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Nested Design

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. Data Description. 2 Formulations of Shampoo (A and B)

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Nested Design

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  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 • N=2x8x5=80 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 (P=0.7390) Conclude no formulation differences on combability H0: sb2 = 0 HA: sb2> 0 T.S. FSwatch(F) = 9.43 (P=.0000) Conclude Swatch effects vary with respect to combability

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