$ι ιι η ι ι!η ηι ι ANOVA. To ANOVA ι ι ι η η η ιη (Analysis of Variance). * ι! ι ι ι ι ι η ιη. ;, ι ι ι! η ιι ηιη ι ι!η ι η η ιη ι ι η ι η.

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Download "$ι ιι η ι ι!η ηι ι ANOVA. To ANOVA ι ι ι η η η ιη (Analysis of Variance). * ι! ι ι ι ι ι η ιη. ;, ι ι ι! η ιι ηιη ι ι!η ι η η ιη ι ι η ι η."

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1 η &, 7!# v # $ι ιι η ι ι!η ηι ι ANOVA. To ANOVA ι ι ι η η η ιη (Analysis of Variance). * ι! ι ι ι ι ι η ιη. ;, ι ι ι! η ιι ηιη ι ι!η ι η η ιη ι ι η ι η. - ι% ιι* ι' F ι ι ι% MS F MS between within MS MS SSbetween ni ( X i X ) between ι df between k 1 within SS df within ( X 1i X 1) ( X i X )... ( X vi X v ) n k within ( k ι ι - ι ηι η ηι η ι n ι ) $ι ηι ι ANOVA ι ι ι % ι, ι ι t-test. 5% 1: 3 ι ι!η, η, ηι ι ι ι ι. 5% : ηη η!ηη η ι ι. 5% 3: ι η!ηη ι η η!ηη (η. ι ) ι ι ι. #! ι. 6 ι ι ι 15 ι ηι ιη ι ι (* ι, η, ι), η ι ι ι ι ι ι, ι ι ι η «ιι». ι ι 1 5, 1 ι ιι. 5! η ηι η ι η ι ι ι ι ιι ι η ι ι (: ι = η= ι ). $ι ιι η η ηι ι ιι ιι F. /η ιι X1 i X 1 X i ) ( 1 X1 ) -,,4 3,8,64 1-1, 1,44 3,8,64 -,,4 X 1=, /η ιι X i X ( X 1 X i 1) =,8 X i ) ( X 3 -,,4 $ι ι ιη F, SSwithin MS within df within ( X1i X1) ( X i X )... ( X vi X v ) n k ( k ι ι - ι ηι η ηι η ι n ι ) ι " (. ι ι): ) ι η ιι ι. 6ι, ι =,, 15

2 η 9 ι -,,4 3,8,64 3,8,64 1-1, 1,44 X =, /η ιι X 3 i X 3 ( X X i ) =,8 X i ) ( 3 X 3 4 1, 1,44 3,,4 3,,4 -,8,64 -,8,64 X 3 =,8 ( X 3 X i 3 ) =,8 $ι ι ιη ι (. ): η &, 7 MS between η=, ι ι =,8. 3η ι ι ι ι ι ι"ι ι η ιι ιι ι η ι η ι. ) $ι ι η ι η η ι η ( X ki X k ). ) η η η ' η ι η η ι ( X ki X k ) ) $ι " ι η η ι ( ( X ki X k ) ).,8,8,8 8,4, MS within, SS df between between n ( X i i k 1 X ) ) #ι ι ( X i X ). ) (' η η η ι (( X i X ) ) ) η η ι" η η η ι ι ι η. ) ( " ι η η, ni ( X i X ) =1,. X i X i X ( X i X ) n ( X X ) i i X 1=, -,,4, X =, -,,4, X 3 =,8,4,16,8 X =,4 ni ( X i X ) =1,, MS between SS df between between n ( X i i k 1 X ) 1,,6 31 MSbetween,6 η ιη: F, 85, ι F (,1), 85 MS,7 within $ι η ηη η ιι ηιη η F ι ι ιη df = ι df =1 ι ι F: ι F ι!ι η ι η ι F, 85 (,1) ι ι ιη ( ι) η ιη F ι ι ιι ηιη 95% (p=3,89) ι ' η ηι η ι η ι 3 ι ι ι ιι ι η ι ι. )ι F ι ( ιι ηιη 1% ι 5%) df ιη df

3 η &, /+N+ο/,ο(,),ANOAA),ο$P$$ η ι! η ηι η ι ι ι ι ι ι ι η ι ι " ιιι ι!. ιι ι! ι ι ιι ηι 'η ι ι ι. # ι ι!η ι ι ιι η ιη ιι ι ι η ι " ιιι ι ι. * ι"ι ι! η " ι ι ηι "ι ' ι ι ι "; η ι, η η ι, ",!ι ι ι ι ιι. ι ι ιι ηι ι 4 η η η educat!: 1= 7ι η, = -ι, 3= 3 ιι ι 4= * ι. ι, 4 (η ι "ι ι «7ι η» ι «* ι») ι!η! ι η ηη η!ηη η ι ι ι ι ι (ι). & ι ιι ι % ι. $ι η % η 3, ι ι η ιι η ι η «Explore», ι t-test. PQA8?GS9:T:9E;BF<BM:$<?<B9<BE9EcFGD;:Zι$*%>>> Q)7%*,%*+,%*8+*$*)$ιC?E<D;IB9<#4ι*ι%=/*+*%,%*8+*.(ι*+,%*8+*$*)$ιT:F:8>:8<IB9<#%=*+,.%,%*8+*.(> VQ *+%)ι4pgd<9ze%)ι.4υ,%*)/*ωa 17

4 η &, 7 XQ9KD8<B8H:: [Q *+%)ι4$<?<b9<be9#8>)/7υezwk@hn(e%)ι.4υ,%t:9e;bf<bm:9> `Q9KD8<B8H:: Q9:#$*)/7υ9EcFGD;::(> ANOVA ι ι ι ι ι ι (η ι ι ). To ANOVA ι ι ι η ι η ι ι ηι!. & ηι ι ι η η,, η, ι ι ι, ι ι η η... # «Explore» ι ι Tests of Normality, ι η ι, ι : υ υη!υ" a. Lilliefors Significance Correction Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig.,167 53,1,96 53,1,11 19,,85 19,,186 1,,886 1,,118 19,1,88 19, η η ι, Kolmogorov-Smirnov ()S) ι ιι ηι ( η Sig.), η ι ι,5, ηι ι η! ι ι. η ιη η, Kolmogorov-Smirnov ()S) ι ι ι ι!η ι ι. ;,! ι ι!η η ι η ι ι ηι!. $ι «Descriptives» ( ι"ι ι!ι η ι «Descriptives» «Statistics» «Explore»). 18

5 η &, 7 Descriptives. Statistic Std. Error Mean 55,66 13,31 /η 95% Confidence Lower Bound 496,15 Interval for Mean Upper Bound 5491,17 5% Trimmed Mean 56,54 Median 5, Variance 97867,34 Std. Deviation 963,59 Minimum 39 Maximum 75 Range 36 Interquartile Range 195 Skewness,148,37 Kurtosis -1,19,644 Mean 596,75 77,14 95% Confidence Interval for Mean Lower Bound 5144,83 Upper Bound 5448,66 5% Trimmed Mean 57,31 Median 5, Variance 11696,6 3 Std. Deviation 161,559 Minimum 36 Maximum 135 Range 99 Interquartile Range 15 Skewness,655,176 Kurtosis 17,714,351 / Statistic Std. Error / Mean 644,5 1,74 95% Confidence Lower Bound 645,9 Interval for Mean Upper Bound 6443,96 5% Trimmed Mean 6177,98 Median 63, Variance 13841,3 7 Std. Deviation 111,673 Minimum 36 Maximum 18 Range 7 Interquartile Range 9 Skewness 1,318,19 Kurtosis 4,39,435!. Mean 1835,56 4,13 95% Confidence Lower Bound 138,47 Interval for Mean Upper Bound 1163,65 5% Trimmed Mean 1494,7 Median 15, Variance , 6 Std. Deviation 4198,345 Minimum 48 Maximum 3199 Range 719 Interquartile Range 5196 Skewness 1,696,31 Kurtosis 5,456,459 ι"ι ιι ιι ι!η ( ιη η η) ι ι. 3η ι ι ι ι /α+ α! η (skewness) ι,148, η "ι, ηι ι ι ι. # η "ι η ι. $ι η ι ηι ι ι (Skewness=,655), η ι ι ι!ι (η ι η ι). $ι α + η ι ι ι (Skewness=1,318), η ι ι!ι (η ι η ι). $ι *α α η ι ι ι (Skewness=1,696), η ι ι!ι (η ι η ι). # η ι η, - ι"ι η η. ι!η ιι ι ι ι ( ι!ι η ι «Histograms» «Options» «Explore»): 19

6 η &, 7 Histogram For EDUCAT= υη Histogram For EDUCAT= Frequency Std. Dev = 963,6 Mean = 56 N = 53, Frequency Std. Dev = 161,56 Mean = 597 N = 19, Histogram Histogram For EDUCAT= For EDUCAT=!υ" Frequency Std. Dev = 111,67 Mean = 645 N = 1, Frequency Std. Dev = 4198,34 Mean = 1836 N = 19, & ι η ι ι ι ι ι ι η ι η "ι η ι, ι ι η ιη η, ι ι ιι η % η ι η ιη η. 6 ι ι η ιη ι ι Q-Q plots: 3 Normal Q-Q Plot of For EDUCAT= υη 3 Normal Q-Q Plot of For EDUCAT= 1 1 Expected Normal -1 - Expected Normal Observed Value Observed Value 13

7 η &, 7 3 Normal Q-Q Plot of For EDUCAT= 3 Normal Q-Q Plot of For EDUCAT=!υ" 1 1 Expected Normal Expected Normal Observed Value Observed Value Q-Q (Quantile-Quantile plots) ηι ιι ι ιη ι () ι η ι ι. η 45 "ι ι ι ι (ι ι ι ) η ι ι. ;, ι η ι ι ι η. 6ι ι ι ι ι ι ιη η ι ι. ιη η ιη ι Levene : Test of Homogeneity of Variance Based on Mean Based on Median Based on Median and with adjusted df Based on trimmed mean Levene Statistic df1 df Sig. 74, , 7, , 7, ,543, 7, , Levene ι ιι ηι ( η Sig.), η ι ι,5, ηι ι ι ιη η ιη. ι Levene ι η ιη η ιη ι, ι η, ι η ιι ηιη ι ιη,5. 131

8 η &, 7 6 η ι"ι ι η η ιι ι ι ι ιι ι boxplot ( ι"ι ι!ι η ι «Factor Levels Together» «Dependents Together» «Plots» «Explore») (.!ι). S@ZWK@BC$υ%)ι*.)υ$υ4%ι/7%%4,,%8/$+).*%$*ι&% ( * % /,%$ $* [q ι q *%**+,'ι> υ*' *ι$*ι&%$*qey*ω,%$ω*ι,-*+,/*ι,-#%3 *%**+,ι'%(#)%ιd%*ι,%*'ι74-ι )+'4,,$*S@ZWK@B(E 8(*+ι/,%$#MNhIJA(*$+,%)υ&ωD%ι*+,/*ι,- $% $,.+ #+ ιd'*ι 4,, $* 74-ι υη )+'4,,*υS@ZWK@B(E 4(*ι%/&ι$*%ιυ\+'*%%)*+,%%*ι,.ι)% %%ι),υ$,.%#@vbkinhc(%#nzbhnmnc(#ι ιd'*ι% 4,,. )/ω ι /*ω )' * 74-ι )+'4,,*υ S@ZWK@B(> ),υ$,.%,/d*ι 75 ι *ι,. )υ ).&υ )' * %44*% *%**+,'ι η )%ι$$'*%)'!eq5.*υ%*%**+,ι%υe (*ι),υ$,.%ι%*ι,.> *)/%ι4,/,e 5 η #( )ι$*/ )%ι)*-$%ι #ljcnc( *ι,- )υ %ι ),υ$,.% ι $*%$#( )ι$*/*ι,.)υ %ι%>ι7,')υ$+,%ι-%*ι))'/7% $*%$ +-%ι *+ $%ι/ $*+ ) 8$%*ι * υ)%,% +)*+$+ υ* $* &% %,.ω*υ ;<;;#%$*)/%ι4,/,)ι)/ω(> η boxplot, η ιη ι ι ι ι ι ιι ηι (ιι ηι ' «ι»). & η ι ι ι, ιι ι ι ιη ι ι ι. $ι ι, η η ι ι ι ( 'η) ιι ι ι ι ( η ι 39 «Data View»), ι ι ι ( η ι 367 ι 415). η η ι ιηι ι ( ι boxplot "ι output- ι ι ι ι ι, ι ι ι ι ι ι ι ι ι). ι -ι ι ι ( η ι 5). # ι ι ηι ι % ι ι η ιη η ι ι!η, ι ι η ιη η ιη ηι ι 13

9 η &, 7 ANOVA. η η, ) ιι η η ιι ι ιη η η ι ) ηι ι η ι ι ι % ι. η ι! η ιι ι. ι" η η η ι, Kruskal-Wallis H ηι ιι η η ηι ιι ιη. +%ι,ι*!! SPSS ), ι ι η ι" ι ι 'η η ( ι) η ( ιι ), ι ι η ιι η ιη ι ι ι ιη. ι ι ιη Pearson r ι ηι ι η. η ιη η!", ι η η!!ηη η. η ι, ι 'η η ι ι ι ι η η ιι ι " η ι ι ιι ι!" ι ι!ι. & η ι ι ι Kolmogorov- Smirnov ι Levene! ι ιη η η ι ι η ιι η η ANOVA. η η ιι η ι ι η ι η. ) η η «Explore» η ι «Plots» ι! η ι «Power estimation»: * η ι (. Output) "ι ι η: 133

10 η &, 7 To Spread vs Level Plot ι"ι ι, ι ιι ι η ηη η ιη η ιη ι! ι. & ι ι ι ι (ι ι η ) ι η ι Slope (η) ι η ι ιι ι ι ιη η ιη. η η ( ιιι ι ), Spread vs Level Plot ι ι η ι η η ιι. η ι ι η ηι $ι ι ι η ι ι! ι ι ι ηι ι ηι ι SPSS: +4υ,%)/ι$*+%* EcFGD;:ƒι%)ι.4υ,%)/ι9PGD<9Z: )ι.4υ,%υ**+5/*4ι9<@pnhncbimjbi@a:e*+%)ι49t;?89wd;_:>:> *+$*%=ι/, %*ι+υ*'*+*,%*$&+,*$υ,%*%,.,,%8/$+υ/,%ι)υ)%ι4/5*ι)/*ω Power Transformations 3 Cube () Square () 1 No Change ( ηι) 1/ Square Root (ι ") Logarithm (ι) -1/ Reciprocal of the square root (ι η ι ") -1 Reciprocal (ι) * ) ) )*+,% '*ι +,+,%*$&+,*ι$,3>r} )υ,)*/7+%)'*+ /υ$+%ι)ι */ $*+,+ QNlIWH@lJK@? BpN C VJHN H@@B#%)ι4 $:; "" $*+ $*(> )'*% %)ι.4υ,% υ*,+ ι )&ω/,% )*-*9KD8<B8H::> Levene ι ι ι ι ιι η ιη, ι η ιη η. $ι ηι ι η ι ι ιι ιι η ι ι ι ι ι" ηι ι η ιη. η ηι ι ι ι ηι ι η ι. η ιι η 134

11 η &, 7 ι ι... ο,),o8:p?sanoaa, ι ιι ι % ι η ιι η ιη ι ιι η ιη η ι η!ηη ι η!ηη, ι ιι ηι ι ANOVA ι! η ηι η ι ι ι ι ι η. PQA8?GSl:KD_F?;:M:?89O8:p?SA8DM?QX%,5ι$*%+'υ7+/* Q )ι.4υ,% *+,%*8+* #%=*+,.+,%*8+*(ι,%*8%/ι *+*)7%*,% $*)% 9T:F:8>:8< IB9<:> $*%E%)ι.4υ,%*+,%*8+* ι *+ *)7%*,% $* )% 9C?E<D;:> VQ *+%)ι49pd9<hdez:,),% %)ι.=υ,%. *%$* )υ 7, %)ι*.\%ι ι)ι$*-$υ,% *υ&' $**ι$*ι/ $+,*ι. ι5. $*υ,.$υ 'υ *ω &ι-,ι$7- /,%$$*D%4+*ω%ι4,/*ω>,5D%*ι+'υ7+/* -υ)/&υ,ι$%ι/)'w@cbp@l BNCBC> )/ω,/ )' *%$* %ι */++ '* υ)/&%ι,ι4.%ι $*+ ι,$+ #EUH?G A?;B?8E:9 A99H_:>( ι + /*ω,/ %ι */++'* ι)ι$*-$υ,%'*ι % υ)/&%ι,ι4.%ι $*+ ι,$+ #EUH?G A?;B?8E:9 ND< A99H_:>(> *+ )%)*ω$+ *ω %,.ω, ι)ι$*-$,%'*ι % υ)/&%ι ι$'*+* $*+ ι,$+ ι.*$ι &+$ι,)ι,%. )'**%$* $*+ $%ι/ /*ω )' *+ )'*$+ E VJK RJHIJAlNCN@BACCVMNh> XQ)ι.=*%B@BNCBT?_Y?8:{9T4ι*%ι*/+'*υ)/&%ι/ι$+ι,$+ι*,.4%7*ω %ι4,/*ωι5.%ι> [Q9KD8<B8H::> `Q-$*+&ι/*#%8,[()*/,%*+%)ι49OF<BD89Z:,5D%*ι,ι./* 135

12 η &, 7 -,),%ι.=υ,%%,5ι$*$*ι&%)%ι45ι $**ι$*ι*ω%,.ω,#%)ι49t:9e;bf<bm::(e/ι %*%.$υ,%**%$* NcNAN#%)ι4 9HD_D^:8:B<S DW M?;B?8E: <:9<:(E*)*.&υ,%+%.4=%ι,%*+%*9cFGD;:Z: T@ 9M:?89 FGD<:%ι.*') )*ι)ι$υ,% ι5. /,%$$%%4,*> Q*/,%9KD8<B8H::> iq *+&ι/*)*/,%9:> Output : Descriptives υη!υ" Total 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 53 55,66 963,59 13, , , ,75 161,559 77, , , ,5 111,673 1, ,9 6443, , ,345 4,19 138, , , ,55 144,64 65,9 79, ) η ι η ι ι ι η, ιι ι ι ι ι., «Descriptives» η η η ι ιηι η ι ( η «Mean»). One-Way #.,VA ι ιι ηι (p<,1), ι ι ι ι ι ι ι 4 ι ιι ηι : ANOVA Between Groups Within Groups Total Sum of Squares df Mean Square F Sig , ,5 16,649, , , ,

13 η &, 7 Multiple Comparisons Dependent Variable: Tamhane (I) υ υη!υ" (J) υ!υ" υη!υ" υη!υ" υη *. The mean difference is significant at the.5 level. Mean Difference 95% Confidence Interval (I-J) Std. Error Sig. Lower Bound Upper Bound -71,9 153,95,998-48,9 34,73-118,86* 166,97, -1464,17-573,56-569,9* 43,337, -6741, -4478,8 71,9 153,95,998-34,73 48,9-947,78* 16,83, -184,7-611, ,81* 49,437, -6634,75-444,87 118,86* 166,97, 573, ,17 947,78* 16,83, 611,48 184,7-4591,4* 414,554, -5699,79-348,8 569,9* 43,337, 4478,8 6741, 5538,81* 49,437, 444, , ,4* 414,554, 348,8 5699,79 «Multiple Comparisons» Post Hoc test Tamhane s T. & ι ι ι ι ιι!. η η Sig. η ιι ηιη η ι ι ι ιι η. 3η ι η 7ι & η, ι - ιι ιι ι ι. ι ι ηι 'η ι ι ι η 7ι & η -ι, ι 3 ιι. 6 One-Way ANOVA ι ηι ι : $ι! η ηι η ι ι ι ι ι ι " ι ιι ηι ι ιι ιι One-Way ANOVA. H!ηη η 4 η: 7ι η, -ι, 3 ιι ι * ι. ιι ηι, F(3)=16,6, p<,1, ι η ηι η ι ηι η ι η ι η ι ιι ηι ι ι ι η. $ι! ιι ι "η ι ιη (Post Hoc test) Tamhane s T. 9ηι ι ι ι ι ι ιη η ιη ι 4, ι ι ι ι ι. ι ι ι ι! ι ι ι ι ηι 'η ι ι η 7ι & η, -ι, ι 3 ιι.,ι ι ιηι 'η ι ι η 7ι & η ι -ι., ι ι ι ι ι 7ι η ι -ι ι!. η, ι η ι ηι ι ι ιι ηιη ( η Sig. (-tailed)) ι η ι F ι (η df degrees of freedom): F(df)=, p<. ( ANOVA ι ). ο+η3+,-,),k;h9n?gp?ggb9h ι η η ι ι ι ι η!ηη ι 137

14 η &, 7 η ι!η ; ι ιι ι % ι η ιη η ηι ι η ι Kruskal-Wallis H: PQA8?GSl:ND8F?;?_:<;BE<:9<9KI8>:F:8>:8<9?_FG:9Z Q)7%*,%*+,%*8+*$*)$ι9m;DHFB8^A?;B?JG::#4ι*+%=/*+*+,%*8+*(ι *+,%*8+*$*)$ι9T:9<A?;B?JG:IB9<:#%=*+,.%,%*8+*.(> VQ9:Q ι : Ranks υ υη!υ" Total N Mean Rank , , , , Test Statistics a,b # $ Chi-Square 47,9 df 3 Asymp. Sig., a. Kruskal Wallis Test b. Grouping Variable: υ Kruskal-Wallis H ι ι ιι ηι ι ι ι ι ι 4 ι: x (3,.=474)=47,, p=,1. & ι ι ι ιι ηιη, ι "η η" 4 ι! ι ι!. Kruskal-Wallis H ι ηι!: $ι! η ηι η ι ι ιι ι ι " ι η " ηι ι ιι ιι Kruskal-Wallis H. ιι ηι, x (3,.=474)=47,, p=<,1, ηι η ι η.,ι ι ι 'η! (Mean Rank= 4,7) ι ιη, ι ι η. 138

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