researchr&d
TRANSCRIPT
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What is research? Another process of “tool” or sense making The world is a complex place
Dynamic, ever-changing Driven by entropy, chaos Built-in rot, decay, obsolescence Need to be always in control
From Science: devices and remedies From Soc. Science: mental tools/strategies
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PENYELIDIKAN PENDIDIKAN (EDUCATIONAL RESEARCH)
GURU MEMBUAT KEPUTUSAN LIBATKAN PILIHAN DAN RISIKO
PERLUKAN MAKLUMAT,FAKTA,PENGALAMAN
MERUPAKAN PROSES PENYELIDIKAN
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EDUCATIONAL RESEARCH
RESEARCH BERMULA DENGAN ADANYA PERASAAN TIDAK PUASHATI TERHADAP SUASANA KERJA,CORAK PENGURUSAN P&p DAN PRESTASI DIRI
PENYELIDIKAN –PROSEDUR YANG TERATUR UNTUK UNTUK MEMPEROLEHI PENGETAHUAN DAN KEMAHIRAN BARU
HASILNYA DINAMAKAN SEBAGAI NISBA ATAU VARIABLE BARU
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PP
Proses penyelidikan libatkan kenalpasti masalah,mengumpul ,menganalisis dan mentafsir bukti untuk membuat keputusan
PP ditafsirkan sebagai prosedur teratur untuk memperolehi pengetahuan dan kemahiran baru dalam kurikulum pendidikan.
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Pendekatan Kuantitatif dan Pendekatan Kualitatif• Quantitative approaches is a deductive
process which attempting to provide evidence for or against a pre-specified objectives focused on testing preconceived outcomes.
• Qualitative approach usually begins with open- ended observation or interviews and analysis, most often looking for patterns and processes that explain “how and why” questions.
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Kajian Kualitatif
Definisi: Satu usaha untuk memahami sesuatu situasi itu dalam keadaannya yang tersendiri. Bagaimana individu itu bertindak, berinteraksi, menjalani kehidupan harian secara neutral, menunjukkan reaksi dalam menghadapi liku-liku kehidupan yang ditempuhi, Input akhirnya ialah satu hasil kajian yang memberi kefahaman yang mendalam mengenai kehidupan sebenar responden yang dikaji (Pattom, 1985).
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Ciri Penyelidikan kualitatif
•Penyelidik adalah instrumen data dan analisis yang akan dibuat
•Penyelidikan kualitatif melibatkan kerja lapangan
•Penyelidikan kualitatif bersifat deskriptif tentang peristiwa, manusia dan proses
•Penyelidikan kualitatif bersifat induktif
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The differences Qualitative research
Introduce new theories Suggest causes Descriptive, bottom-up Uses inductive thinking
Quantitative research Sharpen old/existing tools Suggest a cure Prescriptive, top-down Uses deductive thinking
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What is research? Another process of “tool” or sense making The world is a complex place
Dynamic, ever-changing Driven by entropy, chaos Built-in rot, decay, obsolescence Need to be always in control
From Science: devices and remedies From Soc. Science: mental tools/strategies
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Quantitative Research Sharpen / replace existing practices / tools Prescribe, top-down intervention Paradigms, theories & models play Critical
Roles Justification: “….no study has yet explored
the use of this P / T / M in this context…..”, Title: “The effects of an IV on a DV among
an MV…..”
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Quantitative Research
Create a structure to guide research:Conceptual Framework
Theoretical
Identify an alternativeStructure to guide research:
Framework
Grand theoryMidrange theoryMicro-range theory
Conceptual Definitionsof Study Variables, Research Questions, Hypotheses
Operational Definitions tomeasure the study variables
Problem or Need
Instruments
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What is obtained?
A new cure / remedy A more dynamic & productive
paradigm
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Acute AnomaliesMalaysia:- 5 As + Sc + IS + BSc = killers PhD + Datukship + CEO = CBT Car + Motorcycle + License = accidents Schooling + F in all subjects = millionaireThe US:- Best of everything + Best of
everything + best of everything = killersWorld: Islam + marginalization = terrorists
How to study / solve these problems?
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Qualitative Research Reassess known paradigms, theories &
models in specific contexts Non-invasive data collection Justification: “….no adequate P / T / M
currently explains this phenomenon…..”, Title: “Violence in the Malaysian Premier
Schools-A case study” Or “Social construction of technology in the
Malaysian Smart School-A case study…..”
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What is obtained?
A new mind set / problem situation A hidden/grounded theory
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Qualitative Research
RevealGroundedtheory
Survey related theories to guide the development the research instruments
-
Problem in a given context
Piece together bits & pieces of data toaddress the research questions
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SummarySurvey of issues, paradigms, theories, models, frameworks
Lit. review
Identify a Problem/
need
Suggesta cure
Identifyhiddencauses
ChooseP/T/M/F.
Develop theinstruments
Collect theData &
Analyse
Cured?
GroundedTheory?
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Empat kaedah utama pengumpulan data kualitatif
• Pemerhatian• Temubual • Dokumen• Imej
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Dalam beberapa situasi penyelidik
• Mengumpul maklumat melalui pemerhatian sebagai peserta • Mengumpul maklumat melalui pemerhatian sebagai pemerhati• Melakukan temubual tak berstruktur atau terbuka dan mencatatkan temubual • Melakukan temubual tak berstruktur atau terbuka, merekodkan temubual dan dalam bentuk audio melakukan transkripsi temubual
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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) Interprete 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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Types of Educational Research
Action Research-kajian secara sistematik untuk meningkatkan amalan pendidikanoleh golongan yang terlibat melalui tindakan praktis mereka sendiri
Historical Research - describes What was; involves investigating, recording, analyzing and intepreting the events of the past
Descriptive Research - describes What is; involves the describing, recording, analysing and interpreting the conditions that exist, Comparing two or more groups, seeking relationships between two or more variables.
Experimental Research - describes What will be when certain variables are carefully controlled or manipulated
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Descriptive Research
Survey Research Case studies Correlational Research
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Types of Research Designs
Preexperimental Designs - 1) The One-shot Case study
Design 1: One Group
(a) X Y (Experimental)
(b) X Y (Ex Post Facto)
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Types of Research Designs(contd) Preexperimental Designs: 2) One-
Group Pretest-Posttest DesignDesign 2: One Group, Before - After
(a) Yb X Ya (Experimental)
(b) Yb X Ya (Ex Post Facto)
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Types of Research Designs(contd) Preexperimental Designs: The
Static-Group ComparisonDesign 3: Two-Groups
(a) X Y ---------------- (Experimental) (~ X) Y
(b) X Y ----------------- (Ex Post Facto) (~X) ~ Y
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Types of Research Designs(contd) True Experimental Designs: 1) The
Pretest-Postest Control-Group DesignDesign 4:
R Yb X Ya----------------------------
R Yb Ya
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Types of Research Designs(contd) Quasi Experimental Design (Ex
Post Facto Design) - No random assignment of treatment
Design 5:
Yb X Ya----------------------------
Yb Ya
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a good design is measured by its validity - its capability to answer questions it addresses.
2 types of validity: Internal Validity & External Validity
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Internal Validity
asks the question whether a “treatment” really made the difference
Threats to Internal Validity: a) History, b) Maturation, c) Testing, d) Instrumentation, e) Statistical Regression, f) Selection, g) Experimental Mortality and h) Interactions among factors.
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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) Conbach 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 (2) Construct Validity (3) Criterion-related Validity/ Concurrent Validity (4) Predictive Validity
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Validity
Content Validity - if the instrument tests only those aspects that should be tested
Construct Validity - if the test measures what it is supposed to measure
Criterion-related Validity/ concurrent validity - if the test scores are closely related to another test which measures similar construct
Predictive Validity - if the instrument can predict correctly a particular outcome
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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 same group 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 close succession 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 analyses How to COMPUTE and RECODE
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Outline
How to select cases How to interpret results and report How to draw graphs How to create and edit tables and
place in other applications
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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 the following variables:
a) sexb) racec) 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 Statistical Tests
NominalSimple Classification in Categories without any order e.g Boy / Girl Happy / Not Happy Muslim / Buddhist / Hindu
Non-parametric Chi-square
Ordinal Has order or rank orderinge.g. Strongly agree, agree, undecided, disagree, strongly
disagree (LIKERT SCALE)
Non-parametric
Spearman’s rhoMann-WhitneyWilcoxon
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Types of Measurement Scales and their Statistical Analyses
MeasurementScale
Characteristics Type of Data Statistical Tests
IntervalDo not have true 0 points. Has order as well as equal distance or interval between judgements (Social Sciences) e.g. IQ score of 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
Parametric COMPARISON: 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 correct instruments 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 handoutthen answer the questions
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Exploring Data Graphically
To check normality graphically and decide on its appropriate analyses
1) By displaying data Histogram Boxplot Stem-and-leaf Plot
2) By Statistical Analyses Descriptive Statistics M - Estimators Kolmogorov-Sminov Test Shapiro-Wilk
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Histogram
CHILD REARING PRACTICES
25.022.520.017.515.012.510.0
Histogram
Freq
uenc
y
14
12
10
8
6
4
2
0
Std. Dev = 3.89
M ean = 18.0
N = 41.00
18.05
17.00
3.89
.274 .369
-.573 .724
10
26
Mean
Median
Std. Deviation
Skewness
Kurtosis
Minimum
Maximum
Std.Error
CHILD REARINGPRACTICES
Statistics
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Checking Normality - Skewness
Skewness measures the symmetry of the sample distribution
Skewness = StatisticStandard Error
If Skewness < -2 or > +2, reject normality
If -2 < Skewness < 2 ---> Normal distribution
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Negatively Skewed
If Ratio is negativeIf Mean < Median
2213N =
SEX
FEMALEMALE
CR
A
22
20
18
16
14
12
10
8
635
Boxplot
Negatively skewed
MeanMedian
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Positivity Skewed
If Ratio is positive
If Mean > Median
Mean
Median
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Checking Normality - Kurtosis
Kurtosis measures the spread of the data
Kurtosis = StatisticStandard Error
If Kurtosis < -2 or > +2 reject normality
If -2 < Kurtosis < 2 ---> Normal distribution
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Kurtosis Large Positive value = tails of the
distribution are longer than those of a normal distribution
Normal Graf
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Kurtosis
Negative value of Kurtosis indicates shorter tails (Box like distribution)
Normal Graf
5441N =
CHILD REARING PRACTI
30
20
10
0
Slightly positivelyskewed
Largest observed value that isn’t outlier
Smallest observed value that isn’t outlier
Median
75th Percentile
25th Percentile
BoxplotValues more than 1.5 box-lengths from 75th percentile (outliers)
Values more than 3 box-lengths from 75thpercentile
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Stem-and-Leaf Plot
CHILD REARING PRACTICES Stem-and-Leaf Plot
Frequency Stem & Leaf
1.00 1 . 0 2.00 1 . 23 8.00 1 . 44444455 11.00 1 . 66666777777 3.00 1 . 889 8.00 2 . 00000111 4.00 2 . 2233 3.00 2 . 555 1.00 2 . 6
Stem width: 10 Each leaf: 1 case(s)
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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 population representatively, 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-parametric Tests like Chi-square, Spearman’s rho, Mann-Whitney, Wilcoxon
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To show Normality of Data
15.14 14.30
15.25 14.32
15.20 14.37
15.25 14.32
Huber'sM-Estimator
a
Tukey'sBiweight
b
Hampel'sM-Estimator
c
Andrews'Wave
d
MALE FEMALE
SEX
CRA
M-Estimators
The weighting constant is1.339.
a.
The weighting constant is4.685.
b.
The weighting constantsare 1.700, 3.400, and 8.500
c.
The weighting constant is1.340*pi.
d.
15.08 1.12
12.63
17.52
15.20
16.00
16.410
4.05
7
21
14
6.00
-.279 .616
-.065 1.191
14.36 .77
12.75
15.97
14.39
14.00
13.195
3.63
7
21
14
5.00
.025 .491
-.662 .953
Mean
LowerBound
UpperBound
95% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
Mean
LowerBound
UpperBound
95% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
SEXMALE
FEMALE
CRAStatistic Std. Error
Descriptives
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.129 .151
13 22
.200* .200*
.963 .965
13 22
.751 .581
Statistic
df
Sig.
Statistic
df
Sig.
Kolmogorov-Smirnova
Shapiro-Wilk
MALE FEMALE
SEX
CRA
Tests of Normality
This is a lower bound of the true significance.*.
Lilliefors Significance Correctiona.
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
635
Slightly Negatively Skewed
Slightly PositivelySkewed
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Detrended Normal Q-Q Plot of CRA
For SEX= MALE
Observed Value
2220181614121086
Dev
from
Nor
mal
.4
.2
-.0
-.2
-.4
-.6
Normal Q-Q Plot of CRA
For SEX= FEMALE
Observed Value
2220181614121086
Exp
ecte
d N
orm
al
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
Dev
from
Nor
mal
.2
.1
0.0
-.1
-.2
-.3
-.4
Normal Q-Q Plot of CRA
For SEX= MALE
Observed Value
2220181614121086
Exp
ecte
d N
orm
al
1.5
1.0
.5
0.0
-.5
-1.0
-1.5
Detrended Normal Q-Q Plot of CRA
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ExerciseOpen the data file “PRACTICE’ and check the normality of the ‘Age’ data of the respondents usinga) Histogramb) Boxplotc) Stem-and-leafd) E-estimatorse) Kolmogorov-Sminov & Shapiro Wilkf) Normal Q-Q Plotg) Detrended Normal Q-Q Plot
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Testing equality of variance
Levernes Test (SPSS-DataEditor-Analize-Explore -Plots(Leverne)
.000 1 39 .991CHILDREARINGPRACTICES
LeveneStatistic df1 df2 Sig.
Test of Homogeneity of Variance
If Leverne Statistic is highly significant (p < .001), the groups do not have equal varianceIf Leverne Statistic is not significant (p > .001), the groups have equality of variance and t-tests analyses can be undertaken
NotSig.
MothersFathers
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ExerciseYou wish to compare the ages of male and female respondents using the t-test. To use the t-test, you must make sure the variances in the age of male and female respondents are similar. How are you going to do it? Can you use the t-test to compare the ages of male and female respondents in the sample?
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Compute Data
Please try exercise 3.
SPSS data editor - Transform - Compute -
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RECODESPSS 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 casesSPSS Data Editor - Data - Select cases-
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Select cases
Please try Exercise 5
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Parametric Statistical Analyses(Degree of Association/ Relationship)
SPSS Data Editor - Statistics - Correlate - Bivariate -
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Parametric Statistical Analyses(Degree of Association/ Relationship)Pearson Product-moment Correlation
1.000 .204 .285
.204 1.000 .375*
.285 .375* 1.000
. .239 .097
.239 . .016
.097 .016 .
CRA
SOMETHINGABOUTMYSELF
WHAT KINDOFPERSONARE YOU?
CRA
SOMETHINGABOUTMYSELF
WHAT KINDOFPERSONARE YOU?
PearsonCorrelation
Sig.(2-tailed)
CRA
SOMETHINGABOUT
MYSELF
WHATKIND OFPERSON
AREYOU?
Correlations
Correlation is significant at the 0.05 level (2-tailed).*.
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Presenting Correlation Table
Table 1Pearson 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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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. 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). 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 SAM and WKOPAY (r = .375, p < .05). The correlation is positive, indicating that an increase in SAM scores will result in an increase in WKOPAY scores. Results also show that 14% (r squared) of the variance of SAM scores is explained by WKOPAY scores. About 86% of the variance in SAM is unaccounted for.
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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 population
3) Data must be normally distributed
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Parametric Statistical Analyses( comparisons - t-tests )
SPSS Data Editor - Compare means - Independent Sample t test
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Parametric Statistical Analyses( comparisons - t-tests )
13 15.08 4.05 1.12
22 14.36 3.63 .77
SEXMALE
FEMALE
CRAN Mean
Std.Deviation
Std. ErrorMean
Group Statistics
.006 .936 .538 33 .594 .71 1.33 -1.98 3.41
.523 23.128 .606 .71 1.36 -2.11 3.54
Equalvariancesassumed
Equalvariancesnotassumed
CRAF Sig.
Levene's Test forEquality of Variances
t dfSig.
(2-tailed)Mean
DifferenceStd. ErrorDifference Lower Upper
95% ConfidenceInterval of the Mean
t-test for Equality of Means
Independent Samples Test
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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
79
Effect Size
221
___
21
__
ssXX
EffectSize
X1 = 15.08 s1 = 4.05 X2 = 14.36 s2 = 3.63
75.1884.3
72.0
263.305.436.1408.15
EffectSize
Example:
Result: Effect Size (Cohen’s d) = 18.75 (Small effect size)
Note: Effect size ~ .5 (medium); ~ .8 (high)
80
Effect Size measured by Cohen’s d
Cohen’ d Interpretation ~ .2 Small~ .5 Moderate~ .8 Large
81
Report
The mean CRA scores of fathers and mothers are 15.08 and 14.36 and the standard deviations are 4.05 and 3.63 respectively. These scores are subjected to t-test analysis. The Levern’s Test for equality of variance indicates that the variances are similar. The t-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 effect size indicates that parents’ gender has only a small effect on their creative child-rearing practices.
82
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 which is .005.
83
Paired t-test Assumptions 1) Normality of the population difference of
scores – 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 random sampling from population c) Data must be normally distributed
84
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?
85
Parametric Statistical Analyses( comparisons - Oneway ANOVA )
SPSS Data Editor - Compare Means - One-way ANOVA -
86
Parametric Statistical Analyses( comparisons - Oneway ANOVA )
31.145 2 15.573 .632 .537
936.660 38 24.649
967.805 40
149.208 2 74.604 2.193 .126
1292.743 38 34.020
1441.951 40
BetweenGroups
WithinGroups
Total
BetweenGroups
WithinGroups
Total
WHAT KINDOFPERSONARE YOU?
SOMETHINGABOUTMYSELF
Sum ofSquares df
MeanSquare F Sig.
ANOVA
.469 2 38 .629
3.473 2 38 .041
WHAT KINDOFPERSONARE YOU?
SOMETHINGABOUTMYSELF
LeveneStatistic df1 df2 Sig.
Test of Homogeneity of Variances
87
Understanding the ANOVA table
Variations among the sample meansF = ------------------------------------------- Variance within the samples
Between groups sum of squares / df 1 Between mean squareF = --------------------------------------------- = -------------------------- 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 number of 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.
88
Presentation of One-way ANOVA results
Table 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 TestScheffe Procedure
No groups are significantly different at the .05 level
89
Interpreting F
If the F value is significant, then the groups are significantly different
To ascertain which groups are significantly different, perform the Scheffe test.
F (Groups -1, No. of Participants – Groups – 1) = F Value
90
Report
Results show that the three groups do not differ significantly on CRA scores
(F (2, 37) = .632, p >.05). This represents an effect size of 3.22% [{31 / (31 + 937)} x 100] which indicates that only 3.22% of the variance of CRA scores was accounted for by the 3 groups.
(do the same for SAM)
91
Effect Size
Sum of Squares between GroupsEffect Size = ------------------------------------------- x 100 Total Sum of Squares
Is the degree to which the phenomena exists (Cohen, 1988)
92
Power of a test
Power of a statistical test is the probability of observing a treatment effect when it occurs.
It is the probability that it will correctly lead to the rejection of a false null hypothesis (Green, 2000)
The statistical power is the ability of the test to detect an effect 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 null hypothesis 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)
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There are four components that 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 a treatment effect when it occurs
Usually, experimenters can only change the sample size (population) of the study and/or the alpha value
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Parametric Statistical Analyses( Comparison of more than 2 groups on interval data - ANOVA - Simple Factorial)
Statistics - General Linear Model - GLM General Factorial
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Parametric Statistical Analyses( Comparisonof more than 2 groups on interval data - ANOVA - Simple Factorial) Table 2
14.916 3 4.972 .318 .812
.192 1 .192 .012 .913
12.994 1 12.994 .830 .370
3.346 1 3.346 .214 .648
32.025 3 10.675 .682 .571
8.403 1 8.403 .537 .470
15.077 1 15.077 .963 .335
13.149 1 13.149 .840 .367
2.472 1 2.472 .158 .694
55.588 7 7.941 .507 .821
422.583 27 15.651
478.171 34 14.064
(Combined)
SEX
sam grps
wk grps
Main Effects
(Combined)
SEX * samgrps
SEX * wkgrps
sam grps *wk grps
2-Way Interactions
SEX * samgrps * wkgrps
3-Way Interactions
Model
Residual
Total
CRA
Sum ofSquares df
MeanSquare F Sig.
Unique Method
ANOVAa,b
CRA by SEX, sam grps, wk grpsa.
All effects entered simultaneouslyb.
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ANCOVA
Try exercise on ANCOVA on page 10.
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Presentation of Three-way ANOVA resultsTable 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 .894 Sex x SAM grps x WK grps Model 55.588 7 7.941 .507 ,821Residual 422.583 27 15.651Total 478.171 34 14.064
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Reporting ANOVA – Simple Factorial
As shown in Table 2, there is no significant differences between fathersand 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-wayInteractions 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 do not affect their child rearing practices.
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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
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Multiple Regression - Assumptions
1) Ratio of cases to independent variables: 20 more cases than predictors
2) Variables must be normally distributed – check graphically or statistically (e.g. Box-plot, Histogram, skewness and kurtosis, Kolmogorov-Smirnof or Shipiro Wilk)
3) IV must be linearly related to DV (Use Scatter-plot for Bivariate
Regression, For Multitivariate Use Residual Scatter Plot between Standarized residuals and Standardized Predicted value – if linearly related – points in scatter plot are evenly distributed on both sides of 0)
4) No multicollinearity – IVs must be not be significantly correlated (use Pearson correlation Matrix to check)
5) No multivariate outliers – use Mahalanobis Distance to ascertain this.
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Multivariate Outlier – an example It is usual to find a person who is 15 years old
and will not 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 outlier when you plot a histogram for salary (univariate)
However, if you combine both age and salary (multivariate) a person who is 15 years old earning RM10,000 may become an outlier called multivariate outlier
You need to get rid of multivariate outlier using Mahalanobis Distance before you run your multiple regression
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What havoc a multivariate outlier can do to your results?It can change your R from .08 to .88!
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Methods for Selecting Variables
Forward Selection – starting from the constant term, variable is added to the equation or regression model if it results in the largest significant (at p < .05 for e.g.) increase in multiple R2 .
Backward Selection – all variables are put into the equation or regression model. At each step, a variable is removed if this removal results in only a small insignificant change in R2.
Stepwise variable Selection – most commonly used method for model building. Is a combination of Forward Selection and Backward Selection. Variables already in the model can be removed if they are no longer significant predictors when new variables are added to the regression model.
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Types of Regression Analyses
Standard Multiple Regression Sequential / Hierarchical Multiple
Regression Statistical / Stepwise Multiple
Regression
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Coding for Dummy Variables
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 DV if r = sig + , male has higher significant
effect on DV if r = sig - , female has higher significant
effect on DV
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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?
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Results of Mul Reg for Research Question 1
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Results of Mul Reg for Research Question 2
Descriptive Statistics
13.54 2.797 973
11.01 4.117 973
11.02 3.409 973
.4245 .49452 973
educ
paeduc
maeduc
sexdummy
Mean Std. Deviation 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
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Results of Mul Reg for Research Question 2 (contd)Results of Mul Reg for Research Question 2 (contd)
Model Summaryd
.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
Model1
2
3
R R SquareAdjustedR Square
Std. Error ofthe Estimate
R SquareChange F Change df1 df2 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
Model1
2
3
Sum ofSquares df Mean Square F Sig.
Predictors: (Constant), paeduca.
Predictors: (Constant), paeduc, maeducb.
Predictors: (Constant), paeduc, maeduc, sexdummyc.
Dependent Variable: educd.
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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
Model1
2
3
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig. Lower Bound Upper Bound
95% Confidence Interval for B
Tolerance VIF
Collinearity Statistics
Dependent Variable: educa.
Multiple Regression Results
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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.
Tolerance level must be more than .1
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Collinearity Statistics - VIF
VIF – Variance Inflation Factor - is the reciprocal of the tolerance VIF should be less than 10
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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 (there should not be a systematic trend in the errors)
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Reporting Results of Mul Reg for Research Question 2
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 = .49 R2 = .24SD 2.80 4.12 3.41 Adjusted R2 = .23
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Reporting Multiple Regression Results
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) andrespondents’ 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 standardized Regression, β, R2 and adjusted R2. R for regression was significant, F (3, 969) = 99.93, p < .05. with R2 =.24. The adjusted R2 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 + .20 (PAEDUC) + .19 (MAEDUC) + .380 (SEXDUMMY)
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Multiple Regression
Try exercise on Linear Regression and Multiple Regression on page 10.
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Non-parametric tests
do not require a normal distribution do not require equal group variances used with variables that are ordinal or nominal e.g. Chi-square for determining relationship
between nominal - nominal data or nominal - ordinal data (SPSS-Data Editor-Statistics-Summarize-Crosstabs)
e.g Spearman Rank- Order correlation for seeking relationship between ordinal - ordinal data
e.g. Mann-Whitney U-test to compare 2 different groups on a ordinal/interval data
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Non-parametric tests Kruskall-Wallis Test (To compare >
2 different groups) Fiedman Test (To compare same
group > 2 times)
120
Non - Parametric Statistical Analyses(Degree of Association)
SPSS Data Editor - Statistics - Summarize - Crosstabs
121
Non - Parametric Statistical Analyses(Degree of Association)
Chi-square: used to find the degree of association between 2 nominal variablesCount
16 8 8 32
1 8 9
16 9 16 41
.00
1.00
item29
Total
low cr av cr hi cr
cr groups
Total
12.465a
2 .002
14.696 2 .001
11.389 1 .001
41
PearsonChi-Square
Likelihood Ratio
Linear-by-LinearAssociation
N of Valid Cases
Value df
Asymp.Sig.
(2-tailed)
Chi-Square Tests
3 cells (50.0%) have expected count less than5. The minimum expected count is 1.98.
a.
CR - CREATIVE CHILDREARING
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Reporting Cross Tabulations
Descriptive:Sixteen low, 8 average and 9 high creative
parents answered ‘no’ while 1 average and 8 high creativeparents answered “yes” on item 29. The chi-square analyses reveal a significant association between parents’ creativity and their responses, χ2 (2, 41) = 12.47, p <.05.
Interpretation:The results show that creative parents do answer differently
on item 29 with the creative parents significantly answering “Yes”on the item compared to the non-creative parents.
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Non - Parametric Statistical Analyses (Relationship)
Count
8 2 3 13
8 7 13 28
16 9 16 41
.00
1.00
item30
Total
low cr av cr hi cr
cr groups
Total
Crosstab
4.087a
2 .130
4.063 2 .131
3.520 1 .061
41
PearsonChi-Square
Likelihood Ratio
Linear-by-LinearAssociation
N of Valid Cases
Value df
Asymp.Sig.
(2-tailed)
Chi-Square Tests
1 cells (16.7%) have expected count less than5. The minimum expected count is 2.85.
a.
NS
FINDING:There is no relationship between item 30 and the childrearing practices
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Non-Parametric Statistical Analyses (Relationship)
Count
12 5 8 25
4 4 8 16
16 9 16 41
1
2
sam grps
Total
low cr av cr hi cr
cr groups
Total
sam grps * cr groups Crosstabulation
2.244a
2 .326
2.306 2 .316
2.050 1 .152
41
PearsonChi-Square
Likelihood Ratio
Linear-by-LinearAssociation
N of Valid Cases
Value df
Asymp.Sig.
(2-tailed)
Chi-Square Tests
1 cells (16.7%) have expected count less than5. The minimum expected count is 3.51.
a.
NS
FINDING:There is no relationship between SAM and CR
125
Non - Parametric Statistical Analyses (Comparison of Groups on ordinal data)
SPSS Data Editor - Nonparametric Tests - 2 Independent sample
126
Non - Parametric Statistical Analyses (Comparison of Groups on ordinal data)
15 20.97 314.50
26 21.02 546.50
41
SEXMALE
FEMALE
Total
ARTISTRYN
MeanRank
Sum ofRanks
Ranks
Mann-Whitney U-Test
194.500
314.500
-.014
.989
.989b
Mann-WhitneyU
Wilcoxon W
Z
Asymp. Sig.(2-tailed)
Exact Sig.[2*(1-tailedSig.)]
ARTISTRY
Test Statisticsa
Grouping Variable:SEX
a.
Not corrected forties.
b.
NS
FINDING:Fathers and mothers do not differin the variable Artistry
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Used as data reduction method to reduce a large number of variables to a smaller set of factors that is representative of all the variables
Factor Analyses
128
Used as data reduction method to reduce a large number of variables to a smaller set of factors that is representative of all the variables
129
Conclusion
Research Process Types of data Data Entry and Data Examination Data Exploration - both graphical +
statistical Data Analyses - Parametric & Non-
parametric, Interpreting and Reporting
130
OutputKMO and Bartlett's Test
.466
7478.285
3741
.000
Kaiser-Meyer-Olkin Measure of SamplingAdequacy.
Approx. Chi-Square
df
Sig.
Bartlett's Test ofSphericity
The Kaiser-Meyer-Olkin Measure of Sampling Adequacy is less than .5 (should be more than .5, 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.
131
Interpreting Output
Kaiser-Meyer-Olkin Measure of Sampling Adequacy = is the statistic that indicates the proportion of variance in your variables that might be caused by underlying factors. High values (close to 1.0) generally indicate that a factor analysis may be useful with your data. If the value is less than 0.5, the results of the factor analysis probably won't be very useful
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