RA Prosser SH Cohen and RA Segars 2000 Heat as a Factor of Cloth Ballistic Panels by 022 Caliber Projectiles Textile Research Journal Vol 70 pp 709723 Data Description Response V50 The velocity at which approximately half of a set of projectiles penetrate a fabric pa ID: 179580
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Slide1
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.Slide2
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, InterceptSlide3
Data/Models (t=3, bullet type,
n
i
=9 layers per bullet type)Slide4
Model 1 – Individual Intercepts/SlopesSlide5
Model 2 – Dummy Coding (Sharp (j=2), FSP (j=3))Slide6
Model 1 – Matrix FormulationSlide7
Model 2 – Matrix FormulationSlide8
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.Slide9
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?Slide10
Testing Equality of Slopes
Complete Models (Both 1 and 2)
Reduced Models (Both 1 and 2)
Model 2
Model 2
Conclude Slopes are not all equalSlide11Slide12
Testing Equality of Intercepts – Assuming Equal Slopes
Note: Does not apply to this problem, just providing formulas.Slide13
Bartlett’s Test of Equal Variances
MSE