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Q2: 50% Median.
Q3: 75% .
Q1
Q3
hinges
. Q3-Q1
hspread Inter Quartile Range. Median
. Whiskers: .. outliers Extremes:
1.5 3 :
)Skewness(
) ( ) (
Whiskers .
Q3 (hinge)
MedianQ1 (hinge) hsp
read
Extremes
outliers
Largest Value (not outlier)
smallest value (not outlier)
outliers
Extremes
whiskers
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Boxpolts :Factor Levels together: .
Dependent together: .None: Boxplot.
FactorVariable.
2. Descriptive
:leaf-and-Stem: Stem)(
Leaf)(Stem leaf . 5712151620212330 Stem
Leaf 10 histogram Histogram
Stem-and-Leaf .
VAR1 Stem-and-Leaf Plot
Frequency Stem & Leaf
2.00 0 . 57
3.00 1 . 256
3.00 2 . 013
1.00 3 . 0
Stem width: 10.00
Each leaf: 1 case(s)
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Histogram: .3.Normality Plots with Tests: .4.Level with Levene Test.spread vs: .
)( Factor Variable). 3. (
OK Explore :Explore
Case Processing Summary
56 100.0% 0 .0% 56 100.0%TALLN Percent N Percent N Percent
Valid Missing Total
Cases
Descriptives
68.1607 2.2948
63.5618
72.7596
68.5635
70.0000
294.901
17.1727
32.00
99.00
67.00
26.2500
-.314 .319
-.639 .628
Mean
Lower Bound
Upper Bound
95% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
TALLStatistic Std. Error
Standard ErrorMean = 68.1607, Std.Deviation = 17.1727, Std. Error = 2948.256/1727.17/ ==nSD
Std. Error ) . ( 95% : :
ErrorStdtX .. *55,025.0m
t t0.025) t( n-1=55 SPSS
Transform Compute IDF.T(p,df) Compute Variable
p p = 1-0.025 = 0.975df = 55 IDF.T(0.975,55) =255,025.0.t= 95% :
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Upper Bound = 68.1607+2*2.2948=72.75
Lower Bound = 68.1607-2*2.2948=63.57
:Pr( 57.7257.63
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Quartiles Q1,Q2,Q3 ) Boxplot ( Percentiles
5
% 95
% 10% 90% . Q1 25(25th Percentile)
)(2Q 50(50th Percentile) Q3 75(75th Percentile)
:
Percentiles
34.7000 43.1000 55.2500 70.0000 81.5000 91.3000 93.3000
55.5000 70.0000 81.0000
TALL
TALL
WeightedAverage(Definitio
Tukey's Hinges
5 10 25 50 75 90 95
Percentiles
Q1= 55.2 , Q2= Median= 70 , Q3= 81.5
Inter quartile Range = 81.5 - 55.2 = 26.25
Weighted AverageMethod (n+1)*P = 57*0.05 = 2.85
2.85 .
233 335) Extreme Values( Interpolation :
5th Percentile = 33 * 0.15 + 35 * 0.85 = 34.7
Skewness )Descriptives( 0.314/ 0.319 = - 0.98
(-2,2) Tall . 2 ) ( 2
) . ( M-Estimators
tall.
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M-Estimators
69.1469 69.3859 68.9754 69.3749TALL
Huber'sM-Estimator
aTukey'sBiweight
bHampel's
M-Estimatorc
Andrews'Wave
d
The weighting constant is 1.339.a.The weighting constant is 4.685.b.
The weighting constants are 1.700, 3.400, and 8.500c.
The weighting constant is 1.340*pi.d.
Leaf-and-Stem
Stem-and-Leaf .
TALL Stem-and-Leaf Plot
Frequency Stem & Leaf
4.00 3 . 2357
5.00 4 . 14789
7.00 5 . 0123569
9.00 6 . 001334568
14.00 7 . 00001122344669
9.00 8 . 000233458
8.00 9 . 00122359
Stem width: 10.00
Each leaf: 1 case(s)
togramHis
) . (
TALL
97.5-107.5
87.5-97.5
77.5-87.5
67.5-77.5
57.5-67.5
47.5-57.5
37.5-47.5
27.5-37.5
Histogram
Frequency
16
14
12
10
8
6
4
2
0
Std. Dev = 17.17
Mean = 68.2
N = 56.00
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Boxplots
BoxplotsTall ) . (
Normality Plots with Test: Kolmogrov-Semirnov
:-Normal Q-Q Plot
-Detrended Normal Q-Q Plot
1.Smirnov-Komogrov :
Non-Parametric Goodness of Fit Test . tall.
Tests of Normality
.096 56 .200*TALL
Statistic df Sig.
Kolmogorov-Smirnova
This is a lower bound of the true significance.*.
Lilliefors Significance Correctiona.
D )()(sup xFxFx
DTS
= )(xsF
)(xFT ) ( D Kolmogrov n) (. D= .096P-Value = 0.20>0.05
5% .2.Q Plot-Normal Q
56N =
TALL
120
100
80
60
40
20
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Expected Z Score) Rank Cases
( tall.
Normal Q-Q Plot of TALL
Observed Value
12010080604020
ExpectedNormal
3
2
1
0
-1
-2
-3
(1.5,1.5),(0,0),(-1.5,-1.5).
.
tall .
3.Q Plot-Detrended Normal Q
. SPSS Detrended Normal Q-Q Plot
. ) 95%90( % (-2,2)
. Tall (-2,2)
) 90% ( .
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Linear InterpolationChart Editor .
: Transformation ) 3. (
2
Tall 22 34
)Factor( Factor List Explore
:
Data Editor : Data Editor
Explore AB :
Detrended Normal Q-Q Plot of TALL
Observed Value
10090807060504030
DevfromN
ormal
.2
.1
0.0
-.1
-.2
-.3
-.4
tall factor
80 A
84 A
71 A
72 A
35 A
93 A
91 A
74 A60 A
63 A
79 A
80 A
70 A
68 A
90 A
92 A
80 A
70 A
63 A
76 A
48 A
90 A
92 B
85 B
83 B
76 B
61 B
99 B
83 B
88 B
74 B
70 B
65 B
51 B
73 B
71 B
72 B
95 B
82 B
70 B
33 B
37 B
32 B
41 B
44 B49 B
47 B
50 B
59 B
55 B
53 B
56 B
52 B
64 B
60 B
66 B
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Extreme Values
6 93
16 92
7 91
15 90
22 90
5 35
21 489 60
19 63
10 63
28 99
38 95
23 92
30 88
24 85
43 32
41 33
42 37
44 41
45 44
1
2
3
4
5
1
23
4
5
1
2
3
4
5
1
2
3
4
5
Highest
Lowest
Highest
Lowest
FACTOR
A
B
TALL
Case Number Value
Boxplots :
3422N =
FACTOR
BA
TALL
120
100
80
60
40
20
5
Outlier A 535
Q1=66.75 1.5 3 18.75 Boxplots 5 Label) Label Cases by Explore. (
)62( Test of Homogeneity of Variances
ANOVA )(
) . ( SPSS Levene Test
.
)2,0(~ N. Transformation
.
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Box & Cox . )
. (
Power Transformation
y1-b y 1-b Power :
Slop bPowerTransformation-12Square01None
1\21\2Square Root10Logarithm
3\2-1\2Reciprocal of Square Root2-1Reciprocal
12 1
0 0.671 1-b0.329 0.329 1/2 1
10.Level with Leven Test.Spread vs
) Plots ( )(Levene Statistics
Spread Versus Level Plot) Box & Cox ( )Level(
Inter Quartile Range )Spread( (Slop=0)
Trend .
) . (3: A,B,C,D12
:
DCBATreatments
110004330015208951
86003280016105402
826028800190010203
98303460013504704
7600278009804285
96503280017106206
89002810019307607
.
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60601890019605378
102003140018408459
15500395002410105010
925029000152038711
790022300168549712
9395.83307751701.25670.75Mean
2326.046688.68356.54233.92Std. Deviation
:. 49. .
Data EditorSPSS ) ( depend ) (treat
A,B,C,D. :
AnalyzeDescriptive Statistics Explore
Explore
:
Plots Explore spread vs. Level with levene test) Treat( .
:Power Estimation Plots : :
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Data Editor3
1. Levene.2.
Power Transformation ) . (
Continue.OK :
1
. Levene ) ( ) ( Levene
MeanMedian
10.783 (p-value.000
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Spread vs. Level Plot of DEPEND By TREAT
* Plot of LN of Spread vs LN of Level
Slope = .744 Power for transformation = .256
Level
11109876
Spread
9.0
8.5
8.0
7.5
7.0
6.5
6.0
5.5
A,B,C,D b=0.744
1-b = 0.256 0.256 0)( 1/2) (
) ( Transformed Plots) . (
: Transformed
Explore:Plot Transformed Power Natural Log :
Continue OK ) : (
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Spread vs. Level Plot of DEPEND By TREAT
* Data transformed using P =
Slope = -.087
Level
11109876
Spread
.7
.6
.5
.4
.3
.2
.1
b=-0.087 1-b = 1.087
. :
0.078 0.922 .
.
Spread vs. Level Plot of DEPEND By TREAT
* Data transformed using P =
Slope = .078
Level
18016014012010080604020
Spread
18
16
14
12
10
8
6
4
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Untransformed Plots ) ( )IQR(
:
Spread vs. Level Plot of DEPEND By TREAT
* Data transformed using P =
Slope = .201
Level
400003000020000100000
Spread
7000
6000
5000
4000
3000
2000
1000
0
.)63(
Options Explore Options:
:
Exclude Cases Listwise: ) ( Dependent Factor .
Exclude Cases Pairwise: .
Report Values: .
Data Editor:
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dep1 dep2 fac1 10 12 11 1. . 14 13 2
5 14 .6 . 27 8 2
Analyze Descriptive Statistics Explore Explore :
dep1dep2 Dependent List. fac Factor List. OptionsExclude Cases list Wise.
OK :Case Processing Summary
2 66.7% 1 33.3% 3 100.0%
2 66.7% 1 33.3% 3 100.0%
2 66.7% 1 33.3% 3 100.0%
2 66.7% 1 33.3% 3 100.0%
FAC
1
2
1
2
DEP1
DEP2
N Percent N Percent N Percent
Valid Missing Total
Cases
Descriptives
1.50 .50
.
.
5.50 1.50
.
.
10.50 .50
.
.
10.50 2.50
.
.
Mean
Mean
Mean
Mean
FAC
1
2
1
2
DEP1
DEP2
Statistic Std. Error
) ( Cases ListwiseExclude
Dependent ListFactor List. dep11 fac 12
472 dep21 12....
Exclude Cases Pairwise :
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Case Processing Summary
2 66.7% 1 33.3% 3 100.0%3 100.0% 0 .0% 3 100.0%
2 66.7% 1 33.3% 3 100.0%
2 66.7% 1 33.3% 3 100.0%
FAC
12
1
2
DEP1
DEP2
N Percent N Percent N Percent
Valid Missing Total
Cases
Descriptives
1.50 .50
.
.
5.67 .88
.
10.50 .50
.
.
10.50 2.50
.
.
Mean
Mean
Mean
Mean
FAC
1
2
1
2
DEP1
DEP2
Statistic Std. Error
dep1 fac 12
dep12
4
6
7
dep2. fac Factor List Explore Exclude Cases Pairwise
.
Descriptives
4.17 .95
11.20 1.07
Mean
Mean
DEP1
DEP2
Statistic Std. Error
4.17 124567dep111.02
12457dep2.
Report Values. fac Factor List Explore Report Values
Options. OK Explore :
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Case Processing Summary
1 100.0% 0 .0% 1 100.0%2 66.7% 1 33.3% 3 100.0%
2 66.7% 1 33.3% 3 100.0%
1 100.0% 0 .0% 1 100.0%
2 66.7% 1 33.3% 3 100.0%
2 66.7% 1 33.3% 3 100.0%
FAC
. (Missing)1
2
. (Missing)
1
2
DEP1
DEP2
N Percent N Percent N Percent
Valid Missing Total
Cases
Fac 12 Report Values Missing . ) (Report
Values :
Descriptives
1.50 .50
.
.
5.50 1.50
.
.
10.50 .50
.
.10.50 2.50
.
.
Mean
Mean
Mean
Mean
FAC
1
2
1
2
DEP
1
DEP
2
Statistic Std. Error
Exclude Listwise .
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Crosstabs Crosstabs Tables22) (
Multiway Tables) ( .
.1: 22 a
b treat recover a1
b2 gender m f Data Editor :treat recover gender
a a1 mb a1 m
b b1 m
b b1 m
a a1 m
a a1 m
b b1 m
a b1 m
b b1 m
a a1 m
a a1 m
b a1 m
a a1 m
b b1 m
a a1 f
b b1 f
b b1 f
b b1 f
a a1 fb a1 f
a b1 f
b b1 f
:1. treatrecover
.2. treatrecover
gender.1. :
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Analyze Descriptive Statistics Crosstabs Crosstabs :
:Row(s): .
Column(s): : .DisplayClusteredbar Charts: .
Supress tables: .
Statistics Statistics : :
Chi-Sqare: chi-Square .
Correlation: SpearmanPearson
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Numeric Spearman Ordered Values)Ordinal Measure
Variable view( ) ( Pearson
Variables
Quantitative
Scale
Measure Variable View Interval.Nominal: )(
)( ) . (
Ordinal: .
Nominal by Interval: Eta
Interval Scale Income Categories gender.
.
Nominal) NominalMeasure Variable View( Chi- Square
Phi and Gramers v Nominal Variables.
Continue Statisticsok Crosstabs :
TREAT * RECOVER Crosstabulation
Count
8 2 10
3 9 12
11 11 22
a
b
TREAT
Total
a1 b1
RECOVER
Total
Chi-Square Tests
6.600b 1 .010
4.583 1 .032
6.994 1 .008
.030 .015
22
Pearson Chi-Square
Continuity Correctiona
Likelihood Ratio
Fisher's Exact Test
N of Valid Cases
Value df Asymp. Sig.
(2-sided)Exact Sig.(2-sided)
Exact Sig.(1-sided)
Computed only for a 2x2 tablea.
0 cells (.0%) have expected count less than 5. The minimum expected count is
5.00.
b.
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Chi-Square
(r-1)(c-1) r c :
=iEiEiO
2
)(2
iO iE 6.6p-value= 0.010 < 0.05 5%
.
Symmetric Measures
.548 .010
.548 .010
22
Phi
Cramer's V
Nominal by
Nominal
N of Valid Cases
Value Approx. Sig.
Not assuming the null hypothesis.a.
Using the asymptotic standard error assuming the nullhypothesis.
b.
Phi =548.022
6.62
==
n
p-value =0.010
5% 2
(r-1)(c-1).
1: YatesContinuity Correction
22
=iE
iEiO2)2/1(2.
2: Phi 2*2 Cramer Coefficient C r*c :
548.022
6.6
)1(
2==
=
LNC
N L
2 (r-1)(c-1) Phi.
3: Contingency Coefficient) Nominal Crosstsbs:Statistics ( r*c
:
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480.0226.6
6.6
2
2
=
+
=
+
=
N
C
N 2
(r-1)(c-1). P-Value 0.010. Check Box Display Clustered Bar Charts
Crosstabs :
TREAT
ba
Count
10
8
6
4
2
0
RECOVER
a1
b1
4
:1. Crosstab Cells
Crosstabs Cell Display :Counts :
Observed: iO.Expected: iE.
Percentages :Rows: .
Columns: .Total: .Residuals: :
Unstandardised: EiOi .Standardized:
.Adj.Standardised: .
5
: Format Crosstabs
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2. : Analyze Descriptive Statistics Crosstabs
Crosstabs :
gender Layer)( Control Variable categorical Variable)
gendermf( Crosstabs treatrecover m
f. OK Crosstabs :
TREAT * RECOVER * GENDER Crosstabulation
Count
2 1 3
1 4 5
3 5 8
6 1 7
2 5 7
8 6 14
a
b
TREAT
Total
a
b
TREAT
Total
GENDER
f
m
a1 b1
RECOVER
Total
Chi-Square Tests
1.742b 1 .187
.320 1 .572
1.762 1 .184
.464 .286
8
4.667c 1 .031
2.625 1 .105
5.004 1 .025
.103 .051
14
Pearson Chi-Square
Continuity Correctiona
Likelihood Ratio
Fisher's Exact Test
N of Valid Cases
Pearson Chi-Square
Continuity Correctiona
Likelihood Ratio
Fisher's Exact Test
N of Valid Cases
GENDER
f
m
Value df Asymp. Sig.
(2-sided)Exact Sig.(2-sided)
Exact Sig.(1-sided)
Computed only for a 2x2 tablea.
4 cells (100.0%) have expected count less than 5. The minimum expected count is 1.13.b.
4 cells (100.0%) have expected count less than 5. The minimum expected count is 3.00.c.
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p-valuePearson Chi-Square
5. %
Chi-Square
22
Ei 5 5 100%
.
Symmetric Measures
.467 .187
.467 .187
8
.577 .031
.577 .031
14
Phi
Cramer's V
Nominal byNominal
N of Valid Cases
Phi
Cramer's V
Nominal byNominal
N of Valid Cases
GENDER
f
m
Value Approx. Sig.
Not assuming the null hypothesis.a.
Using the asymptotic standard error assuming the null hypothesis.b.
GENDER=f
TREAT
ba
Count
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
.5
RECOVER
a1
b1
GENDER=m
TREAT
ba
Count
7
6
5
4
3
2
1
0
RECOVER
a1
b1
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CCoommppaarree MMeeaannss)81( Means
subgroups )
( Test ofLinearity eta.
1
16 3 ABC Gender Data Editor : :
degree group gender
70 A Female
90 B Male
88 A Male
86 B Male
68 C Male
64 C Male76 B Male
83 A Female
79 B Female
55 C Female
97 B Male
100 A Male
64 C Female
59 C Female
90 A Male
73 A Female
ABC :
Analyze Compare means Means
Means :
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:Dependent List: Response Variable
Independent Variable. Degree.Independent List: Treatments
ANOVA. group .
Options Means MeansNo. of CasesStandardDeviation Means:Options
:
ContinueOK :
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Report
DEGREE
84.00 6 11.19
85.60 5 8.4462.00 5 5.05
77.63 16 13.65
GROUP
A
B
C
Total
Mean N Std. Deviation
Degree .
2: 1
group gender .
1
Means :
DEGREE * GROUP
DEGREE
84.00 6 11.19
85.60 5 8.44
62.00 5 5.05
77.63 16 13.65
GROUP
A
B
C
Total
Mean N Std. Deviation
DEGREE * GENDER
DEGREE
69.00 7 10.28
84.33 9 12.43
77.63 16 13.65
GENDER
Female
Male
Total
Mean N Std. Deviation
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3 1 degree)( ABC.
Layers
Means
group
gender Means :1. group Independent List Layer1.2. Next Independent List Layer2.3. gender Independent List Layer2.
Means :
Previous Independent List.
OK :
Report
DEGREE
75.33 3 6.81
92.67 3 6.43
84.00 6 11.19
79.00 1 .
87.25 4 8.77
85.60 5 8.44
59.33 3 4.51
66.00 2 2.83
62.00 5 5.05
69.00 7 10.28
84.33 9 12.43
77.63 16 13.65
GENDER
Female
Male
Total
Female
Male
Total
Female
Male
Total
Female
Male
Total
GROUP
A
B
C
Total
Mean N Std. Deviation
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4:) Test of Linearity( Linear trend
One-Way ANOVA.
1
)9
1
( Means
:
ANOVA and etaTest for Linearity Means : Options :
ANOVA Table
402.000 3 134.000 7.053 .012
86.400 1 86.400 4.547 .066
315.600 2 157.800 8.305 .011
152.000 8 19.000
554.000 11
(Combined)
Linearity
Deviation from Linea
BetweenGroups
Within Groups
Total
PRODUCT * METH
Sum ofSquares df ean Square F Sig.
Measures of Association
-.395 .156 .852 .726PRODUCT * METHOD
R R Squared Eta Eta Squared
(F=7.053).
:SS Deviation From Linearity = SS. (Combined) SS. Linearity =402-86.4=315.6
FTest for Linearity:
F=MS. Deviation From Linearity/ within Groups MS.=157.8/19=8.31
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P-value 0.011 5%
) 82 P-Value. (
Eta
)(Measure of association
01 0 1 Eta-Square (product)
(Method) Eta-Square = SS. between Groups / SS. Total =402/554= 0.726.
R Simple Correlation (product)(Method) 14
R Multiple RR-Square
Linear Regression.)82(T Test-One Sample T
Significant Difference Constant.
Confidence Interval (n
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T-Test
One-Sample Statistics
10 1.020 .162 5.121E-02WEIGHT
N Mean Std. Deviation
Std. Error
Mean
One-Sample Test
-4.492 9 .0015 -.230 -.396 -6.36E-02WEIGHT
t df Sig. (2-tailed)Mean
Difference Lower Upper
99% ConfidenceInterval of the
Difference
Test Value = 1.25
t t = ( 1.020-1.25 )/ 0.0512 = -4.492 tt(cal.) tt(tab) 9v = H0 2/,.),(.)( vtabtcalt t)
(t 2/) Two Tailed test( :t,9,0.025 = 2.262 ( %5= )
t,9,0.005 = 3.250 ( %1= )
t(4.492) 1.25 5%1. %
P-value SPSS Sig. . P-value .
P-value . P-value.
-4.492 0
0.00070.0007
T-distribution
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0.85361.186499% 5% 1.25
.)83(T Test-Independent samples T
T.
AB 12
: A B
12.59.49.48.4
11.711.6
11.37.2
9.99.7
8.77.0
9.610.4
11.58.2
10.36.9
10.612.7
9.67.3
9.79.2
5%1. % :
BAH
BAH
=
:1
:0
P-value = Pr( 492.4t ) + Pr( 492.4t ) =0.00075+0.00075=0.0015
Pr Probability P-value < 0.05P-value
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: Data Editor Proten
Group .
Analyze Compare Means IndependentSamples T Test
Independent Samples T Test :
Proten Test VariablesGroup) ( Grouping Variable
AB Define Groups
Group AB) dichotomous Variable( 12
. Cut Point
Define Groups) 10( 10 10 )
(Numeric. Options Independent sample T Test
One Sample T Test.: Test Variables
. OK Independent sample T Test :
Group Statistics
12 10.4000 1.1314 .3266
12 9.0000 1.8742 .5410
GROUP
A
B
PROTEN
N Mean Std. Deviation
Std. Error
Mean
Proten Group12.50 A
9.40 A
11.70 A
11.30 A
9.90 A
8.70 A
9.60 A
11.50 A
10.30 A
10.60 A
9.60 A
9.70 A9.40 B
8.40 B
11.60 B
7.20 B
9.70 B
7.00 B
10.40 B
8.20 B
6.90 B
12.70 B
7.30 B
9.20 B
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Independent Samples Test
2.776 .110 2.215 22 .037 1.400 .6320 8.936E-02 2.7106
2.215 18.08 .040 1.400 .6320 7.267E-02 2.7273
Equal variancesassumed
Equal variancesnot assumed
PROTENF Sig.
Levene's Testfor Equality ofVariances
t dfSig.
(2-tailed)
MeanDifference
Std.ErrorDifference Lower Upper
95% ConfidenceInterval of theDifference
t-test for Equality of Means
22BA
= 22BA
.
P-Value = 0.037 0.01 1. % Leven P-value = 0.11>0.05
)( .
)84(T Test-Samples T-Paired
)(
12.
: )AB(
A B :10987654321
136
141
197
194
175
186
168
172
205
200
143
147
170
182
162
160
195
200
127
135
A
B
5. % :
Analyze Compare Means Paired Samples T Test Paired Samples T Test :
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ab ab Paired variables :
1. a .2. Shift b .3. Paired variables
OK :
Paired Samples Statistics
167.80 10 26.58 8.40
171.70 10 24.60 7.78
A
B
Pair
1
Mean N Std. Deviation
Std. Error
Mean
Paired Samples Correlations
10 .978 .000A & BPair 1
N Correlation Sig.
Paired Samples Test
-3.90 5.74 1.82 -8.01 .21 -2.147 9 .060A - BPair 1
MeanStd.
Deviation
Std.ErrorMean Lower Upper
95% ConfidenceInterval of the
Difference
Paired Differences
t dfSig.
(2-tailed)
0.978 5%1. %
T P-value=0.060>0.05 BAH =:0 .
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AAnnaallyyssiiss ooffVVaarriiaannccee
ANOVA Table.
) Treatments( t .
)91( One Way ANOVA
1
: :
123
155474850
255646461
355495252
450444145
:. 1989 63.
:1. 5.%2. F :. )(
L.S.D. 5. %. 234 1
)( Dunnett.1.
:
4321:0 ===H
4321:1 H
.
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: Data Editor :
method product
1 551 47
1 48
2 55
2 64
2 64
3 55
3 49
3 52
4 50
4 44
4 41
:Dependent List:
. )( Factor Dependent.
Factor: Numeric.
OK
:ANOVA
PRODUCT
402.000 3 134.000 7.053 .012
152.000 8 19.000
554.000 11
Between Groups
Within Groups
Total
Sum ofSquares df Mean Square F Sig.
0.012P-Value=
F
0.05
5% .
Analyze Compare Means One-Way NOVA
One-Way ANOVA :
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2. Multiple
Comparisons L.S.D.Dunnett :
Post Hoc
One-Way ANOVA
Post Hoc
Multiple comparisons :
LSDDunnett Control Category( First , Last ) First
) Test. 5%Significance Level.
Continue OK :Multiple Comparisons
Dependent Variable: PRODUCT
-11.00* 3.56 .015 -19.21 -2.79
-2.00 3.56 .590 -10.21 6.21
5.00 3.56 .198 -3.21 13.21
11.00* 3.56 .015 2.79 19.21
9.00* 3.56 .035 .79 17.21
16.00* 3.56 .002 7.79 24.21
2.00 3.56 .590 -6.21 10.21
-9.00* 3.56 .035 -17.21 -.79
7.00 3.56 .085 -1.21 15.21
-5.00 3.56 .198 -13.21 3.21
-16.00* 3.56 .002 -24.21 -7.79
-7.00 3.56 .085 -15.21 1.21
11.00* 3.56 .037 .75 21.25
2.00 3.56 .896 -8.25 12.25
-5.00 3.56 .409 -15.25 5.25
(J) METHOD
2
3
4
1
34
1
2
4
1
2
3
1
1
1
(I) METHOD
1
2
3
4
2
3
4
LSD
Dunnett t (2-sided) a
MeanDifference
(I-J) Std. Error Sig. Lower Bound Upper Bound
95% Confidence Interval
The mean difference is significant at the .05 level.*.
Dunnett t-tests treat one group as a control, and compare all other groups against it.a.
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LSD 5%
)12()23()24( P-ValueSig. 0.05
.
Dunnett 5
% .:
Options One Way ANOVA :
:Descriptive: .
Homogeneity-of-Variance: ) (Levene. .
Means plot: .Exclude Cases Analysis by Analysis:
.Exclude Cases Listwise: .
. Continue OK One-Way
ANOVA :
Test of Homogeneity of Variances
PRODUCT
.667 3 8 .596
LeveneStatistic df1 df2 Sig.
) ( ) ( Levene P-Value =0.596>0.05
). Explore Levene. (
:Means Plots
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METHOD
4321
MeanofPRODUCT
70
60
50
40
)911( Orthogonal Comparisons
. )(t t-1 Contrast
)( : = .iYiCQ with 0= iC
.iY iiC Coefficients = .11 iYiCQ= .22 iYiCQ )(Orthogonal
021 = iCiC SSt t-1t-1
. :2:
Weight.iY
146404240168
251484742188
336424446168
442424543172
535363736144
:. :
56.
:1. .2. t-1:
0.5.4.3.2.141 == YYYYYQ
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0.5.4.3.22 =+= YYYYQ
0.3.23 == YYQ
0.5.44 == YYQ
Data Editor :treat weight
1 46
1 40
1 42
1 40
2 51
2 48
2 47
2 42
3 363 42
3 44
3 46
4 42
4 42
4 45
4 43
5 35
5 36
5 37
5 36
Contrasts One-Way ANOVA Contrasts
: Coefficients 4 Add 4
. -1 Coefficients Add -
1 . -1 Coefficients Add -
1 . -1 Coefficients Add -
1 . -1 Coefficients Add -
1 .
:
Analyze Compare Means One-Way ANOVA
One-Way ANOVA :
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. Next . .
Contrasts :
Next Previous. Continue OK One-Way ANOVA
:
ANOVA
WEIGHT
248.000 4 62.000 7.154 .002
130.000 15 8.667
378.000 19
Between Groups
Within Groups
Total
Sum ofSquares df Mean Square F Sig.
F )( 5%1. %
Contrast Coefficients
4 -1 -1 -1 -1
0 1 1 -1 -1
0 1 -1 0 0
0 0 0 1 -1
Contrast
1
2
3
4
1 2 3 4 5
TREAT
. t
(Q1=0) 5%P-Value =1 > 0.05 ) ( 5%P-Value < 0.05
. Value of Contrast :Value of Contrast = riYiC /.
r:: 4.
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Contrast Tests
.00 6.58 .000 15 1.000
10.00 2.94 3.397 15 .004
5.00 2.08 2.402 15 .030
7.00 2.08 3.363 15 .004
.00 6.39 .000 4.727 1.000
10.00 2.97 3.365 6.823 .012
5.00 2.86 1.750 5.880 .132
7.00 .82 8.573 4.800 .000
Contrast
1
2
3
4
1
2
3
4
Assume equal varianc
Does not assume equvariances
WEIGHT
Value ofContrast Std. Error t df Sig. (2-tailed)
)912( Trend Analysis
Polynomialt-1 t
. 5-1=4
. Contrasts :
Contrasts. Coefficients Polynomial
4th. Continue OK One-way ANOVA :
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ANOVA
WEIGHT
248.000 4 62.000 7.154 .002102.400 1 102.400 11.815 .004
145.600 3 48.533 5.600 .009
92.571 1 92.571 10.681 .005
53.029 2 26.514 3.059 .077
1.600 1 1.600 .185 .674
51.429 1 51.429 5.934 .028
51.429 1 51.429 5.934 .028
130.000 15 8.667
378.000 19
(Combined)
Contrast
Deviation
Linear Term
Contrast
Deviation
QuadraticTerm
Contrast
Deviation
Cubic Term
Contrast4th-order Ter
BetweenGroups
Within Groups
Total
Sum ofSquares df ean Square F Sig.
Between Groups
5% Cubic term.)92( y ANOVATwo Wa
RCB
Design .
3: ) ( ) (
) ( )( :
ABCD
141-10
211
-1-2300-3-240-5-4-4
:
1984 83.
Tyre car 5. %
Data Editor :
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car tyre thin
A 1 4
A 2 1
A 3 0A 4 0
B 1 1
B 2 1
B 3 0
B 4 -5
C 1 -1
C 2 -1
C 3 -3
C 4 -4
D 1 0
D 2 -2D 3 -2
D 4 -4
Fixed Factors Random Factors.
Fixed Factor One-Way ANOVA Factor . Model Model Custom Full Factorial
Interaction (car*tyre) Model :
Include Intercept in Model .
Build Terms Effects tyrecar Factors & Covariates Model
:
:
Analyze General Linear Model Univariate
Univariate :
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Build TermsInteraction Model.
tyrecar Factors & Covariates ) tyre
Shift
car
. ( Model.
Full Factorial Model.2. GLM .
4) : ( Shelf Location
) ( Store Size) ( :
Shelf Location SizeABCD
Small45
50
56
63
65
71
48
53
Medium57
65
69
78
73
80
60
57
Large70
78
75
82
82
89
71
75
Size Location Size*Location 5% .
Data Editor :location size sales
A Small 45A Small 50
A Medium 57
A Medium 65A Large 70
A Large 78
B Small 56B Small 63
B Medium 69
B Medium 78B Large 75
B Large 82
C Small 65
C Small 71
C Medium 73
C Medium 80C Large 82
C Large 89
D Small 48D Small 53
D Medium 60
D Medium 57D Large 71
D Large 75
:
:
Analyze General Linear Model Univariate
Univariate :
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ModelFull Factorial Interaction .
) Custom ( Full Factorial
Default
. Plots size
Location Profile PlotsInteraction Plot
:
: size Factors Horizontal Axis. LocationSeparate Lines. Add size*location Plot
. Separate Plots .
Continue Univariate. Options Estimated Marginal Means
location*size Options :
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ContinueOK Univariate .
Tests of Between-Subjects Effects
Dependent Variable: SALES
3019.333a 11 274.485 12.767 .000
108272.667 1 108272.667 5035.938 .000
1102.333 3 367.444 17.090 .000
1828.083 2 914.042 42.514 .000
88.917 6 14.819 .689 .663
258.000 12 21.500
111550.000 24
3277.333 23
SourceCorrected Model
Intercept
LOCATION
SIZE
LOCATION * SIZE
Error
Total
Corrected Total
Type III Sum
of Squares df Mean Square F Sig.
R Squared = .921 (Adjusted R Squared = .849)a.
:
Tests of Between-Subjects Effects
Dependent Variable: SALES
1102.333 3 367.444 17.090 .000
1828.083 2 914.042 42.514 .000
88.917 6 14.819 .689 .663
258.000 12 21.5003277.333 23
Source
LOCATION
SIZE
LOCATION * SIZE
ErrorCorrected Total
Type III Sumof Squares df Mean Square F Sig.
F Location
size 5%p-Value = 0.663> 0.05.Estimated Marginal Means
LOCATION * SIZE
Dependent Variable: SALES
74.000 3.279 66.856 81.144
61.000 3.279 53.856 68.144
47.500 3.279 40.356 54.644
78.500 3.279 71.356 85.644
73.500 3.279 66.356 80.644
59.500 3.279 52.356 66.644
85.500 3.279 78.356 92.644
76.500 3.279 69.356 83.644
68.000 3.279 60.856 75.144
73.000 3.279 65.856 80.144
58.500 3.279 51.356 65.644
50.500 3.279 43.356 57.644
SIZE
Large
Medium
Small
Large
Medium
Small
Large
Medium
Small
Large
Medium
Small
LOCATION
A
B
C
D
Mean Std. Error Lower Bound Upper Bound
95% Confidence Interval
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LocationSize
sizelocation F.Profile Plots
Estimated Marginal Means of SALES
SIZE
SmallMediumLarge
EstimatedMarginalMeans
90
80
70
60
50
40
LOCATION
A
B
C
D
)93( Covariance Analysis
)(Covariates X
Y Dependent Variable )( Y X )
( . X .
5: )(
. Y X .
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treat
Observations
T1X
Y30
165
27
170
20
130
21
156
33
167
29
151
T2
X
Y
24
180
31
169
20
171
26
161
20
180
25
170
T3X
Y3415632189
35
13835
19030
16029
172T4
X
Y41
201
32
173
30
200
35
193
28
142
36
189
X) . (
Data Editor :
treat X Y
T1 30 165
T1 27 170
T1 20 130
T1 21 156
T1 33 167
T1 29 151
T2 24 180
T2 31 169
T2 20 171T2 26 161
T2 20 180
T2 25 170
T3 34 156
T3 32 189
T3 35 138
T3 35 190
T3 30 160
T3 29 172
T4 41 201
T4 32 173T4 30 200
T4 35 193
T4 28 142
T4 36 189
:
Analyze General Linear Model Univariate
Univariate :
OK :
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Tests of Between-Subjects Effects
Dependent Variable: Y
2845.956a 4 711.489 2.572 .071
6938.602 1 6938.602 25.087 .000682.831 1 682.831 2.469 .133
1609.595 3 536.532 1.940 .157
5255.002 19 276.579
699323.000 24
8100.958 23
SourceCorrected Model
InterceptX
TREAT
Error
Total
Corrected Total
Type III Sumof Squares df Mean Square F Sig.
R Squared = .351 (Adjusted R Squared = .215)a.
:
Tests of Between-Subjects Effects
Dependent Variable: Y
a
1609.595 3 536.532 1.940 .157
5255.002 19 276.579
6864.597 22
Source
TREAT
Error
Total+Error
Type III Sumof Squares df Mean Square F Sig.
R Squared = .351 (Adjusted R Squared = .215)a.
> 0.050.157P-Value= 5% X.
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CCoorrrreellaattiioonn && RReeggrreessssiioonn AAnnaallyyssiiss )101(Correlation
Correlation ) (
) ( Linear Non Linear. CorrelationCoefficients r 11)11( r.
)102( Simple Linear Correlation
) (
) . (1:
10 Lang
Math Data EditorSPSS :Lang Math5660
606864608274768072847480
667264628682
:1. Pearson Spearman.2. 5. %
: Analyze Correlate Bivariate
Bivariate Correlation :
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Correlation Coefficients :Pearson: .
Kendalls Tau: Ranks .
) ( .
Spearman: Kendall. PearsonSpearman.
Test significance Two Tailed . One Tailed.Flag Significance Correlation: ) Star. (
OK :
Correlations
1.000 .776**
. .008
10 10
.776** 1.000
.008 .
10 10
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
LANG
MATH
LANG MATH
Correlation is significant at the 0.01 level**.
LANGMATHr = 0.776 ) : (
0:
1
0:0
=
H
H
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T T n-k n k.
48.3
2
776.01
210776.0
2
1
=
=
=
r
knrT
P-Value Transform Compute T 008.02*))8,48.3(.1( = TCDF. P-Value=0.008
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Correlations
1.000 .776**
. .004
10 10.776** 1.000
.004 .
10 10
Pearson Correlation
Sig. (1-tailed)
NPearson Correlation
Sig. (1-tailed)
N
LANG
MATH
LANG MATH
Correlation is significant at the 0.01 level**.
T 3.48 P-Value Transform Compute
T 004.0))8,48.3(.1( = TCDF 2
. P-Value=0.004
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Variables Controlling for )( .
Ok .
- - - P A R T I A L C O R R E L A T I O N C O E F F I C I E N T S - - -
Controlling for.. X3
Y X2
Y 1.0000 .2851
( 0) ( 10)
P= . P= .369
X2 .2851 1.0000
( 10) ( 0)
P= .369 P= .
(Coefficient / (D.F.) / 2-tailed Significance)
" . " is printed if a coefficient cannot be computed
285.03.2 =xyxr ) (
T . 10 Tdf = n k = 13-3 = 10T
:
941.0
22851.01
313)2851.0(
21
=
=
=
r
knrT
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P-Value=0.369 > 0.05 5. %
YX2X3X4) (
Partial Correlations
:
:- - - P A R T I A L C O R R E L A T I O N C O E F F I C I E N T S - --
Controlling for.. X3 X4
Y X2
Y 1.0000 .2338
( 0) ( 9)
P= . P= .489
X2 .2338 1.0000
( 9) ( 0)
P= .489 P= .
(Coefficient / (D.F.) / 2-tailed Significance)
" . " is printed if a coefficient cannot be computed
43.2 xxyxr 5. %
:
Pearson Options Partial Correlations Zero Order Correlations.
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)104( Regression Analysis
Dependent Variable Independent VariablesRegressors
Simple Regression model
Multiple regression Model Linear Model Non Linear Model.
)1041(
:eXBBY ++= 10 :
Y: X: 0B: Intersection Parameter.
1B: Slop ParameterX
YB
=1
e: Y Y residualYYe =.
0B1B
Least Squares Method(OLS) :1. YX.2. .
3. 2) Homoscedasticity. (
4. OLS 0B1B.
5. Autocorrelation .
Scatter plotsy )x( e Standardized Residuals
es .
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Residuals
)a( ) . ()b( y.
)c( ) . ()d( ) . (
3: X Y) ( 10
Data Editor:Obs. X Y
1 35 112
2 40 128
3 38 130
4 44 1385 67 158
6 64 162
7 59 140
8 69 175
9 25 125
10 50 142 :
1. Y/X .2
. 95
% 0B
1B
.
e
ores
e
ore
s
eores
y
a
c d
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3. ANOVA.4. ) ( R2
.5
. . : :
Regression LinearAnalyze Linear
Regression :
:Dependent: .
Independent:) . ( Block Block Next
Previous. X Z Y XBlock1Z
Block2.
Method: ) Enter. (Selection Variable:
) Observat 5( Rule.
Case Lebels: Scatterplots. Statistics Statistics :
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:Estimate: t.
Confidence Interval: 95% .Model Fit:R2ANOVA.
Plots Plots Normal Probability Plot ) . (
Save Save :
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Unstandardized Predicted ValuesyStandardizedResidualses Scatterplots
) ( Data Editor X
Y
Observat
Unstandardized Predicted Values
Pre_1
Standardized ResidualsZre_1. Options
Linear Regression.
OK Linear Regression :
Coefficientsa
85.044 9.970 8.530 .000027 62.052 108.036
1.140 .195 .900 5.846 .00038 .690 1.589
(Constant)
X
Model
1
BStd.Error
Unstandardized Coefficients
Beta
Standardized
Coefficients
t Sig.LowerBound
UpperBound
95% Confidence Intervalfor B
Dependent Variable: Ya.
:
xy 140.1044.85 +=
(9.97) (0.195)
1.140 . .
T B1: 01:0 =BH
01:1 BH T ) (B0:
00:0 =BH 00:1 BH
P-Value T : P-Value < 0.05 5. % P-Value < 0.01 1. %
.P-value 0.00038 0.01 P-value
0.000027 0.01
.
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Standardized Coefficient Beta SXX /)(
B0 *x* =y *y*x .
95% :%95)036.1080052.62Pr( = B
Pr 95% :%95)589.10690Pr(. = B
ANOVA F B1 T )
P-Value ( F=T2.
ANOVAb
2661.050 1 2661.050 34.174 .00038a
622.950 8 77.869
3284.000 9
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
Predictors: (Constant), Xa.
Dependent Variable: Yb.
Coefficient OfDetermination R2 .
:
120 R81.03284
05.2661
Variations
2====
SST
SSR
Total
ariationsExplainedVR
81% ) Y( 19%
. R2100% .
2Rr = r r .
Model Summary
.900a .810 .787 8.82
Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
Predictors: (Constant), Xa.
R2
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SSR SST Adjusted R Square
) ( 79%
. Standard Error of Estimate
. Scatterplots y
s
e ) : ( Graphs Scatter Simple
Scatterplots.
Zre_1 Y Scatter. Pre_1 X. OK SPSS Viewer. SPSS Chart Editor. Chart Reference LineReference Line
. :
Unstandardized Predicted Value
170160150140130120110
StandardizedResidual
1.5
1.0
.5
0.0
-.5
-1.0
-1.5
.
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:
y
se
: Plots Linear Regression Plots :
DEPENDENT ) ( X )(
ZRESID Y Continue OK
Linear Regression :
Scatterplot
Dependent Variable: Y
Y
180170160150140130120110
RegressionStandardized
Residual
1.5
1.0
.5
0.0
-.5
-1.0
-1.5
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) ( : 95% (-2,2)
(-1.5,1.5)
. Normal probability Plot
Plot :Normal P-P Plot of Regression Standardized Residual
Dependent Variable: Y
Observed Cum Prob
1.00.75.50.250.00
ExpectedCumPr
ob
1.00
.75
.50
.25
0.00
. )1042( Weighted Least Squares Method Homoscedasticity
Cross-Section Data .
C Y Y
22var Ye = 2/1 yW = Weight
:eYC ++= 10
YW /1= :
Y
eB
Y
B
Y
C++= 1
0
222
2Y
1evar
2
1
Yvar === Y
Y
e
.
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1B 0B .
SPSS
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Data editorSPSS )w : (c y w
10600 12000 6.9444E-09
10800 12000 6.9444E-09
11100 12000 6.9444E-09
11400 13000 5.9172E-09
11700 13000 5.9172E-09
12100 13000 5.9172E-09
12300 14000 5.1020E-09
12600 14000 5.1020E-09
13200 14000 5.1020E-09
13000 15000 4.4444E-09
13300 15000 4.4444E-09
13600 15000 4.4444E-09
13800 16000 3.9063E-09
14000 16000 3.9063E-09
14200 16000 3.9063E-09
14400 17000 3.4602E-09
14900 17000 3.4602E-09
15300 17000 3.4602E-09
15000 18000 3.0864E-09
15700 18000 3.0864E-09
16400 18000 3.0864E-09
15900 19000 2.7701E-09
16500 19000 2.7701E-09
16900 19000 2.7701E-09
16900 20000 2.5000E-09
17500 20000 2.5000E-09
18100 20000 2.5000E-09
17200 21000 2.2676E-09
17800 21000 2.2676E-09
18500 21000 2.2676E-09
:1. CY OLS
.
2. Y 22var Ye = .
2 1982 .217.
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:1. OLS
:
dYC 788.00.1408 +=97.02=R(449.6) (0.27)
. C
Standardized Residuals :Analyze Regression Linear Linear
Regression Save Save
Unstandardized Predicted Values C Data editor) Pre-1( Standardized
Residuals ) Zre-1. ( Graphs Scatter Simple
ScatterPlots : Zre-1 Y-axis. Pre-1 X-Axis. OK.
Reference Line :
Y .
Unstandardized Predicted Value
200001800016000140001200010000
StandardizedResid
ual
3
2
1
0
-1
-2
-3
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2. Y 22var Ye =
2/1 yW = Transform Compute Data Editor
Linear Regression :
W WLS Weight WLS. OK :
Coefficientsa,b
1421.278 395.496 3.594 .001
.792 .025 .986 31.511 .000
(Constant)
YD
Model
1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Ca.
Weighted Least Squares Regression - Weighted by Wb.
:97.02 =RdYC 792.0278.1421
+=
(395.496) (0.25)
.
)1043(
:e
kX
kX
Xy +++++= ...2210
1
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0: .
k ,...,2,1: Partial regression Coefficients .
e: .
P = K+1)K . (
(Multicollinearity).5:
y) ( x1)( x215 31981. Data
Editor :y x1 x26 9 8
8 10 13
8 8 11
7 7 10
7 10 12
12 4 16
9 5 10
8 5 10
9 6 12
10 8 14
10 7 12
11 4 16
9 9 14
10 5 10
11 8 12
:1. yx1x2 .2. ANOVA .3. DW.
: Analyze Regression Linear
Linear Regression : Y Dependent. X1,X2 Independent. Method Enter.
3 1982 172.
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Statistics Linear Regression Statistics :
Estimate: .Model Fit
:R2
ANOVA
. Durbin - Watson: DW. OK Linear regression :
Model Summaryb
.833a .693 .642 1.01 .946
Model
1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
Durbin-Watson
Predictors: (Constant), X2, X1a.
Dependent Variable: Yb.
Coefficientsa
6.203 1.862 3.331 .006
-.376 .133 -.461 -2.834 .015
.453 .120 .615 3.786 .003
(Constant)
X1
X2
Model
1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Ya.
:
64.02 =R2453.01376.0203.6 XXy +=
(1.862) (0.133) (0.120)
X1 1% 376 X2
453 X1
2
R
. SST
2)( yy SSR SSE. F :
021:0 == H
021:1 H
F B0. :
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ANOVAb
(SSR)27.728 (p-1) 2 (MSR) 13.864 13.557 .001a
(SSE)12.272 (n-p) 12 (MSE) 1.023 F =MSR/MSE(SST)40 (n-1) 14
Regression
Residual
Total
Model
1
Sum ofSquares df Mean Square F Sig.
Predictors: (Constant), X2, X1a.
Dependent Variable: Yb.
P = 3 n . P-Value= 0.001< 0.05 5%
B1B2 .
t)Coefficients ( X1X2 5%
. 5%
n =15p = 3 DW .6) : / (
4 Y X1,X2,X3 Data Editor :
Y X1 X2 X3 X443 5 3 18 12
63 9 5 27 9
71 10 7 34 11
61 8 4 24 10
81 11 6 33 6
44 12 5 22 8
58 9 4 28 9
71 7 7 32 7
72 8 5 23 8
67 13 8 20 5
64 4 5 21 4
69 10 9 36 10
68 11 10 30 11
1. .2. Multicollinearity .3. Stepwise Regression.1. :
4. 1988277.
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Analyze Regression Linear Linear Regression :
Y Dependent.
X1,X2,X3
Independent
. Method Enter.
Statistics Linear Regression Statistics
Estimate: .Model Fit:R2ANOVA.
Part & Partial Correlations: .Collinearity Diagnostics: .
OK Linear regression :Model Summary
.810a .656 .484 7.72
Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
Predictors: (Constant), X4, X1, X3, X2a.
Coefficientsa
47.06 13.0 3.611 .007
-.430 1.010 -.104 -.425 .682 .210 -.149 -.088 .713 1.403
1.199 1.486 .232 .807 .443 .540 .274 .167 .520 1.925
1.153 .476 .631 2.423 .042 .634 .651 .502 .633 1.580-2.038 .950 -.462 -2.1 .064 -.331 -.604 -.445 .928 1.077
(Constant)
X1
X2
X3X4
Model
1
BStd.Error
Unstandardized
Coefficients
Beta
StandardizedCoefficients
t Sig.Zero-order
Partial Part
Correlations
Tolerance VIF
CollinearityStatistics
Dependent Variable: Ya.
:
48.02 =R4038.23153.12199.1143.006.47 XXXXy ++=
(13) (1.01) (1.486) (0.476) (0.950)
X1 0.430 X2X3.
.
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P-value t X3 5) % . (
.
: Zero-order Correlation: .Partial Correlation: )
. (Part Correlation:
.
X3 t
X4 . Tolerance
Tolerance = 1-2.othersX
Ri
2.othersX
Ri
i . VIF
)(Variance Inflation Factor Tolerance
VIF1
=.
)
t (. VIF 510 , VIF
, XX )X
( . ConditionIndex
:
1813.4
4.813Index ==Condition
X1 :
7.0200.09868
4.813Index ==condition
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15 . 30 . 16
. Variance Proportion Principle Component
Condition Index .
X3 :
Collinearity Diagnosticsa
4.813 1.000 .00 .00 .00 .00 .00
9.768E-02 7.020 .01 .06 .17 .00 .35
4.345E-02 10.525 .01 .71 .29 .08 .01
2.907E-02 12.868 .30 .05 .26 .22 .63
1.669E-02 16.983 .68 .18 .28 .70 .01
Dimension
1
2
3
4
5
Model
1
EigenvalueCondition
Index (Constant) X1 X2 X3 X4
Variance Proportions
Dependent Variable: Ya.
: Analyze Regression Linear
Linear Regression : Y Dependent. X1,X2,X3 Independent. Method :
1.Enter: ) . (2.Stepwise:
.3.Remove: .4.Backward: .5.Forward:
. Stepwise) . (
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Statistics Linear Regression Statistics
Estimate: .Model Fit
:R2
ANOVA
. Options Linear Regression Options
:
Stepwise F
. Stepping Method criteria :Use Probability of F:
. Entry.
Removal.Use F Value: F F F .
Entry. Removal.
FPartial F Test
F t
F . Use Probability of F0.05 0.10
.
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OK Linear regression :
Variables Entered/Removeda
X3 .
Stepwise (Criteria:Probability-of-F-to-enter= .100).
X4 .
Stepwise (Criteria:Probability-of-F-to-enter= .100).
Model
1
2
VariablesEntered
VariablesRemoved Method
Dependent Variable: Ya.
Stepwise .
X3 t. Coefficients
P-Value t0.02 0.05) Entry( X3 ) t F(
:
3158.1007.33 Xy +=
X3 X4 T) P-Value t0.033 0.05) Entry(
X4 :
4147.23345.1152.46 XXy +=
tX3X4 P-Value
t
X4
0.033
0.10
) Removal( . X1X2
0.05. .
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Coefficientsa
33.007 11.648 2.834 .016
1.158 .426 .634 2.720 .020
46.152 11.011 4.191 .002
1.345 .360 .737 3.735 .004
-2.147 .871 -.486 -2.466 .033
(Constant)
X3
(Constant)
X3
X4
Model
1
2
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: Ya.
)1( )2( )(
: Use F ValueStepping Method Criteria t2 F t2 >F (Enter)
. >F(Remove)t2 . :
Excluded Variablesc
.027a .108 .916 .034 .915
.267a .941 .369 .285 .682
-.486a -2.466 .033 -.615 .955
-.012b -.058 .955 -.019 .909
.175b .721 .489 .234 .663
X1
X2
X4
X1
X2
Model1
2
Beta In t Sig.Partial
Correlation Tolerance
Collinearity
Statistics
Predictors in the Model: (Constant), X3a.
Predictors in the Model: (Constant), X3, X4b.
Dependent Variable: Yc.
Beta in .
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FFaaccttoorr AAnnaallyyssiiss)111(
Factors Variations Response Variables
Factors Linear Compounds .
.
.
)112( Principal Components Method
. ) ( Response
Variables. p :
pXpaXaXaZ 1.......2211111 +++= aij Loadings .
:
pXpaXaXaZ 2.......2221122 +++=
Variance) (
... Orthogonal
: 1. Variance-Covariance Matrix
XX .
2. Correlation Matrix Standardized Variables .
1:
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regions)( 1977 Data Editor
SPSS:Region gdp literacy higheduc doctors hospbed
Dohok 17.2 30.1 1.09 17 139 Nineveh 24.0 44.2 1.85 14 172
Arbil 22.2 35.2 1.18 13 163
Sulayman 16.2 33.5 1.01 10 115
Ta'meem 32.3 49.4 1.85 18 143
Salah AL-Deen 98.4 37.9 1.32 15 80
Diala 23.1 44.1 1.93 10 153
Anbar 22.7 44.3 1.58 16 144
Baghdad 75.0 61.6 4.04 36 280
Wasit 19.5 36.7 1.11 28 199
Babylon 22.8 44.1 1.82 18 145
Kerbala 21.5 47.7 1.53 24 173
Najaf 18.7 46.2 1.59 27 190
Qadisia 21.0 35.2 .95 9 195
Muthana 21.3 33.5 .84 18 178
Thi-Qar 18.1 33.8 .73 12 144
Maysan 20.4 34.4 .90 11 301
Basrah 19.0 53.6 2.24 25 219
gdp literacy higheduc
doctors 100000 hospbed 100000 .
. :
Analyze Data Reduction Factor Factor Analysis :
Region .
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Descriptives :
:1.Statistics :
univariate descriptives: MeanStandardDeviation
Initial solution: Communalities ) (Eigen Values .
2.Correlation Matrix: Inverse.
Extraction Factor Analysis
:
:Method: )
. (Analyse: :
Correlation Matrix:
.
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covariance Matrix: : .
Extraction: ) ( :Eigenvalues Over
: ) ( ) . (Number of Factors: )( .
Maximum Iteration for Convergence: .
Display: :Unrotated factor solution Factor Matrix
Component Matrix .
Scree Plot: Eigen Values. Rotation Factor Analysis Rotation
(Loadings) .
. )VarimaxDirect Oblimin
QuartimaxEquamaxPromax. ( None . Scores Factor Analysis Factor Scores
:
:Save as Variables: Factor Scores)
( Data Editor Factor Score
Z Scores ) (i)
p( :
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1
pjp
jjzijwiF =
=
=
: z: w: Factor Scores Coefficients :
Display Factor Score Coefficient Matrix .: )RegressionBartlettAnderson-Rubin(
. Option Factor Analysis
Components Matrix) ( .
OK Factor Analysis :
Communalities
1.000 .797
1.000 .843
1.000 .896
1.000 .704
1.000 .772
GDP
LITIRACY
HIGHEDUC
DOCTORS
HOSPBED
Initial Extraction
Extraction Method: Principal Component Analysis. Communalities
2R .
GDP 0.797 GDP ) ( 01