anova sesiuneppt
DESCRIPTION
metoda anovaTRANSCRIPT
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Analiza variaional ANOVA metod de optimizare a proceselor organizaionaleDaniela COSMA
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De ce analiz variaional
Existena unor diferene semnificative ntre nivelul de pregtire al studenilor, metodele de predare istrucie sau evaluare ale cadrelor didactice, caracteristicile disciplinelor de nvmnt fac ca strategiile, modelele i metodele de utilizare optima a resursei umane n procesul de nvmnt fundamentate pe tendina central s fie mai puin eficiente sau eficace.
Rezultatele depind i de factori independei cum ar fi caracteristicile psiho-individuale
Rezultatul implementrii unei stategii de promovare, selecie, formare, perfectionare poate fi evideniat nu mumai pritr-un nivel superior al tendinei centale ci mai ales prin creterea omogenitii populaiei investigate.
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De la testul T la FAm putea folosi testul T ca ca s comparm dou cte dou valorile medii ale unui numr de caracteristici.
Aceast metod in cazul cercetrii noastre nu e adecvat din urmtoarele motiveE dificil de luat n considerare toate combinaiile posibile.Orice statistic care are n vedere date pariale (ca n cazul considerrii unei combinaii de dou variabile) e mai puin consistent ca cea care folosete totalitatea informaiilor.Unele comparaii vor furniza rezultate eronate pentru c la nivelul eantioanelor ipoteza va fi admis din ntmplare.
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De la T (STUDENT)la F(FICHER)Avem nevoie de un test cu caracter global care va identifica diferenele semnificative ntre caracteristicile diferitelor srategii sau impactul factorilor de mediu asupra procesului de implementare.Dac rspunsul la ntrebarea noastr va fi negativ cercetarea ulterioar nu pateu conduce la rezultate consistente..Un asemenea test de semnificaie aplicabil pe un numr mare de variabile e testul F, sau analiza de variaie, sau ANOVA.
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Logica metodei ANOVAIpoteza care se testeaz prin metoda ANOVA se refer la existena unor diferene semnificative ntre tendinele centrale (efectul pe care aplicarea unor srategii l are asupra eantioanelor supuse experimentului) i ne ateptm evident ca ipoteza nul s fie admis.Aceast ntrebare dei se refer la medii i gsete rspunsul prin analiza variaiei.Printre alte motive pentru care ne concentrm atenia asupra variaiei este acela c dorim s testm diferena dintre medii.
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DOU SURSE ALE VARIABILITIIIn ANOVA, o estimaie a variabilitii ntre grupuri e comparat cu variabilitatea n cadrul grupurilor.Variabilitatea ntre grupuri crora li s-au aplicat tratamente diferite (s-au experimentat diverse strategii de promovare a profesiei, instituiei militare) conduce la diferene intre medii cu caracter aleatoriu i datorit efectului unor factori de mediu dac e semnificativ desigur variabilitatea n cadrul grupurilor se datoreaz caracteristicilor .Diferite ale elementelor din eantion care evident au participat la acelai experiment.
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Variaia ntre grupuriExist o variaie mare ntre mediiMari diferene ntre medii nu se datoreaz ntmprii.E dificil de imaginat c toate grupurile sunt eantioane aleatoare ale aceleiai populaii.Ipoteza nul e respins indicnd un efect al tratamentului adic eficiena cel puin unei stategii utilizate.
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Variabilitatea n cadrul grupurilorExist o oarecare variaie ntre mediile grupurilor.Totui variaia n cadrul grupurilor e mai mare pentru fiecare din grupuri.Cu ct variaia n cadrul grupurilor e mai mare cu att sigurana unor ipoteze referitoare la populaie se micoreaz.
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RAPORTUL F
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DOU SURSE DE VARIAIE
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DOU SURSE DE VARIAIE
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RAPORTUL F
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RAPORTUL FEstimarea abaterii mediilor de grup fa de media populaieiGrade de libertatesum of squares betweensum of squares withindegrees of freedom withindegrees of freedom between
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RAPORTUL Fsum of squares totaldegrees of freedom total
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RAPORTUL F : SS intergrup Abateri individualeVolumul populaiei
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RAPORTUL F : SSintragrupDispersia la nivelul populaieiNumrul de indivizi din fiecare grup
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RAPORTUL F : SS TotalNumr total de subieci.
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Un exemplu: ANOVA
Jocul 1
Jocul 2
Jocul 3
X1
X2
X2
X2
X3
X2
Eantionul ex grupa mic
12
144
81
6
36
Eantionul de control grupa mic
10
100
7
49
7
49
Eantionul ex grupa mijlocie
11
121
6
36
2
4
Eantionul de control grupa mic
7
49
9
81
3
9
Eantionul ex grupa mare
10
100
4
16
2
4
50
514
35
263
20
102
MEDIA=
10
7
4
_1256058706.unknown
_1256058755.unknown
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ANOVA INDEX
A=514+263+102=879;
B=(50+35+20)2/15=735
C=(50)2/5+(35)2/5+(20)2/5=825
ANOVAs index va fi:
Table nr :2
DISPERSION
SS
Df
MS
F
INTERGROUP
90
2
45
10,00
INTRAGROUP
54
12
4,5
SCORE
144
14
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An Example: ANOVAIpoteza testat.EXISTA DIFERENE SEMNIFICATIVE NTRE STATEGII?Ipoteza statistic corespunzatoare.
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Rezultat Test
F(2,12)=10,00,p
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ANOVA cu msuratori repetate
Table nr: 3
S
Primul ex grupa Mmruelor
Primul ex grupa Iepurailor
Al doilea ex grupa Mmruelor
Al doilea ex grupa Iepurailor
x
X2
X
X2
x
X2
x
X2
1
6
36
9
81
12
144
11
121
2
8
64
10
100
14
196
15
225
3
5
25
6
36
10
100
11
121
4
7
49
9
81
9
81
10
100
5
4
16
8
64
10
100
9
81
6
9
81
6
36
11
121
10
100
39
271
48
398
66
742
66
748
M
6,5
8,0
11,0
11,0
Calculm A,B,C values:
A=271+398+748=2159
B=(39+48+66+66)2/24=1998,375
C=[(6+9+12+11)2+(8+10+14+15)2+(5+6+10+11)2+(7+9+9+10)2+(4+8+10+9)2+(9+6+11+10)2]/4+2039,75
D=(392+482+662+662)/6=2089,5
Calculm SS
SS individual=C-B=2039,5-1998,375=41,375
SS true(experiment)=D-B=2089,5-1998,375=91,125
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SS residual=(A-B)-(C-B)+(D-B)=(2159-1988,375)-[(2039,75-1988,375)+(2089,5-1998,375)]=28,125.
SS total = A-B = 2159-1998,375=160,625.
SS total = SS individual + SS experiment + SS residual
Calculam gradele de libertate:
df individual =n-1=6-1=5.
df experimental =k-1=4-1=3.
df residual =(k-1)(n-1)=(6-1)(4-1)=15.
df total = N-1=24-1=23.
calculame(MS):
MS individual=SS individual / df individual = 41,375/5=8,275.
MS experimental=SS experiment / df experimental=91,125/3=30,375.
MS residual=SS residual / df residual = 28,125/15=1,875
calculam F pentru ANOVA cu msurtori repetate:
F=MS experimental/MS residual;
F=30,375/1,875=16,2.
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Table nr: 4
The source of the dispersion
SS
df
MS
F
F, (p
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Repartitia F (Fisher Snedecor)Valorile functiei F (F = s12/ s22 ) pentru l1, l2 grade de libertate si =0,05, = 0,01 nivel de semnificatie
l 2
1
l1 = 1
l1 = 2
l1 = 3
l1 = 4
l1 = 5
= 0,05
= 0,01
= 0,05
= 0,01
= 0,05
= 0,01
= 0,05
= 0,01
= 0,05
= 0,01
1
23
161,40
4052,00
199,50
4999,00
215,70
5403,00
224,60
5625,00
230,20
5764,00
2
34
4
18,51
98,49
19,00
99,00
19,16
99,17
19,25
99,25
19,30
99,30
3
10,13
34,12
9,55
30,81
9,28
29,46
9,12
28,71
9,01
28,24
4
5
6
7,71
21,20
6,94
18,00
6,59
16,69
6,39
15,98
6,26
15,52
5
6,61
16,26
5,79
13,27
5,41
12,06
5,19
11,39
5,05
10,97
6
7
8
9
10
11
12
13
14
5,99
13,74
5,14
10,91
4,76
9,78
4,53
9,15
4,39
8,75
7
5,59
12,25
4,74
9,55
4,35
8,45
4,12
7,85
3,97
7,45
8
5,32
11,26
4,46
8,65
4,07
7,59
3,84
7,01
3,69
6,63
9
5,12
10,56
4,26
8,02
3,86
6,99
3,63
6,42
3,48
6,06
10
4,96
10,04
4,10
7,56
3,71
6,55
3,48
5,99
3,33
5,64
11
4,84
9,65
3,98
7,20
3,59
6,22
3,36
5,67
3,20
5,32
12
4,75
9,33
3,88
6,93
3,49
5,95
3,26
5,41
3,11
5,06
13
4,67
9,07
3,80
6,70
3,41
5,74
3,18
5,20
3,02
4,86
14
15
16
17
18
4,60
8,86
3,74
6,51
3,34
5,56
3,11
5,03
2,96
4,69
15
4,54
8,68
3,68
6,36
3,29
5,42
3,06
4,89
2,90
4,56
16
4,49
8,53
3,63
6,23
3,24
5,29
3,01
4,77
2,85
4,44
17
4,45
8,40
3,59
6,11
3,20
5,18
2,96
4,67
2,81
4,34
18
19
20
21
22
23
4,41
8,28
3,55
6,01
3,16
5,09
2,93
4,58
2,77
4,25
19
4,38
8,18
3,52
5,93
3,13
5,01
2,90
4,50
2,74
4,17
20
4,35
8,10
3,49
5,85
3,10
4,94
2,87
4,43
2,71
4,10
21
4,32
8,02
3,47
5,78
3,07
4,87
2,84
4,37
2,68
4,04
22
4,30
7,94
3,44
5,72
3,05
4,82
2,82
4,31
2,66
3,99
23
24
4,28
7,88
3,42
5,66
3,03
4,76
2,80
4,26
2,64
3,94
24
25
26
27
4,26
7,82
3,40
5,61
3,01
4,72
2,78
4,22
2,62
3,90
25
4,24
7,77
3,38
5,57
2,99
4,68
2,76
4,18
2,60
3,86
26
4,22
7,72
3,37
5,53
2,98
4,64
2,74
4,14
2,59
3,82
27
28
29
30
40
4,21
7,68
3,35
5,49
2,96
4,60
2,73
4,11
2,57
3,78
28
4,20
7,64
3,34
5,45
2,95
4,57
2,71
4,07
2,56
3,75
29
4,18
7,60
3,33
5,42
2,93
4,54
2,70
4,04
2,54
3,73
30
60
120
4,17
7,56
3,32
5,39
2,92
4,51
2,69
4,02
2,53
3,70
40
4,08
7,31
3,23
5,18
2,84
4,31
2,61
3,83
2,45
3,51
60
4,00
7,08
3,15
4,98
2,76
4,13
2,52
3,65
2,37
3,34
120
3,92
6,85
3,07
4,79
2,68
3,95
2,45
3,48
2,29
3,17
3,84
6,64
2,99
4,60
2,60
3,78
2,37
3,32
2,21
3,02
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The following program was designed to perform ANOVA methods.
Enter your data for a Analysis of Variance. For this to make sense you should have several groups of data (at least 3; maximum: 26).Number of groups:
Each group includes a certain number of data items. (Often all the groups have the same number of items, but that is not required.) What is the size (i.e., the number of items) of largest group? (maximum: 99)Size of largest group:
There is no harm is over estimating the group size: blanks will be ignored. You do need to correctly enter the number of groups.
_1257287740.unknown
_1257287741.unknown
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Data Entry: ANOVA
Enter in the below set of boxes your data for each group (order makes no difference within a group) and then click on the Calculate Now button. Empty boxes will be ignored.
Partea superioar a machetei
HTMLCONTROL Forms.HTML:Hidden.1
HTMLCONTROL Forms.HTML:Submitbutton.1
HTMLCONTROL Forms.HTML:Reset.1
Data for Group A
A01= A02= A03= A04= A05=
Data for Group B
B01= B02= B03= B04= B05=
Data for Group C
C01= C02= C03= C04= C05=
_1257288052.unknown
_1257288057.unknown
_1257288059.unknown
_1257288061.unknown
_1257288063.unknown
_1257288064.unknown
_1257288062.unknown
_1257288060.unknown
_1257288058.unknown
_1257288054.unknown
_1257288056.unknown
_1257288053.unknown
_1257288048.unknown
_1257288050.unknown
_1257288051.unknown
_1257288049.unknown
_1257288046.unknown
_1257288047.unknown
_1257288045.unknown
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ANOVA: Results
The results of a ANOVA statistical test performed at 09:56 on 12-NOV-2007
Source of Sum of d.f. Mean F
Variation Squares Squares
between 90.00 2 45.00 10.00
error 54.00 12 4.500
total 144.0 14
The probability of this result, assuming the null hypothesis, is 0.003
Group A: Number of items= 57.00 10.0 10.0 11.0 12.0
Mean = 10.0 95% confidence interval for Mean: 7.933 thru 12.07 Standard Deviation = 1.87 Hi = 12.0 Low = 7.00 Median = 10.0 Average Absolute Deviation from Median = 1.20
Group B: Number of items= 54.00 6.00 7.00 9.00 9.00
Mean = 7.00 95% confidence interval for Mean: 4.933 thru 9.067 Standard Deviation = 2.12 Hi = 9.00 Low = 4.00 Median = 7.00 Average Absolute Deviation from Median = 1.60
Group C: Number of items= 52.00 2.00 3.00 6.00 7.00
Mean = 4.00 95% confidence interval for Mean: 1.933 thru 6.067 Standard Deviation = 2.35 Hi = 7.00 Low = 2.00 Median = 3.00 Average Absolute Deviation from Median = 1.80
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An Example: ANOVACalculate the test statistic.Grand Total: 104
ImaginedRetrospectiveCurrent7491214486463686410100525981121446361112110100T:24146T:40410T:40408
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An Example: ANOVACalculate the test statistic.Grand Total: 104
ImaginedRetrospectiveCurrent7491214486463686410100525981121446361112110100T:24146T:40410T:40408
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An Example: ANOVA
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An Example: ANOVADetermine if your result is significant.Reject H0, 9.61>4.26Interpret your results.There is a significant difference in the ratings of the intensity of unrequited love depending on when (or if) the emotion was felt.ANOVA Summary TableIn the literature, the ANOVA results are often summarized in a table.SourcedfSSMSFBetween Groups242.6721.349.61Within Groups9202.22Total1162.67
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After the F TestWhen an F turns out to be significant, we know, with some degree of confidence, that there is a real difference somewhere among our means.But if there are more than two groups, we dont know where that difference is.Post hoc tests have been designed for doing pair-wise comparisons after a significant F is obtained.
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An Example: ANOVAA psychologist interested in artistic preference randomly assigns a group of 15 subjects to one of three conditions in which they view a series of unfamiliar abstract paintings. The 5 participants in the famous condition are led to believe that these are each famous paintings. The 5 participants in the critically acclaimed condition are led to believe that these are paintings that are not famous but are highly thought of by a group of professional art critics. The 5 in the control condition are given no special information about the paintings. Does what people are told about paintings make a difference in how well they are liked? Use the .01 level of significance.
FamousCritically AcclaimedNo Information10547165391073843
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An Example: ANOVAState the research hypothesis.Does what people are told about paintings make a difference in how well they are liked?State the statistical hypothesis.
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An Example: ANOVASet decision rule.
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An Example: ANOVAGrand Total: 85
FamousCritically AcclaimedNo Information101005254167491163652539981101007493986441639T:40338T:20100T:25151
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An Example: ANOVAGrand Total: 85
FamousCritically AcclaimedNo Information101005254167491163652539981101007493986441639T:40338T:20100T:25151
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An Example: ANOVAGrand Total: 85
FamousCritically AcclaimedNo Information101005254167491163652539981101007493986441639T:40338T:20100T:25151
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An Example: ANOVA
- An Example: ANOVADetermine if your result is significant.Retain H0, 4.06