Mixed Design vs. Nested Design: An Analysis of Factorial Effects in Experimental Design - , Exams of Engineering

Download Mixed Design vs. Nested Design: An Analysis of Factorial Effects in Experimental Design - and more Exams Engineering in PDF only on Docsity! 4/28/2009 1 MIXED DESIGN AND NESTED DESIGN Dr. Yan Liu Department of Biomedical, Industrial and Human Factors Engineering Wright State University Mixed Design
Mixed Factorial Design  Has both with-subject and between-subject factors
Two-Factor Mixed Design: A×(B×S)  One between-subject factor A
Each participant only receives one level of A  One with-subject factor B
Each participant receives all levels of B
Three-Factor Mixed Design: A×B×(C×S)  Two between-subject factors A and B  One with-subject factor C
Three-Factor Mixed Design: C×(A×B×S)  One between-subject factor C  Two with-subject factors A and B 2 4/28/2009 2 A×(B×S) Design Factor A Participant (S) Factor B S Totals A TotalsB1 B2 … Bb A1 s11 y111 y112 … y11b y11. y1.. s12 y121 y122 … y12b y12. … … … … … … s1n y1n1 y1n2 … y1nb y1n. A2 s21 y211 y212 … y21b y21. y2.. s22 y221 y222 … y22b y22. … … … … … … s2n y2n1 y2n2 … y2nb y2n. … … … … … … … Aa sa1 ya11 ya12 … ya1b ya1. ya.. sa2 ya21 ya22 … ya2b ya2. … … … … … … san yan1 yan2 … yanb yan. B Totals y..1 y..2 y..b y… 3 B B1 B2 B3 B4 A A1 x x x x A2 x x x x A3 x x x x A4 x x x x A and B are Crossed (A×B) • Includes all possible combinations of levels of A and B • Can study the interaction effect of A and B B B1 B2 B3 B4 A A1 x A2 x A3 x A4 x A5 x A5 x A7 x A8 x A and B are Nested (B/A) • Each level of B contains a unique set of levels of A • Cannot study the interaction effect of A and B Nested Design 4 4/28/2009 5 Sources of variation df sum of squares mean squares F p- value A a-1 SSA MSA MSA/MSS/AB B b-1 SSB MSB MSB/MSS/AB A×B (a-1)(b-1) SSA×B MSA×B MSA×B/MSS/AB C c-1 SSC MSC MSC /MSS×C/AB A×C (a-1)(c-1) SSA×C MSA×C MSA×C/MSS×C/AB B×C (b-1)(c-1) SSB×C MSB×C MSB×C/MSS×C/AB A×B×C (a-1)(b-1) (c-1) SSA×B×C MSA×B×C MSA×B×C/MSS×C/AB S/AB ab(n-1) SSS/AB MSS/AB S×C/AB ab(c-1)(n-1) SSS×C/AB MSS×C/AB ANOVA Table for A×B×(C×S) Design 9 AB S C C1 C2 C3 A1B1 S1 11 5 3 S2 12 10 5 A1B2 S3 17 11 11 S4 18 16 13 A2B1 S5 20 14 13 S6 12 10 9 A2B2 S7 16 10 10 S8 20 18 14 10 4/28/2009 6 Sources of variation df sum of squares mean squares F p- value A a-1 SSA MSA MSA/MSS×A/C B b-1 SSB MSB MSB/MSS×B/C A×B (a-1)(b-1) SSA×B MSA×B MSA×B/MSS×A×B/C C c-1 SSC MSC MSC /MSS/C A×C (a-1)(c-1) SSA×C MSA×C MSA×C/MSS×A/C B×C (b-1)(c-1) SSB×C MSB×C MSB×C/MSS×B/C A×B×C (a-1)(b-1) (c-1) SSA×B×C MSA×B×C MSA×B×C/MSS×A×B/C S/C c(n-1) SSS/C MSS/C S×A/C c(a-1)(n-1) SSS×A/C MSS×A/C S×B/C c(b-1)(n-1) SSS×B/C MSS×B/C S×A×B/C c(a-1) (b-1)(n-1) SSS×A×B/C MSS×A×B/C ANOVA Table for C×(A×B ×S) Design 11 C S A 1 A 2 A 3 B1 B2 B3 B1 B2 B3 B1 B2 B3 C1 S1 1 1 2 1 3 2 2 4 2 S2 2 3 3 2 4 4 3 5 4 S3 1 2 3 3 3 5 2 5 5 C2 S4 2 1 1 2 2 2 3 3 2 S5 3 2 3 3 4 3 5 5 4 S6 1 2 1 2 3 3 1 3 2 12