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	Cluster Randomized Solomon Four-Group Design	बहुस्तरीय मॉडलिंग
क्षेत्र	प्रयोगात्मक अभिकल्प	अनुसंधान सांख्यिकी
परिवार	Process / pipeline	Process / pipeline
उद्भव वर्ष	1949 (Solomon design); cluster extension formalized in 1990s	1992
प्रवर्तक	Richard L. Solomon (four-group logic, 1949); cluster randomization methods developed by Murray and colleagues in the 1990s	Anthony Bryk and Stephen Raudenbush
प्रकार	Experimental design	Method
मौलिक स्रोत	Solomon, R. L. (1949). An extension of control group design. Psychological Bulletin, 46(2), 137–150.	Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE Publications.
उपनाम	CR-S4GD, cluster-randomized four-group design, group-randomized Solomon design, Solomon four-group cluster trial	HLM, mixed-effects models, random effects models, MLM
संबंधित	6	3
सारांश	The cluster randomized Solomon four-group design combines cluster randomization — assigning intact groups such as schools, clinics, or communities to conditions — with the Solomon four-group structure that isolates the effect of pretesting. Four clusters (or sets of clusters) are created: two receive the treatment and two serve as controls, with only one treatment cluster and one control cluster receiving a pretest, while the others go straight to the posttest. This structure simultaneously controls for pretest sensitization and the logistical constraint that individual randomization is infeasible.	Multilevel modeling (also called hierarchical linear modeling, mixed-effects modeling) is a statistical framework for analyzing data organized in nested or clustered structures—students within schools, patients within hospitals, repeated measures within individuals. Developed by Bryk and Raudenbush (1992), it accounts for dependency among observations and partitions variance into levels (within-cluster and between-cluster), enabling valid inference and revealing context effects. Essential in education, medicine, organizational research, and any field where data have natural hierarchies.