Stepwise Multiple Regression
Coding for Dummy Variables
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Example:
Gender – dichotomous
Male – 1
Female - 2
Need to convert to dummy variable
Male - 1
Female - 0
to study the effect of gender on the DVif r = sig + , male has higher significant effect on DV
if r = sig - , female has higher significant effect on DV
U i PRACTICE d t fil
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Using PRACTICE data file
Research Question:
1) To what extent do PAEDU and MAEDU
predict EDUC?2) To what extent do PAEDU, MAEDU and
SEX predict EDUC?
3) To what extent do PAEDU, MAEDU,SIBS and SEX predict EDUC?
Results of Mul Reg for Research Question 2
Descripti e Statistics
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Descriptive Statistics
13.54 2.797 973
11.01 4.117 97311.02 3.409 973
.4245 .49452 973
educ
paeducmaeduc
sexdummy
Mean Std. Dev iation N
Correlations
1.000 .450 .429 .112
.450 1.000 .672 .102
.429 .672 1.000 .065
.112 .102 .065 1.000
. .000 .000 .000
.000 . .000 .001
.000 .000 . .021
.000 .001 .021 .
973 973 973 973
973 973 973 973
973 973 973 973
973 973 973 973
educ
paeduc
maeduc
sexdummy
educ
paeduc
maeduc
sexdummy
educ
paeduc
maeduc
sexdummy
Pearson Correlation
Sig. (1-tailed)
N
educ paeduc maeduc sexdummy
Results of Mul Reg for Research Question 2 (contd)
Model Summaryd
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.450a .203 .202 2.499 .203 246.937 1 971 .000
.481b .232 .230 2.454 .029 36.704 1 970 .000
.486c .236 .234 2.448 .004 5.670 1 969 .017 1.738
Model
1
2
3
R R Square
Adjusted
R Square
Std. Error of
the Estimate
R Square
Change F Change df 1 df 2 Sig. F Change
Change Statistics
Durbin-
Watson
Predictors: (Constant), paeduca.
Predictors: (Constant), paeduc, maeducb.
Predictors: (Constant), paeduc, maeduc, sexdummyc.
Dependent Variable: educd.
ANOVAd
1541.572 1 1541.572 246.937 .000a
6061.733 971 6.243
7603.305 972
1762.582 2 881.291 146.361 .000b
5840.724 970 6.021
7603.305 972
1796.560 3 598.853 99.934 .000c
5806.745 969 5.993
7603.305 972
Regression
Residual
Total
Regression
Residual
Total
Regression
Residual
Total
Model
1
2
3
Sum of
Squares df Mean Square F Sig.
Predictors: (Constant), paeduca.
Predictors: (Constant), paeduc, maeducb.
Predictors: (Constant), paeduc, maeduc, sexdummyc.
Dependent Variable: educd.
Multiple Regression Results
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Coefficientsa
10.178 .229 44.499 .000 9.729 10.627
.306 .019 .450 15.714 .000 .268 .344 1.000 1.000
9.254 .272 34.077 .000 8.721 9.787
.201 .026 .295 7.768 .000 .150 .251 .548 1.826
.189 .031 .230 6.058 .000 .128 .250 .548 1.826
9.142 .275 33.250 .000 8.602 9.681
.196 .026 .288 7.574 .000 .145 .246 .544 1.837
.189 .031 .231 6.085 .000 .128 .250 .548 1.826
.380 .160 .067 2.381 .017 .067 .693 .990 1.011
(Constant)
paeduc
(Constant)
paeduc
maeduc
(Constant)
paeduc
maeduc
sexdummy
Model
1
2
3
B St d. Error
Unstandardized
Coeff icients
Beta
Standardized
Coeff icients
t Sig. Lower Bound Upper Bound
95% Confidence Interval for B
Tolerance VIF
Collinearity Statistics
Dependent Variable: educa.
Reporting Results of Mul Reg for Research Question 2
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Table XX
Standard Multiple Regression of PAEDUC, MAEDUC and SEXDUMMY on EDUC
Variables EDUC PAEDUC MEADUC B β t p < .05
PAEDUC .45 .20 .29 7.57 Sig
MEADUC .43 .67 .20 .19 .23 6.09 Sig
SEXDUMMY .11 .10 .07 .38 .07 2.38 Sig
Intercept = 9.14
Means 13.54 11.01 11.02 R = .49R 2 = .24
SD 2.80 4.12 3.41 Adjusted R 2 = .23
Reporting Multiple Regression Results
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A standard multiple regression was performed between respondents’
level of education, EDUC as the dependent variable and fathers’ levelof education (PAEDUC), mothers’ level of education (MAEDUC) and
respondents’ gender (SEXDUMMY). The assumptions were evaluated
using SPSS EXPLORE.
Table XX displays the correlations between the variables, the
unstandardized regression coefficients, B, and intercept, the standardizedRegression, β , R 2 and adjusted R 2.
R for regression was significant, F (3, 969) = 99.93, p < .05.
with R 2 =.24.
The adjusted R 2 of .23 indicates that more than one-fifth of the variability
of EDUC is predicted by the three predictors.
The regression equation is:
EDUC = 9.14 + .380 + .20 (PAEDUC) + .19 (MAEDUC) + .380 (SEXDUMMY)
Multiple Regression
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Multiple Regression
Try exercise on Linear Regression and
Multiple Regression on page 26.
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Hierarchical Multiple Regression
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Hierarchical Multiple Regression
Is used when there is a need to control for certain
variables
For example, if we wish to study how PEADUC
and MEADUC predict EDUC while controlling
for Age of the respondent and the number of
siblings (SIBS)
We enter Age and SIBS in the first batch ofvariables and then enter PEADUC and MEADUC
in the second batch as predictors of EDUC
Coefficientsa
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Coefficients
15.528 .263 59.086 .000-.038 .005 -.226 -7.463 .000 -.254 -.233 -.225 .986 1.014
-.233 .030 -.238 -7.842 .000 -.264 -.244 -.236 .986 1.014
9.855 .512 19.230 .000
-.007 .005 -.044 -1.391 .165 -.254 -.045 -.039 .786 1.272
-.126 .029 -.128 -4.387 .000 -.264 -.140 -.122 .900 1.111
.219 .028 .303 7.825 .000 .463 .244 .217 .516 1.938
.137 .033 .159 4.098 .000 .419 .131 .114 .513 1.948
(Constant) Age of Respondent
Number of Brothers
and Sisters
(Constant)
Age of Respondent
Number of Brothers
and Sisters
Highest Year School
Completed, Father
Highest Year School
Completed, Mother
Model
1
2
B Std. Error
Unstandardized
Coeff icients
Beta
Standardized
Coeff icients
t Sig. Zero-order Partial Part
Correlations
Tolerance VIF
Collinearity Statistics
Dependent Variable: Highest Year of School Completeda.
Model Summaryc
Model R R Square
Adjusted
R Square
Std. Error of
the Estimate
R Square
Change F Change df 1 df 2 Sig F Change
Change Statistics
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.347a .120 .118 2.802 .120 66.311 2 971 .000
.502b .252 .249 2.586 .132 85.238 2 969 .000
Model
1
2
R R Square R Square the Estimate Change F Change df 1 df 2 Sig. F Change
Predictors: (Constant), Number of Brothers and Sisters, Age of Respondenta.
Predictors: (Constant), Number of Brothers and Sisters, Age of Respondent, Highest Year School Completed, Father, Highest
Year School Completed, Mother
b.
Dependent Variable: Highest Year of School Completedc.
APA Report:
Hierarchical Multiple Regression was used to assess the ability of PAEDUC and
MAEDUC in predicting EDUC while controlling for Age and Sibs,
Age and Sibs were entered at Step 1 (Model 1) explaining 12% of the
variance in EDUC. On entering PAEDUC and MAEDUC at Step 2
(Model 2), the total variance explained was 25.2%, F(4, 969) = 81.53,
p < .001)
PEADUC and MEADUC explained 13.2% of the variance on EDUC
after controlling for Age and SIBS, R squared change = .13,
F change (2, 969) = 85.24.
In the final model, only Sibs, PAEDUC and MAEDUC were
statistically significant, with PAEDUC having a higher sig effect on
EDUC than MAEDUC or SIBS.
Exercise
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Exercise
1) Are PAEDUC and MAEDUC significant
predictors of SIBS if we control for Age and
EDUC? Report your findings in the APAformat.
Binary Logistic Regression
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Binary Logistic Regression
Used when you want to predict a binary
criterion (dependent) variable.
Eg. of binary dependent variable0 – No diabetes, 1 – Has diabetes
0 – No default, 1 – defaults
0 – Does not graduate, 1 - graduates
134
Assumption of binary logistic regression
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Dependent variable must be binary (1 for the desired
outcome and 0 for the other outcome) for binary logisticregression
Dependent variable must be ordinal for Ordinal or
Multinormial logistic regression.
Does not need to make many of the assumptions of linearregression. Eg does not need to satisfy conditions of
linearity, normality, homoscedasticity and measurement
level.
Does not need a linear relationship between the dependentand independent variables.
Can handle all types of relationships because it uses non-
linear log transformation to predict odds-ratio.135
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Eg
of Research Question: Do EDUC, PAEDUC and
MAEDUC predict
HAPPYrec
(1 = happy 0 = not
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MAEDUC predict HAPPYrec (1 happy, 0 not
happy)
Record HAPPY to HAPPYrec. (Happy 1 and 2 recode to 1
and Happy 3 record to 0)
In SPSS: Analyze Regression Binary Regression.
Enter HAPPYrec into Dependent box.
Enter EDUC, PAEDUC and MAEDUC into Covariates
box.
Click Save – check Probabilities and Group membership
(In the datafile, the respondents will be classified into
groups)
Click Options – select Hosmer-Lemeshow goodness-of-fit
(to test to what extent the model fits the data) and Iteration
History. 137
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In the Output: A) Step 1: is like the test of the null hypothesis when there
are no predictors in the equation. The prediction is 90.7%
accurate.
138
The predictors are
all not sig.
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B) Step 2: when the predictors are entered,
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All 3 predictors are
not sig. not
included in the model.
The percentage
accuracy is still
90.7%
One
-
way Repeated Measures
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ANOVA
This analysis is used to compare one sample onthree or more variables.
Click Analyze General Linear Model
Repeated Measures You will get the Repeated Measures Define
Factors Dialogue box.
Example of Research Question: Are there
significant differences in Health1, Health2 andHealth3?
One
-
way Repeated Measures
ANOVA
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ANOVA In Within-Subject Factor Name: box, type Health which is measured at 3
different times, (assuming). In the Number of Levels: type 3
Click Add.
Click Define and in the Repeated Dialogue Box click the 3 variables: Health1,Health2 and Health3.
If you want to compare this between male and female, click on the Betweensubjects variable – in this case – Sex and move it to Between-subjects Factors box.
Click on Options, then Display and click on Descriptive stats, Estimates ofeffect size, Homogeneity tests and power, then Continue.
Click on Plots, then click on Within group variable (in this case Health) andmove it to the box labeled Horizontal Axis.
In the Separate Lines box, click on the grouping variable (i.e. Race)
Click Add Click Continue and OK.
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Mauchly's Test of Sphericityb
Measure: MEASURE_1
Epsilona
Test equality of Variance or Sphericity
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.666 408.769 2 .000 .750 .751 .500
Within Subjects Ef fect
health
Mauchly 's W
Approx.
Chi-Square df Sig.
Greenhous
e-Geisser Huynh-Feldt Lower-bound
Epsilon
Tests the null hypothesis that the error covariance matrix of the orthonormalized transf ormed dependent variables is
proportional to an identity matrix.
May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in
the Tests of Within-Subjects Ef fects table.
a.
Design: Intercept
Within Subjects Design: health
b. Mauchly’s W sig at p < .05, there is sig difference in variance
among the 3 measures so statistical correction must be made
choose Hunyh-Feldt correction F value = 810.81 which is Sig
with df = 1.50 and 1513.40.If Mauchly’s W is NOT sig at p < .05, read F value in the
Sphericity Assumed row.
Tests of Wi thin-Subjects Effects
Measure: MEASURE_1
171.779 2 85.889 810.813 .000 .446 1621.626 1.000
171.779 1.500 114.546 810.813 .000 .446 1215.939 1.000
171.779 1.501 114.413 810.813 .000 .446 1217.347 1.000
171.779 1.000 171.779 810.813 .000 .446 810.813 1.000
213.555 2016 .106
213.555 1511.651 .141
213.555 1513.402 .141
213.555 1008.000 .212
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sourcehealth
Error(health)
Type III Sum
of Squares df Mean Square F Sig.
Part ial E ta
Squared
Noncent.
Parameter
Observed
Power
a
Computed using alpha = .05a.
Effect Size
df 1
df 2
Check Assumptions of Equality of
Error Variance and Equality of
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Error Variance and Equality of
Covariances Matrices In the output check the Levene’s Test of
Equality of Error Variance. If not sig at
p =.05, then assumption of homogeneity ofvariances is not violated.
Then check Box’s Test of Equality of
Covariance Matrices. If sig at p = .001, thenassumption of equality of Covariance is
violated.
Tests of Within-Subjects Effects
Measure: MEASURE_1
S h i it A d
Source
HEALTH
Type III Sum
of Squares df Mean Square F Sig.
Partial Eta
Squared
Noncent.
Parameter
Observed
Power a
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35.625 2 17.813 169.004 .000 .144 338.008 1.000
35.625 1.497 23.802 169.004 .000 .144 252.953 1.000
35.625 1.501 23.727 169.004 .000 .144 253.749 1.000
35.625 1.000 35.625 169.004 .000 .144 169.004 1.000
1.496 4 .374 3.548 .007 .007 14.193 .871
1.496 2.993 .500 3.548 .014 .007 10.621 .788
1.496 3.003 .498 3.548 .014 .007 10.655 .789
1.496 2.000 .748 3.548 .029 .007 7.096 .660
212.059 2012 .105
212.059 1505.710 .141
212.059 1510.448 .140
212.059 1006.000 .211
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
HEALTH
HEALTH * RACE
Error(HEALTH)
Computed using alpha = .05a.
Within Subject Table shows F is sig at p
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2178.266 1 2178.266 17697.670 .000 .946 17697.670 1.000
.698 2 .349 2.836 .059 .006 5.672 .557
123.821 1006 .123
Source
Intercept
RACE
Error
of Squares df Mean Square F Sig. Squared Parameter Power a
Computed using alpha = .05a.
If compared between subjects (Race – White, Black and Others)
RACE line shows F is not sig at p < .05. See Plot to
Confirm this.
Estimated Marginal Means of MEASURE_1
HEALTH
321
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
Race of Respondent
White
Black
Other
2.0
1.9
1.8Means
Estimated Marginal Means of MEASURE_1
Pairwise Comparisons
Measure: MEASURE_1
(J) health
(I) health
Mean
Dif f erence
(I-J) Std. Error Sig.a
Lower Bound Upper Bound
95% Confidence Interval for
Dif f erencea
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321
health
1.8
1.7
1.6
1.5
1.4
Es
timatedMarginalM
APA style report:
There are sig differences in the health measures,
F (1.50, 1513.40) = 810.00, p < .05 with a moderate effect size
(Eta squared = .45). LSD (Least Sig Difference) comparisons revealthat Health3 is significantly higher than Health2 and Health 1 while
Health2 is significantly higher than Health1.
-.494* .017 .000 -.526 -.461
-.516* .016 .000 -.548 -.485
.494* .017 .000 .461 .526
-.023* .009 .016 -.041 -.004
.516* .016 .000 .485 .548
.023* .009 .016 .004 .041
(J) ea t
2
3
1
3
1
2
( ) ea t
1
2
3
( J) Std o Sg o e ou d Uppe ou d
Based on estimated marginal means
The mean dif f erence is signif icant at the .05 lev el.*.
Adjustment f or multiple comparisons: Least Signif icant Dif f erence (equivalent to no
adjustments).
a.
Exercise: Try exercise 23 on p. 12 (SPSS Module Part 2/Advanced)
Exercise 23 (additional Q)
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1. Are there significant differences in EDUC, MAEDUand PAEDU?
2. Are there significant differences in EDUC,
PRESTIG80 and OCCAT80?
3. Assuming hlth1, hlth2 and hlth3 are interval data,
are there significant differences in these 3 variables?
For each analysis, write a report using the APA style.
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Formulate a research question
based on your study which will
require One-way repeatedmeasures ANOVA
MULTIVARIATE ANOVA
(MANOVA)
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(MANOVA)
MANOVA is used when you wish tocompare two or more dependent variables(INTERVAL DATA) among a grouping
independent variable (NOMINAL DATA),e.g. REGION.
For example, you wish to check whether
respondents in the various locations(REGION) (IV) defer in the level of EDUC,MAEDU and PAEDU (several DVs).
Assumptions of MANOVA 1) Sample size – each subgroup n > 30.
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) p g p
2) Linearity between DVs. Can be tested using
Scatter-plots among pairs of the DVs across IVgroups. (Click Graph Legacy DialoguesScatter/PlotMatrix Scatter Define – send alldependent var to Matrix variable box, IV to row box
continue, OK) 3) Univariate and Multivariate Normality – Test
univariate normality using skewness and kurtosis (orKolmogorov-Smirnov) or use EXPLORE in
descriptive statistics (Box Plot). Test Multivariate Normality using Mahalanobis Distance in MultipleRegression Analysis (use ID as the Dependentvariable and the predictors as independent variable)
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4) Univariate test of equality of variance – UseLevene’s test in Output to test this. If Levene’stest is not significant at p < .05 there is equalityof variance among each DV.
5) Homogeneity of variance – covariancematrices – Use the Box’s M test. If Box’s M isnot significant at p < .001 (you need to set at .001
because Box’s M test is very sensitive), it means
that there is homogeneity of variance-covariance). 6) Multicollinearity - use Pearson r (consider
removing one of the DV pairs with r > .8)
MULTIVARIATE ANOVA
(MANOVA)
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(MANOVA)
Analyze General Linear ModelMultivariate
Send the DV to the Dependent variables box
The independent variable to the Fixed Factor box.
Click Options, click REGION and enter it intoDisplay Means
Click Compare Main Effects and click Bonferroniand check Descriptive Statistics and Homogeneitytests.
Click Continue and OK.
Descriptive Statistics
13.53 2.719 454
13.33 3.060 239
13.75 2.679 280
13.54 2.797 973
Region of the
North East
South East
West
Total
Highest Year of
School Completed
Mean Std. Dev iation N
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11.20 3.218 454
10.59 3.466 239
11.10 3.633 280
11.02 3.409 97311.04 3.838 454
10.69 4.421 239
11.22 4.282 280
11.01 4.117 973
North East
South East
West
Total
North East
South East
West
Total
Highest Year School
Completed, Mother
Highest Year School
Completed, Father
The Box’s M tests the homogeneity of
the variance-covariance matrices at p < .001.
Box’s M is not significant at p < .001,
so there are no sig diff in the
variance-covariance homogeneity of
variance
Box's Test of Equality of Covariance Matricesa
26.711
2.215
12
2786265
.009
Box's M
F
df1
df2
Sig.
Tests the null hypothesis that the observed cov ariance
matrices of the dependent variables are equal across groups.
Design: Intercept+regiona.
Levene's Test of Equality of Error Variancesa
1.529 2 970 .217
4 363 2 970 013
Highest Year of
School Completed
Highest Year School
C l t d M th
F df 1 df 2 Sig.
The univariate tests for homogeneityof variance for each DV shows that
for EDUC (not sig at p < .05), there is
no sig diff in var there is equality
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4.363 2 970 .013
5.416 2 970 .005
Completed, Mother
Highest Year School
Completed, Father
Tests the null hypothesis that the error variance of the dependent variableis equal across groups.
Design: Intercept+regiona.
no sig diff in var there is equality
of var.
For MAEDU and PAEDU sig diffno equality of variance need to
Interpret the F for MAEDU and PAEDU
at higher Alpha level say p < .01
Multivariate Tests
.008 1.323 6.000 1938.000 .243
.992 1.322b 6.000 1936.000 .244
.008 1.321 6.000 1934.000 .244
.006 1.800c 3.000 969.000 .146
Pillai's trace
Wilks' lambda
Hotelling's trace
Roy's largest root
Value F Hypothesis df Error df Sig.
Each F tests the multiv ariate eff ect of Region of the United States. These tests are
based on the linearly independent pairwise comparisons among the estimated
marginal means.
Computed using alpha = .05a.
Exact statisticb.
The statistic is an upper bound on F that yields a lower bound on the
significance level.
c.
These Multivariate Tests test whether
there is sig group (REGION) diff
on the linear combination of the DVs.
Pillai’s Trace (most robust of statistic
against Violation of assumptions) is
NOT sig at p < .05so no sig
Multivariate Effect for REGION.
No need to interpret the univariate
between-subject (REGION).
Tests of Between-Subjects Effects
23.697b
2 11.848 1.516 .220 .003 3.033 .324
59.902c
2 29.951 2.586 .076 .005 5.172 .517
38 095d
2 19 047 1 124 325 002 2 248 249
Dependent VariableHighest Year of School Completed
Highest Year SchoolCompleted, Mother
Highest Year School
SourceCorrected Model
Type III Sum
of Squares df Mean Square F Sig.
Partial Eta
Squared
Noncent.
Parameter
Observed
Power a
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38.095 2 19.047 1.124 .325 .002 2.248 .249
165616.187 1 165616.187 21194.722 .000 .956 21194.722 1.000
108579.532 1 108579.532 9375.498 .000 .906 9375.498 1.000
109037.361 1 109037.361 6433.135 .000 .869 6433.135 1.000
23.697 2 11.848 1.516 .220 .003 3.033 .324
59.902 2 29.951 2.586 .076 .005 5.172 .517
38.095 2 19.047 1.124 .325 .002 2.248 .249
7579.609 970 7.814
11233.765 970 11.581
16440.855 970 16.949
186109.000 973
129423.000 973
134366.000 973
7603.305 972
11293.667 972
16478.950 972
g
Completed, Father
Highest Year of School Completed
Highest Year SchoolCompleted, Mother
Highest Year SchoolCompleted, Father
Highest Year of School Completed
Highest Year SchoolCompleted, Mother
Highest Year SchoolCompleted, Father
Highest Year of
School CompletedHighest Year SchoolCompleted, Mother
Highest Year School
Completed, Father
Highest Year of
School Completed
Highest Year SchoolCompleted, Mother
Highest Year SchoolCompleted, Father
Highest Year of School Completed
Highest Year SchoolCompleted, Mother
Highest Year SchoolCompleted, Father
Intercept
region
Error
Total
Corrected Total
Computed using alpha = .05a.
R Squared = .003 (Adjusted R Squared = .001)b.
R Squared = .005 (Adjusted R Squared = .003)c.
R Squared = .002 (Adjusted R Squared = .000)d.
As shown in Pillai’s
Trace test that
multivariate tests are
not sig, (using Bonferroni Correction,
alpha = .05/3 = .017). There are no
significant EDUC, MAEDU and PAEDU
differences by REGION
APA report
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p
MANOVA was undertaken to investigate Region differences in
PAEDUC, MAEDUC, EDUC. All assumptions relating to normality,
linearity, univariate and multivariate outliers (Mahalanobis Distance
within required limits) , homogeneity of variance – covariance
matrices (Box’s M was not sig at p .05.
Note:
(If F is significant, you will need to state Pillai’s trace and effect size –
partial eta squared. Check the mean scores of the DV that is significantfor the 3 regions to check which two regions this DV is significantly
different)
Another example of MANOVA output
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Statistical assumptions of the analyses are met, and descriptive
statistics are reported in Table xx. A one-way between-groups
MANOVA partially supported the first hypothesis of
there being a difference in procrastination types between
students and white-collar workers, Pillai’s Trace=.05,
F (3, 181) = 3.2, p=.03, η p2 = .05, power =.73.
Another eg of MANOVA table with Tukey
Jin Hwang, YoungHo Kim (2011). Adolescents’ physical activity and its
related cognitive and behavioral processes, Biology of Sports, 28, 19-22. (ISI TIER 4)
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g p gy p ( )
DISCRIMINANT ANALYSIS
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Is used when you wish to find out, for example,students with which personality characteristics or
interests (Independent Scale data) will be choosing
which career (Dependent Nominal data).
So the independent variable will be the students’
personality characteristics or interests e.g.
extrovert, creative, etc (Scale Data) and the
dependent variable will be the choice of the careere.g. Medicine or Architecture (Nominal Data)
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To analyze click :
ANALYZE CLASSIFY DISCRIMINANT
Let’s say you wish to find out if you classify
students into Happy, Pretty Happy and Not So
Happy (assume Nominal Variable - HAPPY)
using the information from the Age, EDUC and
Prestig80.
Move the dependent variable (e. g Career) to GroupingVariable Click Define Range to indicate how many
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Variable. Click Define Range to indicate how manydifferent types of Career you wish to study and indicate theMaximum and Minimum number.
Click independent variables (e.g. Personality variables) tothe independents box.
Click Use Stepwise Method.
Click STATISTICS, and select Means, UnivariateANOVAs, Box’s M and Unstandardized FunctionCoefficients and Total Covariance Matrix and SeparateGroup Covariance. Click Continue.
Click CLASSIFY and select Summary table, clickContinue.
Click METHOD button – Wilk’s Lambda selected asdefault as statistic that will be used for the addition and
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default as statistic that will be used for the addition andsubtraction of variables to and from the discriminant
functions. The criteria set for entry and removal are 3.84and 2.71 respectively. [Or check the lower radio button toset using the F values i.e. at .05 and .01]
Click SAVE to get Discriminant Analysis: Save dialogue
box which give Discriminant Scores and Predicted GroupMembership in the Data File.
If you wish to analyze for Male students only, you can useSelection Variable and click 1 for male in the Value Box.
Then click OK to execute the Discriminant Analysis
165
OUTPUTGroup Statistics
47 28 17 766 441 441 000Age of Respondent
General Happiness
Very Happy
Mean Std. Deviat ion Unweighted Weighted
Valid N (listwise)
No of
respondents
in each
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47.28 17.766 441 441.000
13.52 2.987 441 441.000
45.19 12.883 441 441.000
44.82 17.422 814 814.000
12.87 2.914 814 814.000
42.22 12.925 814 814.000
46.66 17.329 147 147.000
12.28 2.835 147 147.000
40.35 13.653 147 147.000
45.79 17.547 1402 1402.000
13.01 2.952 1402 1402.000
42.96 13.080 1402 1402.000
Age of Respondent
Highest Year of School
Completed
R's OccupationalPrestige Score (1980)
Age of Respondent
Highest Year of School
Completed
R's Occupational
Prestige Score (1980)
Age of Respondent
Highest Year of School
Completed
R's Occupational
Prestige Score (1980)
Age of Respondent
Highest Year of School
Completed
R's Occupational
Prestige Score (1980)
Very Happy
Pretty Happy
Not Too Happy
Total
group
Tests of Equality of Group Means
.996 3.018 2 1399 .049
.983 12.109 2 1399 .000
Age of Respondent
Highest Year of School
Completed
Wilks'
Lambda F df 1 df 2 Sig.
There is sig diff
among the 3 group
(Happy, Pretty Happy
Not so Happy) on the
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.985 10.823 2 1399 .000
Completed
R's Occupational
Prest ige Score (1980)
Not so Happy) on the
3 IVS (AGE, EDUC,
PRESTIG80) at p < .05
Variables in the Analysis
1.000 12.109
.929 15.166 .996
.929 6.042 .983
Highest Year of
School Completed
Highest Year of School Completed
Age of Respondent
Step
1
2
Tolerance F to Remove
Wilks'
Lambda
High Tolerance value
means that IVs can contribute
to the discrimination.
“F to Remove” tests the sig of
the decrease in discrimination
if the variable is removed.
Since Prestig80 has F less than
2.71 (default) i.e. 1.993, it is
removed from prediction.
Variables Not in the Analysis
1.000 1.000 3.018 .996
1.000 1.000 12.109 .983
1.000 1.000 10.823 .985
.929 .929 6.042 .975
.737 .737 3.146 .979
.716 .665 1.993 .972
Age of Respondent
Highest Year of School
Completed
R's Occupational
Prest ige Score (1980)
Age of Respondent
R's Occupational
Prest ige Score (1980)
R's Occupational
Prest ige Score (1980)
Step
0
1
2
Tolerance
Min.
Tolerance F to Enter
Wilks'
Lambda
Eigenvalues
.024a 91.1 91.1 .152
.002a 8.9 100.0 .048
Function
1
2
Eigenvalue % of Variance Cumulativ e %
Canonical
Correlation
First 2 canonical discriminant f unctions were used in thea
Function 1 has
The highest
% of variance
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First 2 canonical discriminant f unctions were used in the
analysis.
a.
Wilks' Lambda
.975 36.038 4 .000
.998 3.244 1 .072
Test of Function(s)
1 through 2
2
Wilks'
Lambda Chi-square df Sig.
Wilks’ Lambda
is sig for Function
1 and 2.
Structure Matrix
.837* -.547
.509* -.160
.305 .952*
Highest Year of School
Completed
R's Occupational
Prestige Score (1980)a
Age of Respondent
1 2
Function
Pooled within-groups correlations between discriminating
variables and standardized canonical discriminant f unctions
Variables ordered by absolute size of correlation within f unction.
Largest absolute correlation between each v ariable and
any discriminant f unct ion
*.
This variable not used in the analysis.a.
Classification Resultsa
214 105 148 467
310 227 329 866
General HappinessVery Happy
Pretty Happy
CountOriginalVery Happy Pretty Happy
Not TooHappy
Predicted Group Membership
Total
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47 39 77 163
5 1 6 12
45.8 22.5 31.7 100.0
35.8 26.2 38.0 100.0
28.8 23.9 47.2 100.0
41.7 8.3 50.0 100.0
Not Too Happy
Ungrouped cases
Very Happy
Pretty Happy
Not Too Happy
Ungrouped cases
%
34.6% of original grouped cases correctly classif ied.a.
The success rate of
predicting HAPPY using
EDUC, AGE and
PRESTIG80 is 34.6%
Those in Not Too Happy
were most accuratelyclassified (47.2%) followed
by those in Very Happy (45.8%).
Pretty Happy is least successfully
classified (26.2%)
Those not classified in Very Happy
tend to be classified as Pretty Happy
than in Not Too Happy
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Note: if we click ‘Save’ and ‘Predicted
Group Membership’ you will get a column
in the datafile with the predicted group each
respondent will belong to!
Testing for
Moderating
Effects of
a Variable
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a Variable
Use Multiple Regression with the
Moderating Variable as Dummy Variable.
Eg. If sex is the moderating variable,RECODE Male = 1 and Female = 0 to s
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