Cited by 716Statistical Methods and ApplicationsPsychometric Methodologies and TestingAdvanced Statistical Methods and Models

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An Introduction to Applied Multivariate Analysis

Raykov, Tenko, Marcoulides, George A.·2008·Routledge eBooks

DOI 10.4324/9780203809532

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Abstract

This comprehensive text introduces readers to the most commonly used multivariate techniques at an introductory, non-technical level. By focusing on the fundamentals, readers are better prepared for more advanced applied pursuits, particularly on topics that are most critical to the behavioral, social, and educational sciences. Analogies betwe

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“The Mardia’s coefficient for the current sample data was 481.131, which is below the expected value of 1224 when computed for the 34 observed items in the model (Raykov & Marcoulides, 2008).”
Influential
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AÇIKGÜL, K., & Şad, S. N. (2026) · SAGE Open · doi:10.1177/21582440251413449 · Cited by 10
“Also, the data can be considered to meet multivariate normality since the Mardia kurtosis value of 357.825 is less than the critical threshold of 1,763 (p[p+2] = 41 3 43) (Raykov & Marcoulides, 2008).”
Influential
Emotional attachment and resistance to change in the use of technology: A study among Chinese university music teachers
Wang, J., Huang, F., & Teo, T. P. (2025) · PLoS ONE · doi:10.1371/journal.pone.0327205 · Cited by 8
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“Russell’s (1980) circumplex model provides a framework for the IAPZ (see Russell, 1980, 1997; Russell, Weiss, & Mendelsohn, 1989; Watson, 2002).”
BackgroundInfluential
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Lai, C. (2020) · Journal of Computers in Education · doi:10.1007/s40692-020-00163-8 · Cited by 5
“In addition, Mardia’s coefficient was 240.22, indicating a multivariate normal distribution of the data (Bollen 1989; Raykov and Marcoulides 2008).”
BackgroundMethodInfluential
Continuing CHAAOS: Vocabulary Intervention for Students With Disabilities in Eighth Grade Who Are Also English Learners
O’Connor, R. E., Sanchez, V. M., Jones, B. T., Suchilt, L., Youkhanna, V., & Beach, K. D. (2020) · Learning Disability Quarterly · doi:10.1177/0731948720922818 · Cited by 6
“Multivariate analysis of covariance (MANCOVA) allowed us to examine group differences on several dependent variables simultaneously while also controlling for Type I error and taking into account the interrelations among variables (Raykov & Marcoulides, 2008).”
Method
Development and initial validation of the nonalcoholic fatty liver disease self‐management questionnaire
Kwon, O. Y., Jang, Y., Lee, J. Y., Kim, S. U., & Ahn, S. H. (2021) · Research in Nursing & Health · doi:10.1002/nur.22164 · Cited by 6
Effectiveness of an Innovative Sensory Approach to Improve Children’s Nutritional Choices
Meleleo, D., Susca, G., Buccheri, V. A., Lamanna, G., Cassano, L., Chirico, V. D., Mustica, S., Caroli, M., & Bartolomeo, N. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph18126462 · Cited by 4
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The Influence of Proof Understanding Strategies and Negative Self-concept on Undergraduate Afghan Students’ Achievement in Modern Algebra
Mowahed, A. K., Song, N., Yang, X., & Chang-gen, P. (2019) · International Electronic Journal of Mathematics Education · doi:10.29333/iejme/5886 · Cited by 7
“As suggested by Raykov and Marcoulides (2008) the value for Mardia’s s multivariate skewness coefficient 62.89 was less than p(p+2) = 16 (18) = 288 where p = total number of observed indicators or items = 16, so the requirement of multivariate normality was therefore satisfied and the data…”
BackgroundInfluential
Performance of Some Factor Analysis Techniques
Nwosu, D. F., Ekhosuehi, V. U., & Mbegbu, J. I. (2020) · Annals of Data Science · doi:10.1007/s40745-020-00260-6 · Cited by 5
Inbound Halal Logistics Practices: A Case of Local Mosques
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“The Bartlett’s test of sphericity showed significant at 1% level of significance, showing that the factor analysis with variables was appropriate (Raykov & Marcoulides, 2012). are valid and reliable.”
Method
KALKINMA AJANSLARININ KURUMSAL SORUNLARI VE ÇÖZÜMLERİNE İLİŞKİN AMPİRİK ANALİZ: TÜRKİYE ÖRNEĞİ
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Examining the Effects of Relationship Education for Same-Sex Couples: A Randomized Control Trial
Barden, S. M., Carlson, R. G., Toomey, T. M., Locklear, L. R., Taylor, D. D., & Silverio, N. (2021) · Marriage & Family Review · doi:10.1080/01494929.2021.1921896 · Cited by 5
“Finally, we conducted a multilevel model to examine the influence of completion status on our outcomes of interest (following the recommendations of Raykov & Marcoulides, 2008).”
Method
Imagen de Responsabilidad Social Corporativa e Intención de Compra Millennial
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Effect of Conscientiousness on Social Loafing Among Male and Female Chinese University Students
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Modelling mathematics teachers’ intention to use the dynamic Geometry environments in Macau: An SEM approach
Zhou, M., Chan, K. K., & Teo, T. P. (2016) · Murdoch University Research Portal · Cited by 5
The Development of Mathematical Literacy Self-Efficacy Scale for Middle School: A Reliability And Validity Study
Baypinar, K., & Tarım, K. (2019) · Cukurova University Faculty of Education Journal · doi:10.14812/cuefd.415291 · Cited by 5
Influencia de los factores internos en la competitividad actual y futura en el sector comercial y servicios. Análisis multivariante percepcional / Influence of internal factors on current and future competitiveness in the commercial sector and services. Perceptional multivarial analysis
Díaz, D. A. (2018) · RICEA Revista Iberoamericana de Contaduría Economía y Administración · doi:10.23913/ricea.v7i13.110 · Cited by 5
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“Mardia’s (1974) Multivariate kurtosis values were calculated (575), which exceeded the model’s value (28.20) (Raykov & Marcoulides, 2008).”
Influential
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“For the test for multivariate normality, the Mardia’s coefficient was 185.051, which was higher than the value of 120 computed based on the Formula p (p + 2), where p stands for the number of observed variables in the model 56 .”
MethodInfluential
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“CFA using the maximum likelihood estimation method was assessed to account for possible correlation amongst the higher-order factor components (Raykov & Marcoulides, 2008; Schumacker & Lomax, 2004).”
Method
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“The value for the KMO-measure is relatively low, but on an acceptable level (Bühl, 2008, p.540; Raykov and Marcoulides, 2008, p.226).”
Influential
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“Se realizó análisis de factores exploratorio (34).”
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“This rate is lower than 5% (Çokluk et al., 2010; Raykov & Marcoulides, 2008).”
Background
Simultaneous confidence tubes for comparing several multivariate linear regression models
Peng, J., Liu, W., Bretz, F., & Hayter, A. J. (2021) · Biometrical Journal · doi:10.1002/bimj.202000148 · Cited by 5
“For the data mentioned in Section 1, we follow Raykov and Marcoulides (2008) and fit a bivariate linear model of the responses y1 = fr and y2 = cf on the covariate pretest measurement on inductive reasoning, which is the only predictor x = ir for each of the two groups of students: untrained (group 1) and trained (gro…”
Method
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“In contrast, the statistic of Pillai’s Trace was checked if the result of Box’s M was statistically significant (Raykov & Marcoulides, 2008).”
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Abbas, M. A. Y., Setyadi, D., Paminto, A., et al. (2023) · Journal of Law and Sustainable Development · doi:10.55908/sdgs.v11i9.991 · Cited by 4
“The hypothesis testing in this work utilized multiple linear regression analysis using the moderated regression analysis (MRA) model, as described by Raykov and Marcoulides (2008), Booth (2003), and Timm (2002).”
Method
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Origin and Production of Silver in Early Medieval Poland
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“If the chi-square test statistics has a significant value, it indicates that the data comes from the multivariate normal distribution (Field, 2013; Raykov & Marcoulides, 2008).”
BackgroundInfluential
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Soares, F., Cunha, N., & Frisoli, P. (2021) · Journal on Education in Emergencies · doi:10.33682/f059-7nxk · Cited by 4
“164 Journal on Education in Emergencies SOARES, MENEZES CUNHA, AND FRISOLI They are similar to correlation coefficients and range between -1.00 and 1.00 (Raykov and Marcoulides 2008).”
BackgroundInfluential
The Role of Discipline in Determining Turkish Pre-Service Teachers' Behavioral Intentions to Use ICT
Ursavaş, Ö. F., Şahin, S., & McIlroy, D. (2014) · TED EĞİTİM VE BİLİM · doi:10.15390/eb.2014.3357 · Cited by 4
“For multivariate normality, the critical value was found to be 288 based on the equation, p(p + 2) advocated by Raykov and Marcoulides (2008). In this equation, p refers to the number of observed variables (scale items), which was 16 in the case of the present study.”
Method
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Vibration and sound signal analysis in gas stirred ladles
Yenus, J. (2017) · Swinburne figshare (Swinburne University of Technology) · doi:10.25916/sut.26279200 · Cited by 4
Validation and Reliability of the Dyslexia Adult Checklist in Screening for DyslexiaPreprint
Stark, Z., Elalouf, K., Soldano, V., et al. (2023) · doi:10.31234/osf.io/2r5ct · Cited by 4
Evaluation of Maximal Reliability for Multidimensional Measuring Instruments Using Structural Equation Modeling
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“Hence, the OLC weights also exist and are unique (up to sign and once normalized so that their vector has unit length; e.g., Raykov & Marcoulides, 2008) in the setting of interest to this article.”
Self-citation
Psychometric testing of the Moral Neutralization Scale-Nurse Version (MNS-NV): An exploratory and confirmatory factor analyses
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Psychological resilience and post-traumatic stress disorder as serial mediators between social connectedness and quality of life among individuals exposed to 2023 Kahramanmaras earthquakes
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“Factor correlations exceeded |0.32| (Raykov and Marcoulides 2008), and four factors with eigenvalues above 1 were identified.”
Influential
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Critical Success Factors for Supplier Selection and Performance Enhancement in the Medical Device Industry: An Industry 4.0 Approach
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Transcriptomic and lipid profiling analysis reveals a functional interplay between testosterone and growth hormone in hypothyroid liver
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“We determined the multiple normality assumption with Mardia’s skewness (b1d = 0.039, chi = 1.735, df = 1.00 p = 0.169 > 0.05), Mardia’s kurtosis (b2d = 2.590, z = −1,375, p = 0.188 > 0.05) for this study (Cain et al ., 2017; Gana & Broc, 2019; Hahs-Vaughn, 2017; Raykov & Marcoulides, 2008).”
Influential
Between obligations and leisure: an examination of non-work activities among the generation 55+ in Poland and Czechia
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The Relationships between Teacher Quality and Sixth Grade Students’ Mathematics Competencies in Kenya and Zimbabwe
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6., 7. ve 8. Sınıf Öğrencilerinin Okuma Kaygılarının Türkçe Dersine İlişkin Tutumları Üzerindeki Etkisinde Sınıf Düzeyinin ve Cinsiyetin Rolü
BAKİ, Y. (2018) · Hacettepe University Journal of Education · doi:10.16986/huje.2018038524 · Cited by 3
Psychometric Properties of the Functional Social Support Domain of Perinatal Infant Care Social Support
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“65.(18) Factor extraction was conducted by considering a minimum value of 0.”
Method
Validation of the Job Crafting Scale in Latin American Workers
Gutiérrez-Carvajal, O. I., Polo-Vargas, J. D., Montealegre, A. R. V., Zumárraga-Espinosa, M., Ocaña, X. R., Segovia-Marín, J. V., & Calderín, L. (2022) · Anales de Psicología · doi:10.6018/analesps.472261 · Cited by 3
“According to this test, and following the approach of Raykov and Marcoulides (2008), there is multivariate normality when the Mardia multivariate kurtosis coefficient (CMM) does not exceed the value of p (p + 2), where p is the number of observed variables or, in this case, the items of the…”
Method
SOSYAL DIŞLANMANIN PSİKOLOJİK İYİ OLUŞ ÜZERİNDEKİ ETKİSİNDE BABACAN LİDERLİĞİN ARACI ROLÜ
ÇİÇEK, B., & Aktaş, K. (2022) · İnönü University International Journal of Social Sciences (INIJOSS) · doi:10.54282/inijoss.1064237 · Cited by 4
Assessing the Structural Validity of the Measure of Processes of Care (MPOC-20) in Children with Epilepsy
Joachim, K. C. (2014) · Scholarship@Western (Western University) · Cited by 3
ÜNİVERSİTE ÖĞRENCİLERİNİN GİRİŞİMCİ ÖZELLİKLERİNİN İNCELENMESİ
Akman, S. U., & Bektaş, H. (2015) · Marmara Üniversitesi İktisadi ve İdari Bilimler Dergisi · doi:10.14780/iibd.56366 · Cited by 3
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Self-citation
Dimensions of Familial Allocentrism in Brazilian Mothers from State Capitals and Small Cities
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Effects of poultry building design on indoor air quality in humid climates.
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Retracted
Understanding Contingent Faculty: A Quantitative Study of Engagement, Satisfaction, Commitment, and Mentoring Needs
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“However, Mardia’s multivariate kurtosis and skewness values were found to be statistically significant (p < .05), indicating a violation of the assumption of multivariate normality (Mardia, 1985; Raykov & Marcoulides, 2008).”
Modeling AI‐Assisted English Academic Writing: Insights From L2 Motivational Self System and Technology Acceptance Model
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Testing multivariate mean collinearity via latent variable modelling
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Self-citation
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“Discriminant analysis (DA) is a method that can be used in a multi-group setting to determine how a set of dependent variables or explanatory variables is related to group membership and, in particular, how they may be combined so as to enhance one’s understanding of group differences (Raykov and Marcoulides 2008).”
Method
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“(Brown, 2006; Hu & Bentler, 1999; Jöreskog & Kline, 2005; Sümer, 2000; Raykov & Marcoulides, 2008).”
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“This technique, according to Raykov and Marcoulides (2008), is used to study several characteristics and correlations between various elements of the same problem.”
Okuma Kaygısı ve Hatalarının Okuduğunu Anlama Başarımı Üzerindeki Yordayıcı Rolü: Bir Yapısal Eşitlik Modellemesi
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“Because a departure from MVN can often be detected by finding uni-variate non-normality of attended variables (Raykov & Marcoulides, 2008), we examined values of SK and KU to assess the assumption of normality of score distributions on subscales in the CBI.”
Development and validation of Academic Publishing Involution Scale for College Teachers in China
Zhang, Y., Yang, Y., Xia, J., et al. (2024) · Current Psychology · doi:10.1007/s12144-024-07183-y · Cited by 2
“This value is less than the recommended value p*( p + 2) where p = total number of observed indicators, 12*(12 + 2) = 168, by Raykov and Marcoulides (2008).”
Tourist attitude towards performing arts heritage: case study of Cantonese opera in China
Luo, J. M., Kou, C. F., & Yang, J. (2025) · Cogent Social Sciences · doi:10.1080/23311886.2024.2447395 · Cited by 4
“Given that the multivariate kurtosis value of 180.274 is less than the p(p + 2) = 1155 and the number of observed variable (p) is 33, the data are reasonably assumed to be multivariate normal (raykov & marcoulides, 2008).”
Influential

Authors: Raykov, T., & Marcoulides, G. A.
ORCID: Raykov, Tenko
Venue: Routledge eBooks
Publisher: Routledge
Published: 2008-03-10
DOI: 10.4324/9780203809532
OpenAlex: W619790032
Cited by: 716
References: 0
Citations by year: 2026: 30 · 2025: 54 · 2024: 48 · 2023: 52 · 2022: 55 · 2021: 51 · 2020: 52 · 2019: 57 · 2018: 34 · 2017: 38 · 2016: 42 · 2015: 52 · 2014: 36 · 2013: 50 · 2012: 19
FWCI: 5.12
Type: book
Language: en
Open access: closed
Locations: Routledge eBooks (publishedVersion)
CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
Routledge eBooks
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Keywords: multivariate analysis, multivariate techniques, behavioral science, social sciences, educational sciences, statistical analysis

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An Introduction to Applied Multivariate Analysis

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