An Extended ANOVA F-Test with Applications to the Heterogeneity Problem in Meta-Analysis

The classical F‐test in the one‐way random effects ANOVA model is extended to solve the long outstanding problem of testing the between‐group variance on values also different from zero. This is done first for homoscedastic and heteroscedastic cases in not necessarily balanced models and secondly fo...

Full description

Saved in:
Bibliographic Details
Published inBiometrical journal Vol. 43; no. 2; pp. 135 - 146
Main Authors Hartung, Joachim, Makambi, Kepher Henry, Argaç, Dog̃an
Format Journal Article
LanguageEnglish
Published Berlin WILEY-VCH Verlag Berlin GmbH 01.05.2001
WILEY‐VCH Verlag Berlin GmbH
Wiley-VCH
Subjects
ANOVA F-test
Attained power
Attained significance level
Between-group variance
Exact sciences and technology
Linear inference, regression
Mathematics
Meta-analysis
Multivariate analysis
Probability and statistics
Random effects model
Risk difference
Sciences and techniques of general use
Statistics
F test
Data analysis
Covariance analysis
Meta analysis
Risk
Statistical estimation
Multivariate analysis
Variance analysis
Heteroscedasticity
Hypothesis test
Heterogeneity
One way analysis of variance
Random effect
Linear estimation
Sampling
Online AccessGet full text

Cover

Abstract The classical F‐test in the one‐way random effects ANOVA model is extended to solve the long outstanding problem of testing the between‐group variance on values also different from zero. This is done first for homoscedastic and heteroscedastic cases in not necessarily balanced models and secondly for balanced homoscedastic models. By simulation, the tests are shown to attain acceptable significance levels and high power even in data that do not follow the usual ANOVA model. An important application of the tests is given by the heterogeneity questions concerning the treatment effects across studies in meta‐analysis.
AbstractList The classical F‐test in the one‐way random effects ANOVA model is extended to solve the long outstanding problem of testing the between‐group variance on values also different from zero. This is done first for homoscedastic and heteroscedastic cases in not necessarily balanced models and secondly for balanced homoscedastic models. By simulation, the tests are shown to attain acceptable significance levels and high power even in data that do not follow the usual ANOVA model. An important application of the tests is given by the heterogeneity questions concerning the treatment effects across studies in meta‐analysis.
Author Makambi, Kepher Henry
Hartung, Joachim
Argaç, Dog̃an
Author_xml – sequence: 1
  givenname: Joachim
  surname: Hartung
  fullname: Hartung, Joachim
  organization: University of Dortmund, Dortmund, Germany
– sequence: 2
  givenname: Kepher Henry
  surname: Makambi
  fullname: Makambi, Kepher Henry
  organization: Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
– sequence: 3
  givenname: Dog̃an
  surname: Argaç
  fullname: Argaç, Dog̃an
  organization: University of Dortmund, Dortmund, Germany
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=996055$$DView record in Pascal Francis
BookMark eNqVkE1vEzEQhi1UJNLCf7CEhODgMP7a7QaEtISmSdUmfBTKbeR1vNSw8Ya1qzb_no0ScuLCwbI8Hj_v-DkmR6ENjpCCw5ADiNdcC84UyOylAOCgXyk5Em-51KNROfvA3s-uLvrDOzmE4XjxRrDpIzI4vDkiA5BCMnmq8ifkOMafAFCAEgPyvQz07CG5sHRLWs4X30o6YdcuJnrv0y0t1-vGW5N8GyJNLU23jk5dcl37wwXn04Z-7NqqcSvqA71yybAymGYTfXxKHtemie7Zfj8hXydn1-Mpu1ycz8blJbMKhGai5oWADFyVV3BqoV-mUJW2uc5tnltdZUo5IS0sa1tZzqURFa-VLkQmuMrkCXmx46679vddPziufLSuaUxw7V1EwaEQUkDf-GnXaLs2xs7VuO78ynQb5IBbx7j1hVtfuHOMSmJflRqxd4x7xygRcLzob6Y98_k-3ERrmrozwfp4ABdFBlrLw9fvfeM2_xH779S_pZ7Ldlwfk3s4cE33C7Nc5hpv5ud4Nb9Rk8_5BX6RfwDeT6hk
CODEN BIJODN
Cites_doi 10.1214/aoms/1177706077
10.1016/0197-2456(86)90046-2
10.1002/(SICI)1097-0258(19990215)18:3<321::AID-SIM28>3.0.CO;2-P
10.1002/(SICI)1097-0258(19960330)15:6<619::AID-SIM188>3.0.CO;2-A
10.1080/01621459.1986.10478322
10.1002/sim.4780101105
10.1002/(SICI)1097-0258(19970415)16:7<753::AID-SIM494>3.0.CO;2-G
10.2307/2534003
10.1002/(SICI)1521-4036(199912)41:8<901::AID-BIMJ901>3.0.CO;2-W
ContentType Journal Article
Copyright 2001 WILEY‐VCH Verlag Berlin GmbH, Fed. Rep. of Germany
2001 INIST-CNRS
Copyright_xml – notice: 2001 WILEY‐VCH Verlag Berlin GmbH, Fed. Rep. of Germany
– notice: 2001 INIST-CNRS
DBID BSCLL
IQODW
AAYXX
CITATION
7QO
8FD
FR3
P64
DOI 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H
DatabaseName Istex
Pascal-Francis
CrossRef
Biotechnology Research Abstracts
Technology Research Database
Engineering Research Database
Biotechnology and BioEngineering Abstracts
DatabaseTitle CrossRef
Engineering Research Database
Biotechnology Research Abstracts
Technology Research Database
Biotechnology and BioEngineering Abstracts
DatabaseTitleList
Engineering Research Database
DeliveryMethod fulltext_linktorsrc
Discipline Biology
Statistics
Mathematics
EISSN 1521-4036
EndPage 146
ExternalDocumentID 10_1002_1521_4036_200105_43_2_135__AID_BIMJ135_3_0_CO_2_H
996055
BIMJ135
ark_67375_WNG_MNW4FR7J_S
Genre article
GroupedDBID ---
-~X
.3N
.GA
.Y3
05W
0R~
10A
1L6
1OB
1OC
1ZS
23N
3-9
31~
33P
3SF
3WU
4.4
50Y
50Z
51W
51X
52M
52N
52O
52P
52S
52T
52U
52W
52X
53G
5GY
5VS
66C
702
7PT
8-0
8-1
8-3
8-4
8-5
8UM
930
A03
AAESR
AAEVG
AAHHS
AANLZ
AAONW
AASGY
AAXRX
AAZKR
ABCQN
ABCUV
ABEML
ABHUG
ABIJN
ABJNI
ABPVW
ACAHQ
ACBWZ
ACCFJ
ACCZN
ACGFS
ACIWK
ACPOU
ACPRK
ACSCC
ACXBN
ACXME
ACXQS
ADAWD
ADBBV
ADDAD
ADEOM
ADIZJ
ADKYN
ADMGS
ADOZA
ADXAS
ADZMN
ADZOD
AEEZP
AEIGN
AEIMD
AENEX
AEQDE
AEUQT
AEUYR
AFBPY
AFFPM
AFGKR
AFPWT
AFRAH
AFVGU
AFZJQ
AGJLS
AHBTC
AHMBA
AI.
AIURR
AIWBW
AJBDE
AJXKR
ALAGY
ALMA_UNASSIGNED_HOLDINGS
ALUQN
AMBMR
AMYDB
ASPBG
ATUGU
AUFTA
AVWKF
AZBYB
AZFZN
AZVAB
BAFTC
BDRZF
BFHJK
BHBCM
BMNLL
BMXJE
BNHUX
BROTX
BRXPI
BSCLL
BY8
CS3
D-E
D-F
DCZOG
DPXWK
DR2
DRFUL
DRSTM
DU5
DUUFO
EBD
EBS
EJD
EMOBN
F00
F01
F04
F5P
FEDTE
G-S
G.N
GNP
GODZA
H.T
H.X
HBH
HF~
HHY
HHZ
HVGLF
HZ~
IX1
J0M
JPC
KQQ
LATKE
LAW
LC2
LC3
LEEKS
LH4
LITHE
LOXES
LP6
LP7
LUTES
LW6
LYRES
M67
MEWTI
MK4
MRFUL
MRSTM
MSFUL
MSSTM
MXFUL
MXSTM
N04
N05
N9A
NF~
O66
O9-
P2W
P2X
P4D
PALCI
PQQKQ
Q.N
Q11
QB0
QRW
R.K
RIWAO
ROL
RWI
RX1
RYL
SAMSI
SUPJJ
SV3
TN5
UB1
V2E
VH1
W8V
W99
WBKPD
WIB
WIH
WIK
WJL
WOHZO
WQJ
WRC
WUP
WWH
WXSBR
WYISQ
XBAML
XG1
XPP
XV2
Y6R
YHZ
ZZTAW
~IA
~WT
AITYG
HGLYW
OIG
AAPBV
IQODW
AAYXX
CITATION
7QO
8FD
FR3
P64
ID FETCH-LOGICAL-c4025-2f192060eb7b08c008ca94b5c757c77c5b644e23c0dfcbc113a2b1f4592621463
IEDL.DBID DR2
ISSN 0323-3847
IngestDate Fri Aug 16 05:21:06 EDT 2024
Fri Aug 23 01:21:06 EDT 2024
Sun Oct 29 17:09:36 EDT 2023
Sat Aug 24 00:56:51 EDT 2024
Wed Jan 17 05:01:31 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords F test
Data analysis
Covariance analysis
Meta analysis
Risk
Statistical estimation
Multivariate analysis
Variance analysis
Heteroscedasticity
Hypothesis test
Heterogeneity
One way analysis of variance
Random effect
Linear estimation
Sampling
Language English
License CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c4025-2f192060eb7b08c008ca94b5c757c77c5b644e23c0dfcbc113a2b1f4592621463
Notes ark:/67375/WNG-MNW4FR7J-S
istex:E64362742462896D476FBB93E471FFF4A618931F
ArticleID:BIMJ135
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
PQID 21092320
PQPubID 23462
PageCount 12
ParticipantIDs proquest_miscellaneous_21092320
crossref_primary_10_1002_1521_4036_200105_43_2_135__AID_BIMJ135_3_0_CO_2_H
pascalfrancis_primary_996055
wiley_primary_10_1002_1521_4036_200105_43_2_135_AID_BIMJ135_3_0_CO_2_H_BIMJ135
istex_primary_ark_67375_WNG_MNW4FR7J_S
PublicationCentury 2000
PublicationDate May 2001
PublicationDateYYYYMMDD 2001-05-01
PublicationDate_xml – month: 05
  year: 2001
  text: May 2001
PublicationDecade 2000
PublicationPlace Berlin
PublicationPlace_xml – name: Berlin
PublicationTitle Biometrical journal
PublicationTitleAlternate Biom. J
PublicationYear 2001
Publisher WILEY-VCH Verlag Berlin GmbH
WILEY‐VCH Verlag Berlin GmbH
Wiley-VCH
Publisher_xml – name: WILEY-VCH Verlag Berlin GmbH
– name: WILEY‐VCH Verlag Berlin GmbH
– name: Wiley-VCH
References Biggerstaff, B.J. and Tweedie, R.L., 1997: Incorporating variability in estimates of heterogeneity in the random effects model in meta-analysis. Statistics in Medicine 16, 753-768.
Patnaik, P.B., 1949: The non-central χ2- and F-distributions and their applications. Biometrika 36, 202-232.
Hartung, J., 1999: An alternative method for meta-analysis. Presented at the 45th Biometrical Colloquium of the German Region of the International Biometrical Society, Dortmund, 1999; in: Biometrical Journal 41, 901-916.
Hardy, R.H. and Thompson, S.G., 1996: A likelihood approach to meta-analysis with random effects. Statistics in Medicine 15, 619-629.
Lipsitz, S.R., Dear, K.B.G., Laird, N.M., and Molenberghs, G., 1998: Test for homogeneity of the risk difference when data are sparse. Biometrics 54, 148-160.
Whitehead, A. and Whitehead, J., 1991: A general parametric approach to the meta-analysis of randomized clinical trials. Statistics in Medicine 10, 1665-1677.
Herbach, L.H., 1959: Properties of model II-type analysis of variance tests, A: optimum nature of the F-test for model II in the balanced case. Ann. Math. Statist. 30, 939-959.
DerSimonian, R. and Laird, N., 1986: Meta-analysis in clinical trials. Controlled clinical trials 7, 177-188.
Hartung, J. and Voet, B., 1986: Best invariant unbiased estimators for the mean squared error of variance component estimators. J. Amer. Statist. Assoc. 81, 689-691.
Normand, S.T., 1999: Meta-analysis: formulating, evaluating, combining, and reporting. Statistics in Medicine 18, 321-359.
1959; 30
1949; 36
1997; 16
1986; 81
1999; 41
1986; 7
1998; 54
1991; 10
1996; 15
1999; 18
Hartung (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB5) 1986; 81
Biggerstaff (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB1) 1997; 16
DerSimonian (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB2) 1986; 7
Hardy (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB3) 1996; 15
Lipsitz (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB7) 1998; 54
Herbach (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB6) 1959; 30
Whitehead (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB10) 1991; 10
Patnaik (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB9) 1949; 36
Hartung (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB4) 1999; 41
Normand (10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB8) 1999; 18
References_xml – volume: 54
  start-page: 148
  year: 1998
  end-page: 160
  article-title: Test for homogeneity of the risk difference when data are sparse.
  publication-title: Biometrics
– volume: 41
  start-page: 901
  year: 1999
  end-page: 916
  article-title: An alternative method for meta‐analysis. Presented at the 45th Biometrical Colloquium of the German Region of the International Biometrical Society, Dortmund, 1999; in:
  publication-title: Biometrical Journal
– volume: 16
  start-page: 753
  year: 1997
  end-page: 768
  article-title: Incorporating variability in estimates of heterogeneity in the random effects model in meta‐analysis.
  publication-title: Statistics in Medicine
– volume: 18
  start-page: 321
  year: 1999
  end-page: 359
  article-title: Meta‐analysis: formulating, evaluating, combining, and reporting.
  publication-title: Statistics in Medicine
– volume: 10
  start-page: 1665
  year: 1991
  end-page: 1677
  article-title: A general parametric approach to the meta‐analysis of randomized clinical trials.
  publication-title: Statistics in Medicine
– volume: 81
  start-page: 689
  year: 1986
  end-page: 691
  article-title: Best invariant unbiased estimators for the mean squared error of variance component estimators.
  publication-title: J. Amer. Statist. Assoc.
– volume: 36
  start-page: 202
  year: 1949
  end-page: 232
  article-title: The non‐central χ ‐ and F‐distributions and their applications.
  publication-title: Biometrika
– volume: 15
  start-page: 619
  year: 1996
  end-page: 629
  article-title: A likelihood approach to meta‐analysis with random effects.
  publication-title: Statistics in Medicine
– volume: 30
  start-page: 939
  year: 1959
  end-page: 959
  article-title: Properties of model II‐type analysis of variance tests, A: optimum nature of the F‐test for model II in the balanced case.
  publication-title: Ann. Math. Statist.
– volume: 7
  start-page: 177
  year: 1986
  end-page: 188
  article-title: Meta‐analysis in clinical trials.
  publication-title: Controlled clinical trials
– volume: 30
  start-page: 939
  year: 1959
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB6
  publication-title: Ann. Math. Statist.
  doi: 10.1214/aoms/1177706077
  contributor:
    fullname: Herbach
– volume: 7
  start-page: 177
  year: 1986
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB2
  publication-title: Controlled clinical trials
  doi: 10.1016/0197-2456(86)90046-2
  contributor:
    fullname: DerSimonian
– volume: 18
  start-page: 321
  year: 1999
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB8
  publication-title: Statistics in Medicine
  doi: 10.1002/(SICI)1097-0258(19990215)18:3<321::AID-SIM28>3.0.CO;2-P
  contributor:
    fullname: Normand
– volume: 15
  start-page: 619
  year: 1996
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB3
  publication-title: Statistics in Medicine
  doi: 10.1002/(SICI)1097-0258(19960330)15:6<619::AID-SIM188>3.0.CO;2-A
  contributor:
    fullname: Hardy
– volume: 81
  start-page: 689
  year: 1986
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB5
  publication-title: J. Amer. Statist. Assoc.
  doi: 10.1080/01621459.1986.10478322
  contributor:
    fullname: Hartung
– volume: 36
  start-page: 202
  year: 1949
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB9
  publication-title: Biometrika
  contributor:
    fullname: Patnaik
– volume: 10
  start-page: 1665
  year: 1991
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB10
  publication-title: Statistics in Medicine
  doi: 10.1002/sim.4780101105
  contributor:
    fullname: Whitehead
– volume: 16
  start-page: 753
  year: 1997
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB1
  publication-title: Statistics in Medicine
  doi: 10.1002/(SICI)1097-0258(19970415)16:7<753::AID-SIM494>3.0.CO;2-G
  contributor:
    fullname: Biggerstaff
– volume: 54
  start-page: 148
  year: 1998
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB7
  publication-title: Biometrics
  doi: 10.2307/2534003
  contributor:
    fullname: Lipsitz
– volume: 41
  start-page: 901
  year: 1999
  ident: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H-BIB4
  publication-title: Biometrical Journal
  doi: 10.1002/(SICI)1521-4036(199912)41:8<901::AID-BIMJ901>3.0.CO;2-W
  contributor:
    fullname: Hartung
SSID ssj0009042
Score 1.6481423
Snippet The classical F‐test in the one‐way random effects ANOVA model is extended to solve the long outstanding problem of testing the between‐group variance on...
The classical F-test in the one-way random effects ANOVA model is extended to solve the long outstanding problem of testing the between-group variance on...
SourceID proquest
crossref
pascalfrancis
wiley
istex
SourceType Aggregation Database
Index Database
Publisher
StartPage 135
SubjectTerms ANOVA F-test
Attained power
Attained significance level
Between-group variance
Exact sciences and technology
Linear inference, regression
Mathematics
Meta-analysis
Multivariate analysis
Probability and statistics
Random effects model
Risk difference
Sciences and techniques of general use
Statistics
Title An Extended ANOVA F-Test with Applications to the Heterogeneity Problem in Meta-Analysis
URI https://api.istex.fr/ark:/67375/WNG-MNW4FR7J-S/fulltext.pdf
https://onlinelibrary.wiley.com/doi/abs/10.1002%2F1521-4036%28200105%2943%3A2%3C135%3A%3AAID-BIMJ135%3E3.0.CO%3B2-H
https://search.proquest.com/docview/21092320
Volume 43
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwvV1Pb9MwFLemIRAX_iMyBvjAEBzSOf7TLAUhZaUlq9QUjY3tgGTZriNNk1K0phJw4iNw4BPySXiOk65FXJAQUg6Ro_g5z89-P9svv4fQU8IYOKEiDhMuVMgZsaEG4BuybmIZK7g2hfvfeZx3s2M-OhWnG2je_gvj-SGWG25uZNTztRvgSs93L0lDneOB1Y_LSLJH60SPsHbmDDqW7rB-xATcwZUevAn3D8ajumDAOqTTn-ywfRpmMG87Aj4HpA4vKacSwv3JA2Uhg6n7GkoambtLic-9vBec9egrqLjXW5Hy2st4CRLWfN0V122fXeylmoP6C583Yw3YrsLj2r8Nb6IfrWZ8WMt5Z1Hpjvn6G2nkf1bdLXSjwcs49QZ-G23Y8g666jNofrmLPqYlHjT7-DjNJx9SPPz57fsRfCh2W8w4XTmgx9UMA97FmQsBmsHIsbAEwe98Sh18VuKxrRS83RK13EPHw8FRPwubhBGh4S4tLy0Ar5IusTrWZM8AvDEq4VqYWMQmjo3QgP4sZYZMC6NNFDFFdVRw4UgTwWWw-2iznJX2AcKi0JRPp9FUKcsdnbMSqqsp1coqrrUK0KjtWvnJ84JIzwBNpVOvdOqVXrmSMwmlTEgJKpWNSiWTRPYn8CQL0LPaOJY1qYtzF3AXC3mSv5Xj_IQPD-ORfB-g7TXrWb7gOHaECNCT1pgkzBLu6EeVdraYS1jYA5KnJEB5bRh_0eY_N7kt2vrXFT5E132Yn4sp3Uab1cXCPgLcV-nH9UD9BdbNN8M
link.rule.ids 315,786,790,1382,27955,27956,46327,46751
linkProvider Wiley-Blackwell
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwvV1Lb9NAEB6VVjwuvBGBQvdAERycOvuIm4CQ3DTBCY2DSkp7QFrtbtYSquSg1pGAEz-BC3-QX8KsN04TxAUJIflgbeQdZ3Zm59vd8TcAT0LGMAhlUdDiQgWchTbQCHwD1mxZxjKuTea-dx6mzeSID07EyRoU1bcwnh9iseHmPKOcr52Duw3pnQvWUBd5cPnjSpLs0rLSIy6eOcORpdus02AC7_CK-_vBXn84KBu6rB7WO6NttkeD5BJs4DQhnDvvH16QTrVC7s8eKAsYTt5XoDUXurMQ-cwLfM5Zm77EntvtJTGvvJAXKGIl2m24gfvssi_VOQ5A5itnrEDbZYBcRrjeDfhR6cYntpzWZ4Wum6-_0Ub-b-XdhOtzyExib-O3YM3mt-GyL6L55Q58iHPSnW_lkzgdvY9J7-e372P8p8TtMpN46YyeFFOCkJckLgtois5jcRVC3vqqOuRjToa2UPh0xdVyF4563XEnCeY1IwLDXWVemiFkDZuh1ZEOdw0iHKNaXAsTichEkREaAaClzISTzGjTaDBFdSPjwvEmYtRg92A9n-b2PhCRaconk8ZEKcsdo7MSqqkp1coqrrWqwaAaW_nJU4NITwJNpVOvdOqVXrmSM4mtTEiJKpVzlUomQ9kZ4S9JDZ6W1rHoSZ2dupy7SMjj9LUcpse8dxgN5LsabK6Yz-IBR7MjRA22KmuSOFG40x-V2-nsXOLaHsE8DWuQlpbxF-_851eumh786w634GoyHh7Ig3765iFc81l_LsV0E9aLs5l9hDCw0I9Lr_0Fh0I74w
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwvV3NbhMxELZKKyou_CMChfpAERw23XjsbBMQ0jbJkgSyqfpDe0CybMcroUqbqkkk4MQjcOAJeRLG62yaIC5ICGkPK0fr2YzHnm_s2W8IeRYCoBPKoqDBhQo4hDbQCHwDqDcsQMa1ydz3zoO03j3h_TNxtkYm5bcwnh9iseHmZkaxXrsJfjHKdq9IQ53jwejHVSTZY0WhR4ydOeDAsh1o1UDgHV5xrx3s9wb9oqED1bDaGu7APgu618gGrwNzEVv78IpzqhFyf_TAIABcuzdJYy50dyHyhRf4kkOTvcaem80lMW-8kFcoYsXZbbhx--ySL9UE9Z_5whkryHYZHxcOLrlFfpSq8Xkt59XZVFfN199YI_-z7m6Tm3PATGNv4XfIms3vkuu-hOaXe-RjnNPOfCOfxunwQ0yTn9--H-MfpW6PmcZLJ_R0OqYIeGnX5QCNcepYjEHoga-pQz_ldGCnCp8umVruk5Okc9zqBvOKEYHhri4vyxCwhvXQ6kiHewbxjVENroWJRGSiyAiN8M8yMOEoM9rUaqCYrmVcONZE9BnwgKzn49w-JFRkmvHRqDZSynLH56yEqmvGtLKKa60qpF8OrbzwxCDSU0Az6dQrnXqlV67kILEVhJSoUjlXqQQZytYQf-lWyPPCOBY9qctzl3EXCXmavpWD9JQnh1FfHlXI1or1LB5wJDtCVMh2aUwSlwl39qNyO55NJEb2COVZWCFpYRh_8c5_fuWy6dG_7nCbbB60E_m-l757TG74lD-XX7pF1qeXM_sEMeBUPy3m7C9yWTqS
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Extended+ANOVA+F-Test+with+Applications+to+the+Heterogeneity+Problem+in+Meta-Analysis&rft.jtitle=Biometrical+journal&rft.au=Hartung%2C+Joachim&rft.au=Makambi%2C+Kepher+Henry&rft.au=Do%7B%2Fgiflibrary%2F12%2Fgtilde.gif%7Dan+Argac&rft.date=2001-05-01&rft.issn=0323-3847&rft.volume=43&rft.issue=2&rft.spage=135&rft.epage=146&rft_id=info:doi/10.1002%2F1521-4036%28200105%2943%3A2%3C135%3A%3AAID-BIMJ135%3E3.0.CO%3B2-H&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0323-3847&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0323-3847&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0323-3847&client=summon