دليلك إلي البرنامج الإحصائي spss الجزء 2

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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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* 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 .

.



Slope = .078

Level

18016014012010080604020

Spread

18

16

14

12

10

8

6

4

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Untransformed Plots ) ( )IQR(

:



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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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


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


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


4.17 124567dep111.02

12457dep2.

Report Values. fac Factor List Explore Report Values

Options. OK Explore :

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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


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


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


Likelihood Ratio

Fisher's Exact Test

N of Valid Cases

Pearson Chi-Square


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


DEGREE * GENDER

DEGREE

69.00 7 10.28

84.33 9 12.43

77.63 16 13.65

GENDER

Female

Male

Total


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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


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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


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 .

:

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


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

:

:


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.

:



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


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

:


Univariate :

OK :

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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



:



a

1609.595 3 536.532 1.940 .157

5255.002 19 276.579

6864.597 22

Source

TREAT

Error

Total+Error



> 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


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


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


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

2R,SEE . GLS.

4) : ( c y 302.

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



Durbin-Watson

Predictors: (Constant), X2, X1a.


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


Beta

Standardized

Coefficients

t Sig.


:

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


Predictors: (Constant), X2, X1a.


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



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


:

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


: 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


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


Beta

Standardized

Coefficients

t Sig.


)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

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