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2 This project has been funded with support from the European Commission. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein. -..,.., 2010

3 :..,..,,.. -,,..,.. : -., ISBN,.. MS Excel, SPSS Statistica,, -,,, ;. MS Excel 2003, SPSS 10.0 Statistica 6.0,,,. OpenOffice.org Calc.

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14 3 (Statistica): 1. Statistica C:\Program Files\StatSoft\STATISTICA6\statist.exe. 2. C:\ \STATISTICA6\Examples\Datasets, job_prof.sta, File > Open. 3. Statistica., Variable Specs. 4. (Statistica > Basic Statistics > Descriptive Statistics): Quick (Summary: Descriptive statistics, Frequency tables, Histograms, Bow&whisker plot)., (Workbook).. 5. Advanced (Summary: Descriptive statistics). Data > Transpose > File.. Extract as stand-alone window ( ) Add to report ( ). 6. Frequency tables Histograms Normality, (Number of intervals).. Statistica, RTF HTML. 7. SPSS. 8..xls.,.. 13

15 9. : Data > Sort Statistica, SPSS,, ( Copy Variables ), Data > Rank

16 . 1 MS Excel. MS Excel OpenOffice.org Calc (.. 188).. 2 D 2 ( 2- ) 7. > >

17 . 3 ( ), ( ).. 4,. 5 MS Excel.. 4 = (B2;$B$2:$B$11;1) = ($B$2:$B$11;B2;1) = ($B$2:$B$11;H2) = (B3;$B$2:$B$11;1) = ($B$2:$B$11;B3;1) = ($B$2:$B$11;H3) = (B4;$B$2:$B$11;1) = ($B$2:$B$11;B4;1) = ($B$2:$B$11;H4) = (B5;$B$2:$B$11;1) = ($B$2:$B$11;B5;1) = ($B$2:$B$11;H5) = (B6;$B$2:$B$11;1) = ($B$2:$B$11;B6;1) = ($B$2:$B$11;H6) = (B7;$B$2:$B$11;1) = ($B$2:$B$11;B7;1) = ($B$2:$B$11;H7). 5 1.,, -,, ? 4.?? 5.,,? 16

18 6.?? 7.?? 8.? 9.? 10.? 11.,??? 12.? 13. MS Excel, OpenOffice.org Calc, SPSS, Statistica? 14.? 15.? 16.? 17.,. 18.,? ,,? 20. MS Excel, OpenOffice.org Calc, SPSS, Statistica? 21. MS Excel, OpenOffice.org Calc, SPSS, Statistica? 22. SPSS, Statistica?? 17

19 2: : : ; ; (t- ) (F- ); ; ; ; ;. :, ; ; ; ; ; MS Excel ; SPSS Statistica.,, ( ). ( ) df=n 1 +n 2 2.,. 18

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21 1:. 1. MS Excel t ( ) ( ). 3.,,.. 4., F- ( - - ) ( > ).. 5. MS Excel: ( 1; 2) - (2 ); : k 1 =n 1 1 k 2 =n 2 1 ( n 1, n 2 ); =2 /2; F, F ( ; _ 1; _ 2); F =0,05 =0, : t- t-, F- (.. 4).. 8. t, (p, k),, k (k =n 1 +n 2 2). 9. t ( 6), 20

22 (, k, m), t-, k, m (m=1, m=2 ). 10. MS Excel :,, (1 2). SPSS. 11. SPSS Analyze > Compare Means > Independent Samples t-test. (Test Var), (Grouped Var) (1, 2 ). 12.,. 13. Statistica., ( MS Excel), Basic statistics >t-test, independent, by variables., SPSS ( + ), Basic statistics > t-test, independent, by groups. 14.,. 2:. 1. t- ( ). (. 202) t t Analyze > Compare Means >Pared-Samples T Test SPSS. 6. Statistics > Basic statistics > t-test, dependent samples Statistica. 21

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25 (.. 19)..,,. t - :.. : 0 : 1 2 ( 2 1). 1 : 1 2 ( 2 1). t. t < t,. t. : 0 : 1 2 ( x 1 x2 0 ). 1 : 1 2 ( x 1 x2 0 ).,. SPSS. : 1 :,,. 1 Group Statistics VAR00001 VAR ,00 2,00 Std. Error N Mean Std. Deviation Mean ,2143 9,4314 2, ,5000 6,7622 1,

26 2, -, (Leven s Test for Equality of Variance). -, F=0,573, (Sig. = 0,471),. t- Equal variances assumed (, ). t- (Equal variances not assumed). 2 Independent Samples Test VAR01 Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. t df Sig. (2-tail ed) t-test for Equality of Means Mean Differen ce Std. Error Differe nce 95% Confidence Interval of the Difference Lower Upper,537,471-1,310 24,203-4,2857 3, ,0370 2,4655-1,344 23,345,192-4,2857 3, ,8755 2,3041,, t = 1,31 ( ). - = 0,203, ( ). - ( =0,102). 0. Statistica : t- Valid Valid Mean Mean df p Std.Dev. Std.Dev. F- p value N N ratio Var1 107,21 111,50-1, , ,43 6,76 1,94 0,28 2 ( t- ): 10. ( ).,. 25

27 MS Excel,,. MS Excel t-. A B C 1 X Y (. 6) : E F G t- X Y ,

28 0, df 9 t- -2, P(T<=t) 0, t 1, P(T<=t) 0, t 2, : t- (!); t t ( 0,05.. 6),,. 2,75>2,26 (t >t ), 0,. : P(T<=t) =0, , 0,05.,, ( ), ( ),,., t >t (2,75>1,83), 1, Y. SPSS t- (Analyze > Compare Means >Pared-Samples T Test) : 27

29 3 Pair 1 X Y Paired Samples Statistics Std. Error Mean N Std. Deviation Mean 3286, , , , , ,0847 Paired Samples Correlations Pair 1 X & Y N Correlation Sig. 10,772,009 Paired Samples Test 28 Paired Differences 95% Confidence Std. Std. Error Interval of the Difference Mean Deviation Mean Lower Upper t df Sig. (2-tailed) Pair 1 X - Y -144, , , , ,6738-2,753 9,022 t-. =0,01 ( - = 0,009), =0,05 ( - = 0,022). Statistica Statistics > Basic statistics > t-test, dependent samples : Mean Std.Dv. N Diff. Std.Dv. t df p X 3286, ,9177 Y 3430, , , ,4086-2, , ? 2.? 3.?? 4.?? 5.? ?

30 8.? 9.? 10. ( - )? 11.? 12.? 13.? 14.? 29

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35 1: 1. ( D E,.,.194,.203) ,. 2: SPSS Statistica 1. SPSS.,. 2. SPSS : Analyze > Compare Means > One-Way ANOVA, (Dependent List),, Factor. 3. (Options) Descriptive, Homogeneity-of-variance Means plot.,. 4. Statistica, SPSS. Statistics > ANOVA, One-Way ANOVA. (Dependent variable) ( Statistica ). 5. Summary : Cell statistics, Univariate results, All effects/graphs. 34

36 6. Statistics > Basic Statistics/Tables > Breakdown & one-way ANOVA. Quick Statistics by Groups Results Summary Table of Statistics, Analysis of Variance Interaction plots : 1. (..208). 2. (,,, ) ,. 4: SPSS Statistica 1. SPSS (, ). 2. Analyze > General Linear Model > Univariate. 3. Dependent Variable, - Fixed Factor(s). 4. Options Descriptive statistics Estimates of effect size ( ). 5. Plots, (Horisontal Axis), (Separate Lines). 6.,. 35

37 1.. '. 10. ',? [187,.41]. 6, MS Excel. 6 : 36. 7

38 0,.,. MS Excel (. 7): F =6,72. F =3,35. :,, ,19 3,019 0, ,7 3,97 1, ,97 4,997 2, % SS df MS F P- F 19, , ,672 0, , , , , (. 8) : SPSS Ststistica. 37

39 2. ( 11,. 208): (MAC Dell) (Netscape Communicator Internet Explorer). 8,, MS Excel (,, ). Netscape Communicator Internet Explorer 8 MAC Dell MAC Dell Netscape Communicator 5% ,25 300,5 218,375 61, , ,45 Internet Explorer ,25 297,5 250,375 37, , , , ,87 322,8 ( 9 10). 10 P- F SS df MS F ,76 5,3E-07 4, ,24 3,4E-21 4, ,95 1,1E-07 4, ,

40 , ( ). : 0 :. 1 :. 0 :. 1 :. 0 :. 1 : MAC Dell Netscape Communicator. 9 Internet Explorer Netscape Communicator Internet Explorer MAC Dell. 10 F, 39

41 ,. : (. 9,. 10), Dell, Mac, -. SPSS. :. browser 1 Netscape Communicator 2 Internet Explorer, computer 1 Mac 2 Dell ( 11, 12). 11 Between-Subjects Factors BROWSER COMPUTER 1,00 2,00 1,00 2,00 Value Label N NC 16 IE 16 mac 16 dell 16 40

42 Descriptive Statistics 12 Dependent Variable: T_LOAD BROWSE NC IE Total COMPUTE mac dell Total mac dell Total mac dell Total Dependent Variable: TIME Source Corrected Model Intercept BROWSER COMPUTER BROWSER * COMPUTER Error Total Corrected Total Mean Std. Deviation N 136,2500 7, , , , , ,2500 6, , , , , , , , , , , Tests of Between-Subjects Effects Type III Sum of Mean a. R Squared =,965 (Adjusted R Squared =,961) 13 Partial Eta Squares df Square F Sig. Squared ,5 a ,5 257,7,000, ,E ,000, , ,00 41,758,000, , ,2,000, , ,00 49,954,000, , , ,5 31 ( 13) 2 ( ). Corrected model,. Corrected total. Error,. 41

43 (. 12) MS Excel. 400 Estimated Marginal Means of TIME 400 Estimated Marginal Means of TIME Estimated Marginal Means ,00 BROWSER 1,00 2,00 2, ,00 COMPUTER 1,00 2,00 2,00 COMPUTER BROWSER. 12 Statistica. 1.? ( ). 5..? 6.??? ??? 42

44 4: : : Excel ; ; ; ; ; ;. :, ; ; ;, ; ;..,,.,,,,, 1 r 1. : X x Y y rxy ( )( ), s x, s y N s x s y X Y, x y, X Y ; N. 43

45 ,, ( ),. 2 (d) 8 : r 6 d 1 s 2 N ( N 1. ),. t-. r. r n 2 t ( n 2 1 r ) t- df=n ,.,,,.,,, 5 (. 86).,, Partitial Correlation.. ( ). Y X s yx sxy ( yx ) X Y ( xy ), s y sx ( yx = xy ). s x, s y 8,. 44

46 1 X Y ; s px ( y x y) n 2 yx 1 2 s xy p y ( x y x) n ; p x, p y X Y; x, y ; y x, x y ; n. - [17, 5, 18]., (.. 35, 41). 2. :,,.., X Y,, Y X,. ( ), X Y, Y X.. : X Y,,,. (r 2, 2 ),. - 2 ( m n m ) : F. 2 2 ( 1 )( m 1), m, ; n. F df 1 =m 1 df 2 =mn m [18].,, 45

47 Y=f(X)+,. Y x 1, x 2, x 3, x m. : y = a+bx 1 +cx 2 +.,, ( ), -,. R 2, Y,. 2 2 ( Y Y ) r, Y Y 2 ( Y Y ) ( Y), Y, ( ), Y =a+bx., X. Y X a b : 46 ( y y)( x x) b 2 ( x x) 2 ( y y) b r 2 ( x x) a y bx. X Y. ( )., t >t.,,.,,, F <F, 0. ( F >F ),

48 . - [14, 8, 14]. 1: 1 : MS Excel 1. X, Y, Z 9 (.,.194). 2. ( ), ( ), ( ), ( ). 3. r xy, r xz, r yz ( ). 4. : ) ; ) p- ( ): = (t, n-2, 2).,, (2 1 ). - ( =0,05 =0,01). <, 0 1,. >,,,. 5. ( ). 6.,, ( ). n : 9 ( x, y, z),,,, ( ),. 47

49 48 t n z 2 2 3, n, t, ( =0,05 t=1,96; =0,01 t=2,58); z. (. 1). 7. X Y, (15-20 ). -, (.. 10) (1; N) ( N )... ( ) : SPSS 1. Analyze > Correlate > Bivariate,, : (Pearson), - (Kendall s tau-b) (Spearman). Options. 2., Graps > Scatterplot > Simple. 3. Graps > Scatterplot > 3D. ( - SPSS Chart Object > Open 3D-Rotation ( ).

50 4. MS Excel.. 1 : Statistica 1. Statistics > Correlation Matrices. Advanced/Plot Summary: Correlation matrix ( ), Partitial correlation ( - ), Scatterplot matrix ( ), 3D scatterplots ( ). ( ).. 2. ( Statistics > Nonparametrics > Correlation (Spearman, Kendall tau, gamma) : 1. Y X X Y, () MS Excel. 2. (,, R 2 1).,. 3. Y.. 4. Y Z.. 5. SPSS (Analyze > Regression). SPSS Y Y X Z. 49

51 6. Analyze > Curve Estimation.,,. 7. Statistica (Statistics > Multiple Regression). Y Statistica. 8.,.. 1: ( ).. A B C D 1 (X) (Y) (Z) ,.. : MS Excel., 14, 14, D14 14 X Y (R xy ). 50

52 B14 C14 = (B2:B11;C2:C11) t- : =B14* (10 2)/ (1 B14^2) D14 ( ) = (C14;10 2;2) E14 = (D14<0,05;"H1";"H0") : (r) t- alpha Rxy 0, , , H1 Rxz 0, , , H1 Ryz 0, , , H1. r xy r xz =0,01. r yz =0,05. : 1% 5% = (B14) =2,58^2/$B18^2+3 =1,96^2/$B18^2+3 : n1% n5% Z(xy) 1, , , Z(xz) 1, , , Z(yz) 0, , , , n 10 ( ),,. Y Z 51

53 =0, Y. 13.,.,. Y (Y) ( ). 13 C X Y : A B C D E F G H 1 (X) (Y) (Z) Y ,5 0,5 0, ,5-4,5 20, ,5 0,5 0, ,5-0,5 0, d d^2 52

54 d 2 =37. r s = 0,776., ( ),. 14 Descriptive Statistics X Y Z Mean Std. Deviation N 36,60 7, ,10 4, ,50 1,72 10 SPSS., ( 14). 15. (*), =0,05, (**), =0,01. p-. MS Excel. 15 Correlations X Y Z Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N X Y Z 1,000,827**,821**,,003, ,827** 1,000,718*,003,, ,821**,718* 1,000,004,019, **. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed). 53

55 ( 16). Y Z. Nonparametric Correlations Correlations 16 Kendall's tau_b Spearman's rho X Y Z X Y Z Correlation Coefficient Sig. (2-tailed) N Correlation Coefficient Sig. (2-tailed) N Correlation Coefficient Sig. (2-tailed) N Correlation Coefficient Sig. (2-tailed) N Correlation Coefficient Sig. (2-tailed) N Correlation Coefficient Sig. (2-tailed) N **. Correlation is significant at the.01 level (2-tailed). X Y Z 1,000,682**,732**,,008, ,682** 1,000,458,008,, ,732**,458 1,000,005,080, ,000,772**,806**,,009, ,772** 1,000,565,009,, ,806**,565 1,000,005,089, SPSS Y X

56 (Analyze > Correlate > Partitial Correlation) Y : 17 Partitial Correlation Coefficients Controlling for.. 1,0000,5812 ( 0) ( 7) P=, =,101,5812 1,0000 ( 7) ( 0) =,101 P=, (Coefficient / (D.F.) / 2-tailed Significance) ", " is printed if a coefficient cannot be computed, (Y) (X) (Z) : r xy,z = 0,5812.,.. Statistica Statistics > Correlation Matrices : 1) : Correlations (Spreadsheet1 in Workbook1) Marked correlations are significant at p <,05000 N=10 (Casewise deletion of missing data) Var1 Var2 Var3 Variable Var1 1,00 0,83 0,82 Var2 0,83 1,00 0,72 Var3 0,82 0,72 1,00 2) (. 15) 55

57 3). Correlations (Spreadsheet1 in Workbook1 3v*10c) Var1 Var2 Var : ( ) ( ): A B ,? :, (. 16).,,,, (r ab 0). Analyze > Compare Means > Means SPSS. A, B.. Options Anova table and eta Test for linearity. 56

58 B : 1. Case Processing Summary. 2. Report,. 3. : 18 B * A Between Groups A Within Groups Total (Combined) Linearity Deviation from Linearity. 16 ANOVA Table Sum of Mean Squares df Square F Sig. 170, ,217 5,687,159,275 1,275,110, , ,484 6,194,147 5, , ,600 14, : Deviation from Linearity = 170,325 (Combined) = 170,6. 4. : Measures of Association R R Squared Eta Eta Squared B * A -,040,002,986,972 57

59 R ; R Squared ( ), ; Eta., A,,., : Measures of Association R R Squared Eta Eta Squared A * B -,040,002,793,628 Analyze > Descriptives > Crosstabs > Statistics (Eta): Directional Measures Nominal by Interval Eta A Dependent B Dependent Value,793,986 Analyze > Compare Means > Means 1 : Measures of Association Y * X R R Squared Eta Eta Squared,827,684,941,885 Measures of Association X * Y R R Squared Eta Eta Squared,827,684,951,905,,, Anova ( 19). 58

60 ANOVA Table 19 Y * X Between Groups Within Groups Total (Combined) Linearity Deviation from Linearity Sum of Mean Squares df Square F Sig. 128, ,319 2,198,348 99, ,101 11,892,075 29, ,855,583,743 16, , , % (29, ,233). 3: 1. : MS Excel ().. Y X (Y) y = 0,4339x + 7,2196 R 2 = 0, (X) (Y) ( (Y))

61 (R^2), (. 17).,,,,. (). - - (.. 11).., C14:D14. = (B2:B11; C2:C11; 1; 0). : 14=0,4339 b; D14=7,2196 a. : y=0,4339b+7,2196. (Y; X;.;.) ( ); (, );,, a ( a=0.=0);. = (B2:B11; C2:C11; 1; 1) 5 : 0,4339 7,2196 0,1043 3,8911 0,6839 2, , ,101 45,799 : b 0,4339 a 7,2196 0,1043 3,8911 b a R 2 0,6839 2, ,31 F- df ( ) 8 99,101 45,799 60

62 k+1 ( k ) : 1. : R 0, (R>0) R- 0, R- 0, , : df SS MS F F 1 99, , , , , , ,9 F F,. 3. : - t- - P- - 95% 95% Y- - 7, , , ,1006-1, ,1926 (X) 0, , , , , ,67437,, ( ). t : 61

63 - - (Y) (Y) 1 20, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , (. 18)

64

65 ,.., (. 5,. 89). ( ). SPSS Analyze > Regression > Linear. 19. : 1. : Model Summary b Model 1 Adjusted Std. Error of R R Square R Square the Estimate,827 a,684,644 2,3927 a. Predictors: (Constant), b. Dependent Variable: 2. - : ANOVA b Model 1 Regression Residual Total a. Predictors: (Constant), b. Dependent Variable: 3. : Sum of Mean Squares df Square F Sig. 360, ,018 17,310,003 a 166, , ,

66 Model 1 (Constant) Coefficients a Unstandardize d Coefficients Standardized Coefficients Std. B Error Beta t Sig.,188 8,870,021,984 1,576,379,827 4,161,003 a. Dependent Variable: MS Excel. (, ) SPSS Analyze > Regression > Curve Estimation (. 20).. 20, :, : 65

67 1. (MODEL): Dependent variable.. Method.. LINEAR Listwise Deletion of Missing Data Multiple R,82700 R Square,68392 Adjusted R Square,64441 Standard Error 2,39268 Dependent variable.. Method.. QUADRATI Listwise Deletion of Missing Data Multiple R,82825 R Square,68600 Adjusted R Square,59628 Standard Error 2,54948 :, 68% (R Square 0,68). 2. (Analysis of Variance): Dependent variable.. Dependent variable.. Method.. LINEAR Method.. QUADRATI DF Sum of Mean DF Sum of Mean Squares Square Squares Square Regression 1 99, ,1006 Regression 2 99, ,7005 Residuals 8 45,7994 5,7249 Residuals 7 45,7994 6,4999 F = 17,31038 Signif F =,0032 F = 7,64637 Signif F =,0173, : F = 99,1/5,72 = 17,31., (F = 49,7/6,49 =7,64637), ( =0,01, - = 0,0032, =0,05, - = 0,0173).,. 3. (Variables in the Equation): Dependent variable.. Method.. LINEAR Variable B SE B Beta T Sig T,4339,1043,8270 4,161,0032 (Constant) 7,2196 3,8911 1,855,

68 Dependent variable.. Method.. QUADRATI Variable B SE B Beta T Sig T,1796 1,188,342,151,88410 **2,0035,016,487,215,8359 (Constant) 11, ,329,549,5999. y=0,4339 x+7,2196. y=0,0035 x 2 +0,1796 x+11,7167. t-,,.. SPSS, Observed Linear Quadratic Statistica Graphs > 2D Scatterplots (. 22). 1.? 2.? 3.?

69 5.? 6.,? 7.? 8.? 9.? 10.?? 11.? 12. -?

70 5: : MS Excel, SPSS Statistica : ; -, ; ; MS Excel ;,, ,. :, ; ; ;, ; ; -. 69

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72 , : A 3 D( A ) E 5 D( E ).. (n 20).,,., [8]..., -, [8, 3].,,.,,,,,,,..,.,.,, (, ) ( ). H 0 : F(x)=F(x, ), F(x, ),, ( ). 71

73 H 0 : F ( x ) F( x, ),,. ˆ,. ˆ,.,, ( ) ,.,.. [3] : x i x i+1 xi x xi x zi zi 1 1 ( x S S, S ). X (x i, x i+1 ): Pi ( zi 1 ) ( zi ).,, : n i =N P i. N. N * i. n i ( zi ), i S [5]. 72

74 - -, ( ). -. (n<20) (, ), d emp d kr. d max n ( d ) n,. d ( 20, 21). 20 d max [19], d emp d kr. n p=0,05 p=0,01 n p=0,05 p=0,01 5 0,6074 0, ,1921 0, ,4295 0, ,1753 0, ,3507 0, ,1623 0, ,3037 0, ,1518 0, ,2716 0, , ,248 0, , ,2147 0,2574 >100 1,36/ n 1,63/ n 21 1-p [25] p 0,30 0,25 0,20 0,15 0,10 0,05 0,02 0,01 0,97 1,02 1,07 1,14 1,22 1,36 1,52 1,63,,, : p=0,2 p=0,3 [8, 25]. ( p-,., p<0,2, =0,2., 73

75 p>0,2 ( 0,2 p- ).) (,,, 10., D * 0 85 d n 0, 01. n D * : 22 0,15 0,10 0,05 0,03 0,01 D * 0,775 0,819 0,895 0,955 1,035 - n1 n2 d max, d max = n1 n2 ; n 1 n ,. 2 -,. 10 -,.: II < 74

76 - - (, ). -,. 2 -.,.. (..72). : 2 k i 1 ( f emp 2 f teor ) f teor, k ( ), f emp f teor,. df=k r 1, k, r.,, ( ) x S ( ). r=2, df=k 3.,.,,, ( ) (. 4,. 108). df=(k 1)(m 1), k ( ), m. 75

77 2. - 2,. -,, 5.. -, 2,,.. [5]. 2 - ( ).,,, 4,. ( - ) [22, 5, 18]: 2 2 ad cb : Q ; ad cb ad cb : ; ( a b )( d )( b d )( a c ) mxn 2 - : ; 2 N 2 V, k N ( k 1) ; 2 T, c k N ( c 1) ( k 1). N, 2,. 76

78 , 2,, : (0.05, 0.10,..., 0.95) > P k = (, ), =0.05, > Z k = ( ). 3. (P k, Z k ). 4.., (P k, Z k ) ,. 8. SPSS (Graphs > Q-Q Plots) (Graphs > P-P Plots)., - SPSS,. MS Excel. 9. SPSS Analyze > Descriptive Statistics > Explore: (Dependent List).,, (Factor List). Display Both,,. 77

79 (Stem-and-Leaf Plot). (, ) ( ). (Box Plot),. ( ). Normality plots with tests -. (Sig.) 0,05,. 10.,,. Data > Select Cases If condition 11. filter_$., filter_$= Statistica: Graphs > 2d Graphs > Normal Probability Plot > Quantile-Quantile Plot > Probability-Probability Plot. 12. Statistica, Statistica > Basic Statistics/Tables > Frequency Tables. Normality Frequency Tables 11 Data > Select Cases. Random sample of cases. 78

80 Kolmogorov-Smirnov test Test for normality. 13.., :. 2 : ( ): ) : A B C D 1 X = ( 2,, S, 0) =C2*N*k = ( 3,, S, 0) =C3*N*k 79

81 .. S ( ). 0 ( ) ( ), 1 ( ) ( )., 0.,. D, N, k. k=1 ( ). 1. ) : A B C D E F G 1 X i X i+1 Z i Z i+1 (Z i ) (Z i+1 ) ( (Z i+1 )- (Z i ))*N X i ; X i+1 ; Z i Z i+1. Z i = (X i ; ; ). Z i Z i+1 + ( ). (Z i ) (Z i+1 ). z 1 z 2 F( z ) e 2 2 dz (F(z)= (z)), 80

82 1 F( z ) ( z ), 2. (X i,, S, 1), ( Z i Z i+1 ). ( N), ( ) : ) 2 ( 2 2 ); ) - - (, ). 4.,. : : -,,,,, -, -,,. : (), (), F (), (), (), (), (), (), (), (), 2 : ( )

83 ,. 4., : ( ) SPSS C. 2. ) Transform >Count,. Count (Target Variable), Numeric Variables (Define Value), Range k through L ( k, L,,, 10, ) Range Lowest through L (, L). (Add) Values to Count. 2. ) Transform > Recode > Into Different Variables. Recode (Input Variables), (Output Variable), Old and New Values, Count. (Add) Old > New : Analyze Nonparametric Tests Chi-Square (All categories equal) : Graphs > Bar Charts > Simple. 82

84 6. ( ) Analyze > Nonparametric > 1-Sample K-S ( - ). Analyze > Descriptive Statistics > Explore. : [8], Nonparametric > 1-Sample K-S : p-,,, ( ). 7.. MS Excel. 2 : ( ) Statistica: 1. Statistica Statistica > Distribution Fitting. Distribution Fitting. (Continuous Distribution) (Normal), (Rectangular), (Exponential, Gamma, Log-normal, Chi-square, Weibull, Gompertz). (Descrete Distribution),,. 2. Fitting Continuous Distributions (Variable) (Distribution). Parameters ( ) (Numbers of categories), (Lower limit) (Upper limit). :, 1 (. 6). 3. Options,. 24: Combine Categiries ( ) Chi-Square test, 83

85 Yes (continuous) Kolmogorov- Smirnov test,, - (Frequency distribution) (Raw frequencyes) Graph. 4. Summary Plot of observed and expected distribution Quick :. 1. ( () ( ; )) (50-80 ): 1 ( ), 2 (0-5 ), 3 (1-3 ). : ). 84

86 2. 2: > , 3 >. 2 ( ), 3 ( ).. :!, SPSS 5. 1, 2, (Row) 3 (Column). Analyze > Descriptive Statistics > Crosstabs. 2 - V (. 4), Crosstabs >Statistics. 7.. Graphs > Bar Charts > Clustered. (Category Axis) 2, 3 (Define Clusters by) MS Excel

87 4: ( ). 1. MS Excel (.. 211), SPSS GSS93 subset.sav,.. ( / ) ( gunlaw). (sex), (marital) (relig). Analyze > Descriptive > Crosstabs (Row) gunlaw ( ), ( sex, relig, marital ) (Column). Statistics Chi-Square Phi and Kramer s V. Cells Counts Observed Expected ( )

88 K (Y;k) ( ) 122 0,05 139,6-1, ,1 148,8-1, ,15 152,4-1, ,2 153,4-0, , , , , ,35 155,6-0, ,4 157,6-0, ,45 160,6-0, , , ,55 163,8 0, ,6 166,4 0, ,65 168,4 0, ,7 169,8 0, , , ,8 175,4 0, ,85 177,2 1,04 0,9 179,2 1,28 0,95 183,6 1,64 2,00 1,50 1,00 0,50 0,00-0,50-1,00-1,50-2,

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91 Y Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent ,0% 0,0% ,0% 2. ( - ) - ( 50 ). Tests of Normality Y Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig.,142 17,200*,966 17,713 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction p- (Sig.). =0,2.,. 3. C (,. 188): Descriptives Y Mean 95% Confidence Interval for Mean Lower Bound Upper Bound Statistic Std. Error 162,5294 3, , ,9447 5% Trimmed Mean Median Variance Std. Deviation Minimum Maximum Range Interquartile Range Skewness Kurtosis 163, , ,890 16, ,00 194,00 72,00 20,5000 -,499,550 1,479 1,063 90

92 4. ( ). Histogram Frequency ,0 130,0 140,0 150,0 160,0 170,0 180,0 190,0 Std. Dev = 16,37 Mean = 162,5 N = 17,00 Y 5.. Stem-and-Leaf Plots Y Stem-and-Leaf Plot Frequency Stem & Leaf 1,00 Extremes (=<122) 1, , , , , , Stem width: 10,00 Each leaf: 1 case(s) , , : 14, 15..,. 17 3, 6 8, ,

93 6.. 2,0 Normal Q-Q Plot of Y 1,5 1,0,5 0,0 Expected Normal -,5-1,0-1,5-2, Observed Value, Y.,. 7.. Detrended Normal Q-Q Plots,4 Detrended Normal Q-Q Plot of Y,2 0,0 -,2 -,4 Dev from Normal -,6 -,8-1, Observed Value. (Y=0).

94 8. (Box Plot): N =, , 122 (, ). 17 Y Statistica : Tests of Normality (Spreadsheet1) N max D K-S Variable p Var2 17 0, p >.20 2:, -,. 52%, 20,, 5., 93

95 ?. : 0 : =0,52 ( =0,52, ). 1 : 0,52 ( =0,52, )., : 20*0,52=10,4; 20 10,4=9, df=2 1=1,. ( )., 0,5. R R Q.. f f R 0,5 R^2 Q/f 5 10,4 5,4 4,9 24 2, ,6 5,4 4,9 24 2, = 4,81 df=1 2 =4,81. 2 (, _ ) ,05= 2 (0,05; 1)=3, ,01= 2 (0,01; 1)=6,63.,. =0,05. 2 (, _ ) -.,,. =0,03. =0,05,, 94

96 . ( =0,01). MS Excel 2 ( ; ),,., - =0,016 0,03.,, : =0,05. -, SPSS Analyze > Nonparametric Tests > Chi-Square 1, 2, ( 20 ). Chi-Square Test (. 27) 95

97 (Expected Values). (All categories equal). (1 2). : Observed NExpected N Residual 5 10,4-5,4 15 9,6 5,4 Total 20 Test Statistics Chi-Square 5,841 df 1 Asymp. Sig.,016 a 0 cells (,0%) have expected frequencies less than 5. The minimum expected cell frequency is 9,6.,., MS Excel. ( ), 5,,. 2 : 53.,,? =164,4 S=5,14. 96

98 =5 14. (152) (181) A B C D E 1 2 X i X i , , , , , , ,4 11 5,14 D ( ) : =( (A3;$A$10;$A$11;1) (B3;$A$10;$A$11;1))*$A$9 2, 5. : , , , , ,8 0, , , , , , = 5, = 0, = 0, ( f e f t f t ) 2 d

99 2 ( 2 = 5,138095) 2 -, df=3., (df=4 3=1). 2 0,05 = 3, ,01 = 6, ,, ( 23, ). d max =0,11191.,, D *. 0, p<0,1 ( Explore SPSS Distribution Fitting Statistica). p- ( ). 2 : SPSS. -.. Analyze > Nonparametric Tests > 1- Sample K-S, :, (Uniform),. : 98

100 1) : One-Sample Kolmogorov-Smirnov Test 2 N Uniform Parameters a,b Most Extreme Differences Minimum Maximum Absolute Positive Negative Kolmogorov-Smirnov Z Asymp. Sig. (2-tailed) a. Test distribution is Uniform. b. Calculated from data. 2) : One-Sample Kolmogorov-Smirnov Test N Normal Parameters a,b Most Extreme Differences Kolmogorov-Smirnov Z Asymp. Sig. (2-tailed) a. Test distribution is Normal. Mean Std. Deviation Absolute Positive Negative VAR ,00 178,00,234,234 -,176 1,706,006 VAR ,3774 5,1374,116,116 -,111,846,472 b. Calculated from data. - = 1,706, - = 0,006.,. - = 0,846, - = 0,472. Explore (.. 90) (..74),. Analyze > Nonparametric Tests > Chi-square Test,,

101 ( ). ( Transform > Recode. 28) ,,, Chi-square Test. 6 : V2_RECOD Observed N Expected N Residual 1,00 3 2,9,1 2, ,6 -,6 3, ,3 6,7 Test Statistics: 4, ,5-6,5 V2_RECOD 5,00 5 4,8,2 Chi-Square a 5,277 6,00 1 1,0,0 df 5 Total 53 Asymp. Sig.,383

102 a 3 cells (50,0%) have expected frequencies less than 5. The minimum expected cell frequency is 1,0. : V2_RECOD Observed N Expected N Residual 2, ,5 -,5 3, ,3 6,7 Test Statistics 4, ,5-6,5 V2_RECOD,00 6 5,8,2 Chi-Square a 5,257 Total 53 df 3 Asymp. Sig.,154 a 0 cells (,0%) have expected frequencies less than 5. The minimum expected cell frequency is 5,8. Analyze > Descriptive Statistics > Explore : Tests of Normality VAR00002 Kolmogorov-Smirnov a Statistic df Sig.,116 53,072 a. Lilliefors Significance Correction (. 29). 3 Normal Q-Q Plot of VAR00002,6 Detrended Normal Q-Q Plot of VAR ,4 1,2 0 Expected Normal Dev from Normal 0,0 -,2 -, Observed Value Observed Value

103 2. Statistics > Distribution Fitting Statistica ( : p=n.s., not specified ). 18 Variable: NewVar, Distribution: Normal Kolmogorov-Smirnov d = 0,11617, p = n.s., Lilliefors p < 0,10 Chi-Square test = 10,42295, df = 4 (adjusted), p = 0, No. of observations Category (upper limits) (. 31), 2,., (. 32). 102

104 Variable: NewVar, Distribution: Normal Kolmogorov-Smirnov d = 0,11617, p = n.s., Lilliefors p < 0,10 Chi-Square test = 5,62148, df = 3, p = 0, No. of observations , , , , , , ,8333 Category (upper limits)

105 , Chi-Square Test Statistics > Nonparametric Statistics > Observed versus expected X2. ( ), (.. 33).. 33 (Summary) Observed vs. Expected Frequencies (Spreadsheet5r) Chi-Square = 51,37500 df = 5 p <, NOTE: Unequal sums of obs. & exp. frequencies observed expected O - E (O-E)**2 Case E T /E 104 C: 1 C: 2 C: 3 C: 4 C: 5 C: 6 Sum 3, , , , , , , , , , , , , , , , , , , , , , , , , , , , : : 1= ( ()*100+50;0); 2= ( ()*2+1;0); 3= ( ()+1;0).

106 ( , 2 1, 2, 3; 3 1, 2),,,. A2:C26, E2:G26. J1.,, K10:M13. K16:L18 : =$M10*K$13/$M$13 =$M10*L$13/$M$13 =$M11*K$13/$M$13 =$M11*L$13/$M$13 =$M12*K$13/$M$13 =$M12*L$13/$M$ L23 = 2 (K10:L12;K16:L18) p- 2, K23 = 2 (L23;2).,, 105

107 2 ( 3),., (0,14122), 15. SPSS,.. 35 Crosstabs. 25 (Expected) ,,. 106

108 A2 * A3 Crosstabulation 25 A2 Total 1,00 2,00 3,00 Count Expected Count Count Expected Count Count Expected Count Count Expected Count Chi-Square Tests A3 1,00 2,00 Total ,6 3,4 6, ,2 7,8 14, ,2 2,8 5, ,0 14,0 25,0 26 Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases Asymp. Sig. Value df (2-sided),997 a 2,607,999 2,607,069 1,793 a. 4 cells (66,7%) have expected count less than 5. The minimum expected count is 2, A3 Count 0 1,00 2,00 3,00 1,00 2,00 A2. 36 Statistica Statistics > Basic Statistics/Tables > Tables and banners. 107

109 Crosstabulation Specify tables (select variables) - ( 2 3),. Crosstabulation Tables Results Options,,, Pearson Chi-square Cramer's V. Advanced: Summary ( 27), Detailed two-way tables ( 28),. A Totals 2-Way Summary Table: Observed F Marked cells have counts > 10 A3 A3 Row 1 2 Totals Statistic Pearson Chi-square M-L Chi-square Phi Contingency coefficient Cramer's V 28 Statistics: A3(2) x A2(3) (Spreadsheet5r) Chi-square df p, df=2 p=,60738, df=2 p=,60671, , , :,, ,, 112.,? ( )? : 108

110 : =. 3 =D3-B3 4.,,, (,,, ) ( 124:1876)... : =$D3*B$5/$D$5 =$D3*C$5/$D$5 = (G3:H3) =$D4*B$5/$D$5 =$D4*C$5/$D$5 = (G4:H4) = (G3:G4) = (H3:H4) = (I3:I4) : , ( ), : B C D f e f t 0, 5 2. f e, f t f t 2, 0,5 (Yate), df = 1 [ ]. 2 =84,

111 V = 0,145., 2, 0. = 2 (B3:C4;G3:H4) 1,82165E-20., 2, 1, ( 0,05 0,01 ). ( 0 ) :.,,. MS Excel,,,, 0., SPSS Statistica 4,, (. 3). Statistics > Nonparametric Statistics > Observed versus expected X2 Statistica,,,

112 Statistica 2 2 ( ). Statistica.> Nonparametric Statistics > 2 x 2 Tables : 29 2 x 2 Table (Spreadsheet2) Column 1 Column 2 Row Totals Frequencies, row 1 Percent of total Frequencies, row 2 Percent of total Column totals Percent of total Chi-square (df=1) V-square (df=1) Yates corrected Chi-square Phi-square Fisher exact p, one-tailed two-tailed McNemar Chi-square (A/D) Chi-square (B/C) ,600% 44,400% 50,000% ,600% 49,400% 50,000% ,200% 93,800% 85,98 p=0, ,93 p=0, ,26 p=0,0000, ,02 p=0, ,69 p=0, ? ( )? 2.,? 3. ( / )? 4. -? 5.?,? 6.?? 7.???

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119 2.,, 1, (n 1 +n 2 ) ( ). 5. U : nx ( nx 1) U ( n1 n2 ) Tx, n 1 2 1, n 2 2,, n x. 6. U. U > U 0,05, 0. U,. ( ) H- - U- - :,...,.,. 2 -, 2 - df = m 1, m. 3 ( 2). : 0 :. 1 : ( ). 6: H

120 2.,, 1, (n 1 +n 2 + +n m ) ( ). 5. H : 2 12 T j H 3 ( N 1), N N( N 1) n j, n j j-, j j n j >5, H 2 - df=m 1 (m ),.,. S-., S-,,,. :,, 16. : 0 :. 16 MS Excel, SPSS (Transform > Compute) RND(UNIFORM(N)) Statistica (Function) Rnd(x) Uniform(x)

121 1 :. 7: S- 1., ( ). 4. ( ), (S i ). 5. S i : A= S i, m( m 1) 2 : B n, 2 m, n. 6. : S = 2 A B. 7..,. 120 [8, 19, 21]. ( ) (, ),.. xij M ( M j M ) Pi a ji eij. ( ), j, j-, -, a ji, ij, j- -.

122 : xij M Pj Pg Pi a jg a ji a gi a jgi eij. P j, P g a jg ; a ji, a gi, a jgi. 1),,, ; 2) F- (compound symmetry),, (, ).. -., -,,. F- ( ). (Mauchly)., -. (epsilon ajustment) F-., -, ( ). -, 121

123 . - (Box s M-test). 1: 1. (U- - ) (. 1 2,. 20) SPSS Statistica ( ) ( ) SPSS Statistica : 1. ( - ) 3 ( ) SPSS Statistica ( 2 r ) :. 1 2 (.. 22). MS Excel ( 2 - ), ,, U,. 122

124 SPSS Statistica (, ),. 123

125 SPSS IQ GROUP, Analyze > Nonparametric Tests > 2 Independent Samples,. 39. : Ranks, Test Statistics. Ranks GROUP 1,00 2,00 Total N Mean Rank Sum of Ranks N Mean Rank Sum of Ranks N IQ 14 11,79 165, ,50 186,00 26 Test Statistics b Mann-Whitney U Wilcoxon W Z Asymp. Sig. (2-tailed) Exact Sig. [2*(1-tailed Sig.)] a. Not corrected for ties. b. Grouping Variable: GROUP IQ 60, ,000-1,237,216,231 a, U. - (Asymp. Sig) ( ). Statistica Statistics > Nonparametric Statistics > Comparing two independent samples. Variables (IQ) (group)., SPSS: 124 Mann-Whitney U Test (Spreadsheet1) By variable group Marked tests are significant at p <,05000 Rank Sum Group1 165,0000 Rank Sum Group2 186,0000 U 60,00000 Z -1,23443 p-level 0, Z adjusted -1,23739 p-level 0, Valid N Group1 14 Valid N Group2 12 2*1sided exact p 0,231155

126 20 U, z- -. ( 20) (2*1 sided exact p). 1 U-.,.,. Statistica., :, ( ). 2: ( ). 2 2 (.. 22)

127 G- W- MS Excel.. 40 (X) (Y), D. D19 ( = (D8:D17;"<>0")). D18 G-,,, = (D8:D17;"<0"). E,, ( D). 20 W-,,,,. = (D8:D17;"<0";E8:E17).,.. 41 SPSS Analyze > Nonparametric Tests > 2 Related Samples. Test Pair(s) List; (. 41). G- (Sign Test) ( 31), -, 126

128 (, 0,05),. 31 Y - X Frequencies Negative Differences a Positive Differences b Ties c Total N Test Statistics b Exact Sig. (2-tailed) Y - X,180 a a. Binomial distribution used. b. Sign Test a. Y < X b. Y > X c. X = Y W- (Wilcoxon Signed Ranks Test),.,. z- - 0,028, = 0, Negative Ranks Positive Ranks Ties Total a. Y < X b. Y > X c. X = Y Ranks Y - X Sum Mean of N Rank Ranks 2 a 2,00 4,00 7 b 5,86 41,00 1 c 10 Test Statistics b Z Asymp. Sig. (2-tailed) Y - X -2,203 a,028 a. Based on negative ranks. b. Wilcoxon Signed Ranks Test G-, W- t-,,, P w > P t (0,028 > 0,022),,., 127

129 ,. Statistica Statistics > Nonparametric Statistics > Comparing two dependent samples. (. 42) (Sign test 33), (Wilcoxon matched pairs test 34).,, SPSS Sign Test (Spreadsheet1) Marked tests are significant at p <,05000 No. of Percent Z p-level Pair of Variables Non-ties v < V X & Y 9 77, , ,

130 34 Wilcoxon Matched Pairs Test (Spreadsheet1) Marked tests are significant at p <,05000 Valid T Z p-level Pair of Variables N X & Y 10 4, , , : 1 3 (. 36).,., 1, 2, 3.. SPSS Analyze > Nonparametric Tests > K Independent Samples , (9,809) (0,007),,. 129

131 Ranks Test Statistics a,b 1,00 2,00 3,00 Mean N Rank 10 9, , ,40 Chi-Square df Asymp. Sig. 9,809 2,007 a. Total Kruskal Wallis Test 30 b. Grouping Variable:.,. 35.,, -,,,., ( j <P H ),,. Jonckheere-Terpstra Test a 35 Number of Levels in N Observed J-T Statistic Mean J-T Statistic Std. Deviation of J-T Statistic Std. J-T Statistic Asymp. Sig. (2-tailed) , ,000 26,300 3,384,001 a. Grouping Variable: Statistica Statistics > Nonparametric Statistics > 130

132 Comparing multiple indep. samples (groups). (Summary: Kruskal-Wallis ANOVA & Median Test) ( 36). SPSS. 36 Kruskal-Wallis ANOVA by Ranks; (Spreadsheet1) Independent (grouping) variable: Kruskal-Wallis test: H ( 2, N= 30) =9, p =,0074 Depend.: Code Valid N Sum of Ranks Grp ,0000 Grp ,0000 Grp ,0000 (Box & whisker). 45. SPSS,. -. Statistica. 131

133 Boxplot by Group 7,0 Variable: 6,5 6,0 5,5 5,0 4,5 4,0 3,5 3,0 2,5 2, Mean ±SE ±SD : ( ). 9,,. 5 : 2 3.,???

134 : 0 :,,. 1:,, r MS Excel. H14, ( 3), H15 -, = 2 (H14;4).,.. 46 Analyze > Nonparametric Tests > K Related Samples SPSS Statistics > Nonparametrics > Comparing multiple dep. samples (variables). W ( ), 0 1. W 1 ( W = 0,876). 38, SPSS. 133

135 Friedman Test Kendall's W Test 38 Test Statistics a N 9 Chi-Square 31,545 df 4 Asymp. Sig.,000 a. Friedman Test Test Statistics N Kendall's W a Chi-Square df Asymp. Sig. 9,876 31,545 4,000 a. Kendall's Coefficient of Concordance 39, Statistica, Friedman ANOVA and Kendall Coeff. of Concordance (Spreadsheet1) ANOVA Chi Sqr. (N = 9, df = 4) = 31,54545 p <,00000 Coeff. of Concordance =,87626 Aver. rank r =,86080 Average Sum of Mean Std.Dev. Variable Rank Ranks week1 4, , , , week2 4, , , , week3 2, , , , week4 1, , , , week5 1, , , ,116363

136 4 : 4. : 0( ) : ( ). 1( ) :. 0( ) : ( ) (, ). 1( ) :. MS Excel,, (. 120)., , MS Excel, 135

137 ( B2:F11, ),,.,, ( 40).,,. 48, , , , , , , , ,94444 SS df MS F P- F 2449, ,3 34,1537 2,08E-12 2, , , , ( ), ( 3:F11, ). 41,

138 . 49,., 40 41, ,6 66, ,4 60, ,2 39, ,4 61, ,8 121, , ,8 100, ,8 55, ,2 70,2 SS df MS F P- F 486, , , , , , , , (. 120). Q total = 3166,31, Q A = 2449,2, Q I = 486,71., : Q Z =Q total Q A Q I. : F ( ) Q m 1 Q n 1 Q z (m-1)(n-1) Q total mn 1 S S S 2 A 2 I 2 z QA m 1 QI n 1 ( m Q z 1)( n 1) S FA S S FI S 2 A 2 z 2 I 2 z 137

139 : Q df S 2 F P F 0, , ,30 85,042 1,39E-16 2, , ,84 8,450 7,13E-07 2, , , , ,96 ( ),.. SPSS Analyze > General Linear Model > Repeated Measures., (. 50), (Within-Subject Factor Name) (, week). Add.. 50 (Repeated Measures), Define,. 1 week1 (. 51). (Model). Full Factorial. (Plots) 138

140 (Options),, (Estimates of effect size).. 51 Tests of Within Subjects Effects ) 42). Q A Q z ( Sum of Squares), F A. 42 Tests of Within-Subjects Effects Source WEEK Error (WEEK) Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Type III Sum of Measure MEASURE_1 Mean Parti al Eta Squ Squares df Square F Sig. ared 2449, ,300 85,0,000, ,200 2, ,577 85,0,000, ,200 4, ,300 85,0,000, ,200 1, ,200 85,0,000, , , ,400 21,903 10, ,400 32,000 7, ,400 8,000 28, Measure: MEASURE_1 Transformed Variable: Average Source Intercept Error Tests of Between-Subjects Effects Partial Type III Sum Eta of Squares df Mean Square F Sig. Squared 7893, , ,7,000, , ,

141 Tests of Between-Subjects Effects ( 43), (Q I S 2 I). (Univariate approach) -,. (Mauchly s Test of Sphericity).,, (Epsilon Corrected). (Sig. = 0,537), ( 44). 44 Measure: MEASURE_1 Mauchly's Test of Sphericity b Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig. Greenhous e-geisser Epsilon a Huynh- Feldt Lowerbound WEEK,282 8,114 9,537,684 1,000,250 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table. b. Design: Intercept Within Subjects Design: WEEK ( ). (Linear), ( 2 =0,96). 140

142 45 Measure: MEASURE_1 Source WEEK Error (WEEK) WEEK Linear Quadratic Cubic Order 4 Linear Quadratic Cubic Order 4 Tests of Within-Subjects Contrasts Type III Sum of Mean Partial Eta Squares df Square F Sig. Squared 2016, ,4 190,2,000,960 89, ,175 12,011,008, , ,711 53,918,000,871 86, ,914 14,451,005,644 84, ,600 59, ,425 38, ,761 48, ,014, Graph > Line, Multiple Values of Individual Cases.,. 52,, ,. 48, Data > Transpose. Statistica ( ) Statistics > ANOVA > Repeated measures ANOVA. 141

143 Statistics > General Linear/ Nonlinear Models > General Linear Models > Repeated measures ANOVA WEEK1 WEEK2 10 WEEK3 Value WEEK4 WEEK5 PATIENT. 53 ( week1-week5 ) (, SPSS, ). WEEK (Within effects) (. 54).. 54 Summary GLM results (. 55) : 142

144 1. All effects/ Graphs, : 30 WEEK; LS Means Current effect: F(4, 32)=85,042, p=,00000 Effective hypothesis decomposition Vertical bars denote 0,95 confidence intervals DV_ week1 week2 week3 week4 week5 WEEK 2. Sphericity : Mauchley Sphericity Test (Spreadsheet1) Sigma-restricted parameterization Effective hypothesis decomposition W Chi-Sqr. df p Effect WEEK 0, , , All effects : Repeated Measures Analysis of Variance (Spreadsheet1) Sigma-restricted parameterization Effect Intercept Error WEEK Error Effective hypothesis decomposition SS Degr. of MS F p Freedom 7893, , ,7474 0, , , , ,300 85,0417 0, , ,200 1.?? ?

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152 F- ( ).. F-. F- F-,. [24, 9, 10, 12]. 1: SPSS 1. SPSS, (, cars.sav, world95.sav). 2. SPSS Analyse >Classify >Discriminant. 3., (Grouping Variable).. 4.,, (Independent Variables). 5. (Use stepwise method). 6., Method, Wilk s lambda, F- (Entry) F- (Removal). 7., Statistics,, (Means) (Univariate ANOVAs), Unstandardized Function Coefficients ( ). 8., Classify,, 151

153 (Prior probabilities: Compute of group size); (Display: Casewise results) (Display: Summary table); (Plots: Combined groups)., Territorial map :????. 2: Statistica 1. Statistica : Statistics > Multivariate Exploratory Techniques > Discriminant Function Analysis. (Grouping) (Independent). (Advanced options (stepwise analysis)). 2. (Model Definition) Advanced (.. 60): ) Forward stepwise F- (, F- ). Standart. Backward stepwise F-. 152

154 ),. ) F- F- ( F to enter > F to remove ). ) (,, F / ). ) (At each step) (Summary only). 3. (Discriminant Function Analysis Results)., SPSS.. ( 46)

155 (, )., 14,,,,,,., ( ),,,. 1. SPSS,, ( v1, v2, v3, v4, v5, v6, v7 v8). Discriminant Analysis Classification Statistics Method. 56,. 57,

156

157 : 1. (Tests of Equality of Group Means). 2. (Pooled Within-Groups Matrices). 3. /,. - ( 47). 16. (, F- / ).. 47 Variables Entered/Removed a,b,c,d Step 1 2 Entered Statistic df1 df2 df3 Wilks' Lambda, ,000 17, ,000,001, ,000 10, ,000,000 Statistic df1 Exact F At each step, the variable that minimizes the overall Wilks' Lambda is entered. a. Maximum number of steps is 16. b. Minimum partial F to enter is c. Maximum partial F to remove is d. F level, tolerance, or VIN insufficient for further computation. df2 Sig. 4. Variables in the Analysis ( ), F

158 Step 1 2 Variables in the Analysis Wilks' Tolerance F to Remove Lambda 1,000 17,917,595 29,413,641,595 6,457, Variables Not in the Analysis,. F- :,,., 0,1 F- (2,71). F-. 6. Wilks' Lambda Variables Entered/Removed (. 47),. 7. Eigenvalues ( ), 20 (95,5% 4,5%). Eigenvalues Function 1 2 Canonical Eigenvalue % of Variance Cumulative % Correlation 8,327 a 95,5 95,5,945,396 a 4,5 100,0,533 First 2 canonical discriminant functions were used in the analysis. a. 8. Wilks' Lambda =0,077 (Sig 0) =0,716 (Sig = 0,092).,., 157

159 .,. (Sig < 0,05). Test of Function(s) 1 through 2 2 Wilks' Lambda Wilks' Lambda Chi-square df Sig.,077 21,817 4,000,716 2,837 1, (Standardized Canonical Discriminant Function Coefficients).,. Standardized Canonical Discriminant Function Coefficients Function 1 2 -,959,872 1,283, : Canonical Discriminant Function Coefficients (Constant) Function 1 2 -,393,357,809,117-4,328-3,454 Unstandardized coefficients 11. (Structure Matrix),.,,.,,. 158

160 Structure Matrix a a a a a a Function 1 2,521*,177,506*,175 -,14,990*,672,740* -,10,671* -,26,559*,274,519*,185,291* *. Largest absolute correlation between each variable and any discriminant function a. This variable not used in the analysis. 12. (Functions at Group Centroids),. 1, 2 1, 3. Functions at Group Centroids Function 1 2-3,420,195 2,308,403,713 -,931 Unstandardized canonical discriminant functions evaluated at group means

161 Prior Probabilities for Groups Total Cases Used in Analysis Prior Unweighted Weighted, ,000, ,000, ,000 1, , Territorial Map. *. Territorial Map Canonical Discriminant Function 2-6,0-4,0-2,0,0 2,0 4,0 6, , * *, * , ,0-4,0-2,0,0 2,0 4,0 6,0 Canonical Discriminant Function 1 _Symbols used in territorial map Symbol Group Label * Indicates a group centroid 15. (Casewise Statistics) : (Actual) (Predicted).,,. 160

162 14, Casewise Statistics Original Highest Group Second Highest Group Discriminant Scores Case Number Actual Group Predicted Group P(D>d G=g) P(G=g D=d) p df Squared Mahalanobis Distance to Centroid Group P(G=g D=d) Squared Mahalanobis Distance to Centroid Function 1 Function ,702 2,967,708 2,033 8,493,157-1, ,653 2,840,854 3,160 3,142 1,430, , ,000 1,460 3,000 29,860-4,628,227 ungrouped 1, ,000 1,460 3,000 29,860-4,628, ,540 2,999 1,232 3,001 14,410-2,593, ,260 2,583 2,690 2,417 4,384 2,169-1, ,433 2,972 1,676 3,028 7,764 3,418 -, ,300 2,997 2,410 3,003 12,782 3,072 1, , ,000,239 3,000 15,791-3,009,461 ungrouped 2,100 2,512 4,606 3,484 3,698,228, ,920 2,957,168 3,043 5,352 2,239, ,255 2,760 2,735 2,220 6,238 -,189, , ,000 1,080 3,000 17,327-3,449 -, **,798 2,654,451 2,346 2,748 1,383 -,972 **. Misclassified case 16. Classification Results, 11/12=91,7%. -. (..13) pini = (0,333*4)+(0,417*5)+(0,250*3) = 4, ,17 = 6,833, 12 4,17=7, ,872, 87,2% ( 1 8). 161

163 Original Count % Classification Results a Ungrouped cases Ungrouped cases Predicted Group Membership Total ,0,0,0 100,0,0 80,0 20,0 100,0,0,0 100,0 100,0 50,0 50,0,0 100,0 a. 91,7% of original grouped cases correctly classified. 17. (Canonical Discriminant Functions).. 2,0 Canonical Discriminant Function 1,5 1,0,5 0,0 1 2 Function 2 -,5-1,0-1,5-2, Group Centroid Ungrouped Case Function 1 162

164 1 (Statistica). Statistica (Statistics > Multivariate Exploratory Techniques > Discriminant Function Analysis) Model Definition Descriptives ( Within) (Pooled within-groups covariance & correlation), (Means & number of cases), (Within groups standart deviations) ( ). (Categorized histogram, Box plot of means, Categorized scatterplot, Categorized normal probability plot), All Cases (Total correlation...), (Plot of total correlations) (Box plot of means).. 60 Model Definition,. 60 ( ). (0,01),,. 163

165 Quick Discriminant Function Analysis Results, ( 49 50): 49 Discriminant Function Analysis Summary (liri) Step 2, N of vars in model: 2; Grouping: group (3 grps) Wilks' Lambda:,07679 approx. F (4,16)=10,435 p<,0002 Wilks' Partial F-remove p-level Toler. 1-Toler. N=12 Lambda Lambda (2,8) (R-Sqr.) v8 v3 0, , , , , , , , , , , , N=12 v1 v2 v4 v5 v6 v7 50 Variables currently not in the model (liri) Df for all F-tests: 2,7 Wilks' Partial F to p-level Toler. 1-Toler. Lambda Lambda enter (R-Sqr.) 0, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , SPSS ( ). Advanced (Stepwize Analysis Summary).3 1 (Perform canonical analysis). Advanced Canonical Analysis : 1) (Chi square tests of successive roots) ; 2).9 1 ; 3) (Factor structure Matrix), (.11 1 ); 164

166 4) (Means of canonical variables). Canonical scores Canonical Analysis : 1) (Scatterplot of canonical scores); 3,0 2,5 2,0 1,5 1,0 Root 1 vs. Root 2 Root 2 0,5 0,0-0,5-1,0-1,5-2,0-2, Root 1 G_1:1 G_2:2 G_3: ) (Canonical scores for each case) ( SPSS 48); 3) SPSS, (Save canonical score). Classification Discriminant Function Analysis Results. 62: 1) (Classification functions) ( ); 2) (Classification matrix)., SPSS (.16 1 ), 91,7%. 165

167 3) (Classification of cases). SPSS 48. 4) (Squared Mahalanobis distances) SPSS 48;. 62 Classification Matrix (liri) Rows: Observed classifications Columns: Predicted classifications Group Percent Correct G_1:1 p=,33333 G_2:2 p=,41667 G_3:3 p=,25000 G_1:1 100, G_2:2 80, G_3:3 100, Total 91, ) ( 51) (Posterior probabilities) ( 48 1 ) ( )., 166

168 , Classification Proportional to group sizes (. 62). 51 Posterior Probabilities (liri in Workbook4) Incorrect classifications are marked with * Observed G_1:1 G_2:2 G_3:3 Case Classif. p=,33333 p=,41667 p=, G_3:3 0, , , G_2:2 0, , , G_1:1 0, , , , , , G_1:1 0, , , G_3:3 0, , , G_2:2 0, , , G_2:2 0, , , G_1:1 0, , , , , , G_2:2 0, , , G_3:3 0, , , G 1:1 0, , ,000222,.,,,,., 4 1, 10 2, 14 3, /. 1..? 2.?? 3.?? 4., - 2?? 167

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173 3) : d i j max xit x jt, 1 t m, ; 4) : d M (x i, x j ) = (x i x j ) S -1 (x i x j ) t, ; m 1 xit x jt 5) : d Li j, m t 1 xit x jt,.. [24]. a, b, c, d 2 2-, a d S, 1, a b c d a J a b c. 1 a b 0 c d ( ) : 172 s ij p k 1 S ijk / p k 1 W ijk, W ijk, 1, k, 0 ; S ijk i j k.,,. (, ).,, 1) ( ) ;

174 2) ( ) ; 3) ; 4) ( ); 5) ; 6) :,. SPSS Statistica Cluster Method Amalgamation (linkage) rule Between-group linkage Weighted pair-group average Within-group Unweighted pairgroup linkage average Nearest neightbor Single linkage Furthest neighbor Complete linkage Centroid clustering Unweighted pairgroup centroid Median clustering Weighted pair-group centroid (median) Ward s method Ward s method Measure Distance measure Interval Squared Euclidian Squared Euclidian distance distance Euclidian distance Euclidian distance Block City-block (Manhattan) distances 173

175 Chebyshev Chebyshev distance metric Minkowski Power: SUM(ABS(xy)**p)**1/r Percent disagreement Pearson correlation 1-Pearson r 1 Cosine (1 ) Count Chi-square measure - Phi- square measure Binary 17 Jaccard - ( ) :. k-. k ( ). k..,.,, 17, SPSS. 174

176 ,,.,. k-,,, ( ).,,. Fuzzy C-Means - [7]. [6]. - [24]. 1: SPSS: Analyze > Classify > Hierarchical Cluster... (Variable(s)),. 3. : Plots... Dendrogram; Method (Cluster Method) Betweengroup linkage, (Measure) Squared Euclidian distance. 18 (. 3,. 184).,, SPSS,,. 175

177 , Save (Single solution). 4. : (..173). 5.,, ( ). 6. Statistica: Statistics > Multivariate Exploratory Technics > Cluster Analysis > Joining (Tree Clustering). : (Variables), (Amalgamation rule), (Distance measure), 19 (Input file) : (Cases (rows)) 20 (Variables (columns)). 7. Advanced. 7.,. 2: 1. (, 2-4). 2. k- SPSS: Analyze > Classify > K-Means Cluster Analysis. : (Variables) (Number of clusters. Iterate (Maximum Iterations) Use running means. Save Options. 3. Final Cluster Centers. 4. k- Statistica (Kmeans clustering), 19 (Raw data) (Distance Matrix). 20, (Raw data). 176

178 : (Variables), 21 (Cluster), (Number of clusters), (Number of iterations) 22 (Initial cluster centers). 5.,.. 1: ( ). SPSS, 46 (.153).,,. Cluster Variables (. 63) Sort distances and take observations at constant intervals. 177

179 . 64 Statistica,, Plots Dendrogram. Method (. 64). (. 65),,.. 65 Agglomaration Schedule Vertical Icicle. 178