Linganisha mbinu

	Utafiti wa Kiutendaji wa Nyongeza Nyingi	Path Analysis
Nyanja	Muundo wa Utafiti	Takwimu
Familia	Process / pipeline	Latent structure
Mwaka wa asili	1920s–1930s (multivariate extensions); consolidated in applied social science by 1970s	1921
Mwanzilishi	Developed from Galton and Pearson's bivariate correlation work, extended to multivariate contexts by R.A. Fisher, Harold Hotelling, and others	Sewall Wright
Aina	Non-experimental quantitative research design	Causal / mediation model
Chanzo asilia	Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson. ISBN: 978-0134790541	Wright, S. (1921). Correlation and causation. Journal of Agricultural Research, 20(7), 557–585.
Majina mbadala	multivariate correlational design, multivariate relational research, multiple-variable correlational study, multivariate associational research	PA, path coefficient analysis, observed-variable SEM, causal path modeling
Zinazohusiana	2	5
Muhtasari	Multivariate correlational research is a non-experimental quantitative design that examines the simultaneous associations among three or more variables. Rather than manipulating conditions, the researcher measures naturally occurring variables and uses techniques such as multiple regression, canonical correlation, or structural equation modeling to map the pattern and strength of their interrelationships. It is the dominant design when the goal is to understand how a set of predictors jointly relates to one or more outcome variables.	Path analysis tests a researcher-specified causal diagram among observed variables by decomposing their intercorrelations into direct effects, indirect (mediated) effects, and spurious associations. Developed by Sewall Wright in 1921, it is the observed-variable special case of structural equation modeling and remains a standard tool for theory-driven multivariate causal inference.