Nested Design

1
Nested Design

• Comparison of 2 Shampoo Formulations on Hair
  Combability
• M.L. Garcia and J. Diaz (1976). Combability
  Measurements on Human Hair, Journal of the
  Society of Cosmetic Chemists, Vol.27 pp.379-398

2
Data Description

• 2 Formulations of Shampoo (A and B)
• 16 Hair Swatches Prepared (8 for A, 8 for B)
• 5 Test Runs Made per Swatch (Replicates)
• Combability Measurements made before and after
  shampooing (we consider only AFTER here)
• Shampoo Treated as FIXED Factor, Swatch RANDOM
• N2x8x580 Measurements

3
Statistical Model
Note For Computational purposes, we will label
the swatches 1,,16 and not 1,,8 separately for
each shampoo
4
Data
5
Summary Statistics
6
Sums of Squares
7
ANOVA Tests of Factor Effects
H0 a1 a2 0 HA a1 ? a2 T.S.
FForm 0.112 (P0.7390) Conclude no
formulation differences on combability H0 sb2
0 HA sb2 gt 0 T.S. FSwatch(F) 9.43
(P.0000) Conclude Swatch effects vary with
respect to combability