Εμβαλωτής, Α. Κατσής, Α. & Σιδερίδης, Γ. (2008)....
TRANSCRIPT
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2006
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DataSets : http://research.edu.uoi.gr/aemvalot
SPSS SPSS Inc [www.spss.com, www.spss.gr]
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1. E 7 1.1 8 1.2 11 1.3 - 13 1.4
() 17
2. 19 2.1 Pearson r 21 2.2 26 2.3 28 2.4
Pearson r 30
2.5
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2.6 - 35 3. 37 3.1
SPSS 42
3.2 47 4. 49 4.1 50 4.2 51 4.2.1 52 4.2.1.1 52 4.2.1.2 52 4.2.1.3 54 4.3
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4.4
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4.5 61 4.5.1 61 4.5.1.1 62
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4.5.2 :
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4.6
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5. 71 5.1 72 5.2 ANOVA 73 5.2.1 ANOVA 73 5.2.2 Post hoc 74 5.3 ANOVA 75 5.4 ANOVA 75 6. x2 79 6.1 x2 80 6.2
SPSS 87
7. 89 7.1 90 7.2 92 7.2.1 92 7.2.2
. 93
7.2.3 94 8 97
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0
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5: - (boxplot)
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Pearson r () (.., ). . , - , . Pearson r :
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12 15 16 20 9 6 13 16 18 19 () (scatterplot) SPSS : Graphs SPSS Scatter/Dot. Define, Simple Scatter.
7: . .
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(Study) (Grades) 13. .
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15: . 15 (. ) ( 90-100) . , ( ) () . - () , . , 15 120 130 ( .., IQ ), . (.., 70-80). () Kolmogorov-Smirnov. SPSS . , .
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2.4. Pearson Pearson r; , . r -1 +1. ( ), ( ) . . 0.6 -0.6, . , 1.0 / ( ). 2 (-1 +1), . :
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X Y
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. . . , , , . , . , . , , . SPSS Analyze Correlate Bivariate. (. 16 & 17), , Pearson r 15 . - Spearman Kendall.
15 . : ( . ). , . , . , .
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16 & 17: Pearson r SPSS.
18: Pearson r SPSS. 10 0.964
Correlations
1 .964**.000
10 10.964** 1.000
10 10
Pearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)N
Correlation is significant at the 0.01 level (2-tailed).**.
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: p = .000. , 1. = 5% ( ), .
, . ( 10 ) ( 500 ), . ( ) ( ) . , , .
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2.5. Pearson / Pearson r:
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19: Spearman. 19, r = .985 (p < .001). 2 , . Spearman Pearson, 18.
18 - . .
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2: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 11 9 9 9 8 8 8 6 6 5 5 5 5 5 4 4 4 3 3 26 21 24 21 19 13 19 11 23 15 4 18 12 3 11 15 6 13 4 , , , , . Pearson, .
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() (). 15 . . , Kolmogorov-Smirnov test, ( ) . K-S 0.941 0.457 ( 0.34 0.99, ). 5%, ( ) () . .
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Y abX += Y , (b) (). b . , , ( ), ( ). ( ) ( ).
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21: .
21 , . , () ( 22). (residuals), () . , . / 5 ( ), 12 ( ). 22 . , Pearson r 0.739. , ( ) .
R Sq Linear = 0.546
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/ . ( ) (). (simple linear regression). (multiple linear regression). . 3.1. SPSS
: Analyze Regression Linear.
22 & 22
() Dependent ( ) Independent(s). . .
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23: .
24, .
Model Summary
.739a .546 .519 4.882Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
Predictors: (Constant), a.
24: (1 ).
,
Pearson r, 0.739, () . (), (R Square) . 0.546, . ~55%. / 55% 23. , 23 55% , .
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, (), /. , : () (causal relationships) , () 55% , . . , , - . , (., ) (.., 55% 45%), 10% .
ANOVAb
487.252 1 487.252 20.444 .000a
405.169 17 23.833892.421 18
RegressionResidualTotal
Model1
Sum ofSquares df Mean Square F Sig.
Predictors: (Constant), a.
Dependent Variable: b.
25: : (2 ). 19 ( 18) () . . (ANOVA) r R2 . 19, F24 20.444,
24 (F) . .
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1 17 25 ( , ), 1). , / .
Coefficientsa
.938 3.229 .290 .7752.224 .492 .739 4.522 .000
(Constant)
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
Dependent Variable: a.
26: : (3 output SPSS).
20 . ( ). 20 t-test26. ( ). (constant, ), . :
25 , , (). . 26 t-test, F-test .
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0: :
0.938
. , 77.5%, ( 5%), . ; , ( ) . , b . B 20 (2,224). :
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t 4.522 5%, . () . ( , F-test ), . b; b ( ) ( ). b 2.224 , 2 .
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3.2. , , . .., / 5 . x = 5, :
Y = x+ => Y = .938x + 2.224 => Y = .938(5) + 2.224 => Y = 6.914, ~ 7
, 7 5 . , 7 . / 0 . = 0, 2 . 2 7 . . , () .
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4. 4.1.
, , . ( ). , , . . , ( ) . 1: 2000 ( ). . 2000 . 2: & . , & ( , , ) . , ( & ). 3: . 12 .
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. 12 . , ( ), . . 27.
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.
27 () : . 12 ; . () . . . . Stanley Milgram's Experiment (http://www.cba.uri.edu/ Faculty/dellabitta/mr415s98/EthicEtcLinks/Milgram.htm ) 28 (nominal data). 29 (ordinal data). 1= , 2= , 3= . 30 . 1.2 . . http://www.cmh.edu/stats/definitions.asp
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. ( ). t (t-test). ( ) , t-test .
4.2.1 4.2.1.1
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4.2.1.3
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t p (p-value). p (statistical significance level) . () . 5% ( 0.05) 1% ( 0.01) 10% ( 0.10) . . , p .
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(two-sided test), (one-sided test).
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4.4. . . 1: 12 8 ( , , .). . . 10 12 17 9,5 7,5 6,5 9,5 11 14 8,5 9,5
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. 1: SPSS . (Graphs Histogram Variables) ( 27). Analyze Nonparametric tests-1 Sample K-S. ( 28). Test Variable List Test Distribution Normal. ( 28 29).
4
3
2
1
0
Freq
uenc
y
Mean =10,5Std. Dev. =3,1447
N =10 27: HOURS
28 & 29:
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. .
One-Sample Kolmogorov-Smirnov Test
1010,5003,1447
,225,225
-,102,711,693
NMeanStd. Deviation
Normal Parametersa,b
AbsolutePositiveNegative
Most ExtremeDifferences
Kolmogorov-Smirnov ZAsymp. Sig. (2-tailed)
Hours
Test distribution is Normal.a.
Calculated from data.b.
30: .
: Asymp. Sig. (2-tailed): p . . p ( 5%), . 0,693> 0,05, t (t-test). 2: (0) . (1).
0: 8 .
1: 8 . 3:
5% ( 0,05). 4: t
: Analyze Compare Means One Sample T Test
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Test Variable(s) (hours SPSS). ( 8) Test Value . ( 31 & 32): One-Sample Statistics
N Mean Std. Deviation Std. Error
Mean Hours 10 10,500 3,1447 ,9944
31 One-Sample Test
Test Value = 8 95% Confidence Interval
of the Difference
t df Sig. (2-tailed) Mean
Difference Lower Upper Hours 2,514 9 ,033 2,5000 ,250 4,750
32 5: p
Hours 10.50, 8. Std. Error Mean . : t=(10,5-8)/0,944=2,514 . Sig. (2-tailed) p 0,033. 6: p 0,033
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, , . . , 8. :
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5%. , 1%.
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4.5.
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t . . :
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. . () .
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, t Mann-Whitney, ( ). Mann-Whitney . , SPSS.
4.5.1.1 ( 0-100) (1-, 2-). .
83 1 73 2 75 1 81 2 67 1 49 2 44 1 36 2 28 1 65 2 56 1 56 2 91 1 73 2 39 1 51 2 71 1 44 2 54 1 65 2 38 1 51 2 57 2
(Grades Sex) . . , . Data Select Cases
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33
If condition is satisfied Sex=1.
34
,
.
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(Sex=2). 31, All cases, . : 0: 1: t : Analyze Compare means Independent Samples T Test
35 Grades Test Variable(s) Sex Grouping Variable. Define Groups (1 2 Group 1 Group 2 ).
31 .
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36 Continue OK .
Group Statistics
11 58.73 20.308 6.12312 58.42 13.276 3.833
12
N Mean Std. Deviation
Std. ErrorMean
37
Independent Samples Test
3.068 .094 .044 21 .965 .311 7.093 -14.440 15.061
.043 16.999 .966 .311 7.224 -14.930 15.551
Equal variancesassumedEqual variancesnot assumed
F Sig.
Levene's Test forEquality of Variances
t df Sig. (2-tailed)Mean
DifferenceStd. ErrorDifference Lower Upper
95% ConfidenceInterval of the
Difference
t-test for Equality of Means
38
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Group Statistics (58.73 58.42 ). . 5% . t Sig (2-tailed) 2 p. p . (.965 .966);
. Levene . p Sig . p (.094) 5%, p (.966). .094>.05, .995 .
, . p ( ):
1. p (.996). 2. (t=.005). 2. , (Group 1=) (Group 2=), p , () p . 2. , (Group 1=) (Group 2=,) p :
1 - () p . 2. , (Group 1=) (Group 2=), p () p .
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2. , (Group 1=) (Group 2=), p :
1- () p .
( : ) . 2 p .47. , 5%.
4.5.2. :
. ( ) 0 . : = /
t
(paired samples t-test). . . Wilcoxon signed rank.
: - . . - ( 0-100). :
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(-)
12 23 -11 34 45 -11 67 73 -6 43 54 -11 81 76 5 54 56 -2 56 66 -10 76 78 -2 65 79 -14 56 63 -7
2 (before
after) SPSS (Diff=before-after) : Transform-Compute. Target variable Numeric expression . . diff 0. : 0: - 1: , - T-Test
Paired Samples Statistics
54,40 10 20,533 6,49361,30 10 17,588 5,562
BeforAfter
Pair1
Mean N Std. DeviationStd. Error
Mean
Paired Samples Correlations
10 ,966 ,000Befor & AfterPair 1N Correlation Sig.
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Paired Samples Test
-6,900 5,782 1,828 -11,036 -2,764 -3,774 9 ,004Befor - AfterPair 1Mean Std. Deviation
Std. ErrorMean Lower Upper
95% ConfidenceInterval of the
Difference
Paired Differences
t df Sig. (2-tailed)
39 , : Analyze Compare Means Paired samples T Test
, Paired variables . ( ).
- (54,4 61,3 ). . Paired Sample Test. Sig (2-tailed) p . p diff. , - diff < 0 ( 2). p 0,002 5% -. 4.6.
. t. , . (non-parametric tests). t, (parametric tests). . 2 Mann Whitney: Analyze Non-Parametric Tests 2 Independent Samples
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Grades test variable list, sex group variable Mann Whitney U test type Wilcoxon signed rank: Analyze Non-Parametric Tests 2 related Samples before after test pair list Wilcoxon test type. SPSS . Wilcoxon signed rank . , , (Hours ) ( ew ) 0 . Wilcoxon signed rank hours new test pair list Wilcoxon test type. new : Transform-Compute new Target Variable 0 Numeric Expression. :
() () () .
. , . , // . (alternative hypothesis-research hypothesis). , .
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5
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5. 5.1.
(Analysis of Variance ANOVA)
. , t. . t-test , , . . t :
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( ) (dependent variable), ( ) (independent variables). ( ) (one-way analysis of variance, one-way ANOVA). , . one-way ANOVA 2 t. ANOVA ( t) . . t-test. - ( Kruskal-Wallis). .
, one-way ANOVA, . . 5.2. NOVA
ANOVA, ( ) .
5.2.1 ANOVA ANOVA .
, . ( ) : () , () , ( ) .
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, ( ). , ANOVA ,
= ( ) /
, . F t . p .
5.2.2 Post hoc , . , . post hoc ( a posteriori ) post hoc . post hoc . , :
- LSD (Least Squares Differences). t, . , . - Bonferroni. . - Tukey HSD (Honestly Significant Difference). . ,
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. - Scheffe. . . Tukey .
5.3. ANOVA
ANOVA . , , SPSS ( & ). , , . . post hoc ( ) . . t, , . 5.4. ANOVA
15 PISA (Program for the International Student Assessment32).
32 . http://www.pisa.oecd.org
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33:
1: 469, 474, 478, 465, 459, 489, 478 2: 462, 465, 447, 431, 453, 467, 466 3: 467, 453, 472, 451, 457, 443, 456
SPSS.
34, . one-way ANOV 5% . Analyze General Linear Model Univariate.
40 Dependent Variable scores Fixed Factor(s) school. (: two-way ANOVA, ). Post hoc school Post hoc tests for Scheffe, Tukey. Continue OK .
33 ( ) 34 . 1
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Univariate Analysis of Variance Between-Subjects Factors
777
123
N
41
Tests of Between-Subjects Effects
Dependent Variable:
1308,286a 2 654,143 5,329 ,0154482324,000 1 4482324,000 36512,337 ,000
1308,286 2 654,143 5,329 ,0152209,714 18 122,762
4485842,000 213518,000 20
SourceCorrected ModelInterceptSchoolErrorTotalCorrected Total
Type III Sumof Squares df Mean Square F Sig.
R Squared = ,372 (Adjusted R Squared = ,302)a.
42
Multiple Comparisons
Dependent Variable:
17,29* 5,922 ,024 2,17 32,4016,14* 5,922 ,035 1,03 31,26
-17,29* 5,922 ,024 -32,40 -2,17-1,14 5,922 ,980 -16,26 13,97
-16,14* 5,922 ,035 -31,26 -1,031,14 5,922 ,980 -13,97 16,26
17,29* 5,922 ,031 1,49 33,0816,14* 5,922 ,045 ,35 31,93
-17,29* 5,922 ,031 -33,08 -1,49-1,14 5,922 ,982 -16,93 14,65
-16,14* 5,922 ,045 -31,93 -,351,14 5,922 ,982 -14,65 16,93
(J) 231312231312
(I) 1
2
3
1
2
3
Tukey HSD
Scheffe
MeanDifference
(I-J) Std. Error Sig. Lower Bound Upper Bound95% Confidence Interval
Based on observed means.The mean difference is significant at the ,05 level.*.
43
F p F Sig. 5,329 0,015 . 5% ( 1%) . 3
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( 1=473, 2=455,9 3=457) ( 10). post hoc , Tukey Scheffe, Multiple Comparisons. , (I) 2 (J). Tukey o 1 2 p 0,024. 1 2 ( ), t p 0,012. 1 2 PISA 5% ( 1%). 1 3, 2 3. 2 .
- Kruskal Wallis : Analyze Non-Parametric Tests-K Independent Samples pisa test variable list school group variable.
3:
- t-test
Wicoxon signed rank
( )
t-test
Mann-Whitney
( )
Paired t-test
Wicoxon signed rank
( )
ANOVA
Kruskal-Wallis ( one-way)
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2
6
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6. 2 2 (chi square test of independence) (contingency tables). ( ) ( ) . . X2 . : ( ). ( ). . 2 . 2 :
n > 2535 ( 25%) (n > 250), 36 X2.
6.1. 2 ( )37.
35 n250 ( SPSS random sample) Monte Carlo. 37 : / ;[ =1, =2, =3, =4, =5, =6]
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, (chi square test of independence). :
0 : 1 :
2, ( ) ( ). . SPSS : 4:
5:
37 18.5 18.8 18.840 20.0 20.3 39.131 15.5 15.7 54.869 34.5 35.0 89.811 5.5 5.6 95.49 4.5 4.6 100.0
197 98.5 100.03 1.5
200 100.0
Total
Valid
MissingMissingTotal
Frequency Percent Valid PercentCumulative
Percent
, . SPSS Crosstabs : - Menu Analyse Descriptive Statistics Crosstabs.
83 41.5 41.5 41.5 117 58.5 58.5 100.0 200 100.0 100.0
Total
Valid Frequency Percent Valid Percent
Cumulative Percent
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44: SPSS X2 (rows) (columns).
45: SPSS 2
46:
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. . . SPSS . (Analyse - Descriptive Statistics - Crosstabs), Statistics (. ) ( Chi-square)38 .
47 & 48: SPSS 2
:
38 . .
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7:
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* Crosstabulation
24 19 17 17 2 2 8115.2 16.4 12.7 28.4 4.5 3.7 81.08.8 2.6 4.3 -11.4 -2.5 -1.713 21 14 52 9 7 116
21.8 23.6 18.3 40.6 6.5 5.3 116.0-8.8 -2.6 -4.3 11.4 2.5 1.7
37 40 31 69 11 9 19737.0 40.0 31.0 69.0 11.0 9.0 197.0
CountExpected CountResidualCountExpected CountResidualCountExpected Count
Total
Total
49: . , , . . ( ). ( ), . ( 50):
50: SPSS
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2 . 2. . ( 25%). (recode) .
39. ; Pearson Chi-Square . , . 1 () . X2 (Pearson Chi-Square) 564.786, p-value (Significance level) 0.000 5% ( ) , (. http://home.clara.net/sisa/two2hlp.htm, http://www.graphpad.com/ quickcalcs/contingency1.cfm).
39 .
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6.2. SPSS , SPSS . . - . Count ( ) = . Exp.count ( ) = . Residual ( ) = . Row Total ( ) = . Column Total ( ) = . Chi Square Pearson & Likelihood Ratio (2 ). Degrees of Freedom ( ) = -1 -1, (-1)(-1) Significance () = . (>) 0.05 . Linear by Linear association ( ) = () . Minimum Expected Count ( ). Cells (.x%) have expected count less than 5 = 25% X2 -.
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Phi () = . Phi 2, . , . Cramers V = Cramers V () () . >1, Cramers V 0 1. APA Style : 2(5, =200)= 23.159, p
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7
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7.1 ( ). ( ) . .
0: :
. (grades) SPSS : Statistics NonParametric tests 1-Sample K-S.
1: SPSS Kolmogorov-Smirnov
(Normal) , , 97%. .
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2: SPSS Kolmogorov-Smirnov
. / . . : Statistics Descriptive Statistics Frequencies Variables / () statistics.
3: SPSS
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Skewness/Kurtosis, continue OK. :
4: SPSS +/- 2 . ,
ErrorSkewSkew=
-.690/.687 = -1.004, -.185/1.334 = -.1386. +/-2 . - Explore. 7.2 7.2.1 . Test X2 . : () >30, () > 1 () 80% > 5 . Test Mc Nemar. To test . : () (dichotomous) (b) (value labels)
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. Test Mann & Whitney To test . . Test (Sign test) test Wilcoxon. Sign test ( ), to Wilcoxon test . Sign test test Wilcoxon. . T test o: () . . Mann Whitney test. t-test. F (F-test). . T test o: () . . test Wilcoxon. 7.2.2 . . . n ( n = ) k ( k = ). . 2 test . 2 . o: () >1 80% >5.
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. . n ( n = ) k ( k = ). : () (dichotomous) Test Cohran (Q test). . Kruskal & Wallis test ( test). . . Friedman test. . . ANOVA. : () , () . . . . 7.2.3 . Pearson. : . . Spearman. .
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eta. : - test. . Spearman. . Spearman. . 2 test. . 2 test. . 2 test. . 2 test.
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8
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Stevens, S. (1946) On the theory of scales and measurement.
Science, 103, 667-680. , . (1998).
: . : Gutenberg.
, . (1992). . :
, ., , ., , ., & , . (1999). . : .
Norusis, M. (2005). SPSS 12.0 (., Trans.). : .
Yerkes, R. M., & Dowdson, J. D. (1908). The relation of strength of stimulus to rapidity of habit-formation. Journal of Comparative and Neurological Psychology, 18, 459-482.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.
, ., & , . (2003). . :
Champion, D. J. (1981). Basic statistics for social research (2d ed.). New York: Macmillan.
( ) http://www.ats.ucla.edu/stat/spss/ ( SPSS Starter Kit, What statistical analysis should I use?, Annotated Output Links by Topic) http://www.ats.ucla.edu/stat/spss/notes2/analyze.htm ( )
. : http://bcs.whfreeman.com/ips4e/cat_010/applets/CorrelationRegression.html
http://www.stat.vt.edu/~sundar/java/applets/Correlation.html
http://bcs.whfreeman.com/bps3e/content/cat_010/applets/twovarcalcbps.html
http://bcs.whfreeman.com/bps3e/
http://davidmlane.com/hyperstat/index.html
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-TEST . : http://www.une.edu.au/WebStat/unit_materials/c6_common_statistical_tests/index.html (ANOVA) . : http://www.physics.csbsju.edu/stats/anova.html http://web.umr.edu/~psyworld/virtualstat/anova/anovacalc.html http://faculty.vassar.edu/lowry/ank3.html http://faculty.vassar.edu/lowry/ank4.html http://www.une.edu.au/WebStat/unit_materials/c7_anova/index.html http://www.graphpad.com/quickcalcs/posttest1.cfm http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/ANOVA2Rep.htm http://faculty.vassar.edu/lowry/corr3.html http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/ANOVADep.htm http://faculty.vassar.edu/lowry/anova2x2.html http://faculty.vassar.edu/lowry/anova2x3.html http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/ANOVATwo.htm http://faculty.vassar.edu/lowry/corr4. http://www.une.edu.au/WebStat/unit_materials/c7_anova/twoway_anova.htm
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