مقایسهٔ روش‌ها

	پژوهش علی-مقایسه‌ای چندمتغیره	تحلیل واریانس چندمتغیره (MANOVA)
حوزه	طراحی پژوهش	آمار
خانواده	Process / pipeline	Hypothesis test
سال پیدایش	Mid-20th century onward; multivariate extension systematized 1970s–1990s	1932
پدیدآور	Extension of causal-comparative tradition (cf. Chapin, 1947; Gay, Mills & Airasian)	Samuel Stanley Wilks (Wilks' Lambda, 1932); Roy, Hotelling, Pillai (mid-20th c.)
نوع	Quantitative non-experimental comparative design	Parametric multivariate mean comparison
منبع بنیادین	Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2019). How to Design and Evaluate Research in Education (10th ed.). McGraw-Hill. ISBN: 978-1260085594	Tabachnick, B.G. & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Pearson. ISBN: 978-0205849574
نام‌های دیگر	multivariate causal-comparative design, MANOVA causal-comparative study, multi-outcome ex post facto research, multivariate ex post facto design	Multivariate ANOVA, Çok Değişkenli ANOVA (MANOVA)
مرتبط	6	5
خلاصه	Multivariate causal-comparative research is a quantitative, non-experimental design that investigates whether pre-existing group differences (defined by a naturally occurring categorical variable) are associated with differences across multiple outcome variables considered simultaneously. By extending the classic causal-comparative framework to several dependent variables at once, it reduces Type I error inflation and captures the correlated structure of outcomes that univariate comparisons would miss.	MANOVA is a parametric hypothesis test that simultaneously compares group means across multiple continuous dependent variables, controlling the inflation of Type I error that would result from running separate ANOVAs. Key multivariate test statistics — Wilks' Lambda, Pillai's Trace, Hotelling-Lawley Trace, and Roy's Greatest Root — were developed between the 1930s and 1950s, with Wilks' Lambda formalised by Samuel Stanley Wilks in 1932.