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Experiments with Bullet Proof Panels and Various Bullet Types

Experiments with Bullet Proof Panels and Various Bullet Types R.A. Prosser, S.H. Cohen, and R.A. Segars (2000). "Heat as a Factor of Cloth Ballistic Panels by 0.22 Caliber Projectiles," Textile Research Journal, Vol. 70: pp. 709-723. Data Description.

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Experiments with Bullet Proof Panels and Various Bullet Types

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  1. Experiments with Bullet Proof Panels and Various Bullet Types R.A. Prosser, S.H. Cohen, and R.A. Segars (2000). "Heat as a Factor of Cloth Ballistic Panels by 0.22 Caliber Projectiles," Textile Research Journal, Vol. 70: pp. 709-723.

  2. Data Description • Response: V50 – The velocity at which approximately half of a set of projectiles penetrate a fabric panel (m/sec) • Predictors: • Number of layers in the panel (2,6,13,19,25,30,35,40) • Bullet Type (Rounded, Sharp, FSP) • Transformation of Response: Y* = (V50/100)2 • Two Models: • Model 1: 3 Dummy Variables for Bullet Type, No Intercept • Model 2: 2 Dummy Variables for Bullet Type, Intercept

  3. Data/Models (t=3, bullet type, ni=9 layers per bullet type)

  4. Model 1 – Individual Intercepts/Slopes

  5. Model 2 – Dummy Coding (Sharp (j=2), FSP (j=3))

  6. Model 1 – Matrix Formulation

  7. Model 2 – Matrix Formulation

  8. Equations Relating Y to #Layers by Bullet Type Note: Both models give the same lines (ignore rounding for Sharp). Same lines would be obtained if Baseline Category had been Sharp or FSP.

  9. Tests of Hypotheses • Equal Slopes: Allowing for Differences in Bullet Type Intercepts, is the “Layer Effect” the same for each Bullet Type? • Equal Intercepts (Only Makes sense if all slopes are equal): Controlling for # of Layers, are the Bullet Type Effects all Equal? • Equal Variances: Do the error terms of the t = 3 regressions have the same variance?

  10. Testing Equality of Slopes Complete Models (Both 1 and 2) Reduced Models (Both 1 and 2) Conclude Slopes are not all equal Model 2 Model 2

  11. Testing Equality of Intercepts – Assuming Equal Slopes Note: Does not apply to this problem, just providing formulas.

  12. Bartlett’s Test of Equal Variances MSE

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