lacrosse - 2-Factor ANOVA Impact on Lacrosse Helmets S.V....

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Unformatted text preview: 2-Factor ANOVA Impact on Lacrosse Helmets S.V. Caswell, R.G. Deivert (2002). “Lacrosse Helmet Designs and the Effects of Impact Forces”, Journal of Athletic Training, 37(2):164-171. Data Description • Response: Gadd Severity Index (Higher scores = more severe) • Factor A: Model (a=4 Levels) – Sports Helmets Cascade (i=1) – Sports Helmets Cascade Air Fit (i=2) – Sports Helmets Ultralte (i=3) – Bacharach Ultralte (i=4) • Factor B: Side (b=2 Levels) – Front (j=1) – Back (j=2) • Replicates: n=10 per Treatment • Model: Yijk = µ + α i + β j + αβij + ε ijk i = 1,2,3,4 j = 1,2 k = 1,..,10 Data - Mean (SD) Model\Side SHC (1) SHCAF (2) SHCUL (3) BUL (4) Front (1) 1166.1 (152.4) 1117.6 (216.2) 857.0 (151.5) 1222.8 (123.1) Back (2) 974.5 (73.0) 1022.1 (105.1) 1376.3 (211.4) 1496.5 (184.0) 1166.1 + 974.5 = 1070.3 y 2.. = 1069.85 y 3.. = 1116.65 y 4.. = 1359.65 2 1166.1 + 1117.6 + 857.0 + 1222.8 y .1 . = = 1090.875 y .2. = 1217.35 y ... = 1154.1125 4 y1.. = Data - Factor Level (Interaction) Plot GADD Severity Index by Model and Side 1600 1500 1400 1300 GADD Index 1200 Front 1100 Back 1000 900 800 700 600 0 1 2 3 Model 4 5 ANOVA [ Model (A) : SSA = 2(10) (1070.3 − 1154.1125) 2 + ... + (1359.65 − 1154.1125) 2 = 1155459 [ Side (B) : SSB = 4(10) (1090.875 − 1154.125) 2 + (1217.35 − 1154.125) 2 = 319919 (1166.1 − 1070.3 − 1090.875 + 1154.125) 2 + ... ModelxSide (AB) : SSAB = 10 = 1632179 + (1496.5 − 1359.65 − 1217.35 + 1154.125) 2 [ Error : SSE = (10 − 1) (152.4) 2 + ... + (184) 2 = 1826955 ANOVA Source Model Side ModelxSide Error Total df 3 1 3 72 79 SS 1155459 319919 1632179 1826955 4934512 MS 385153 319919 544060 25374 F 15.18 12.61 21.44 P-value 9.4611E-08 0.00068161 4.9865E-10 Post Hoc Comparisons (Model w/in Side) • MSE=25374, df=72 n=10, 4 Brands, 6 Pairs/Side 25374 W ≈ 3.74 = 188.4 10 2(25374) B ≈ 2.715 = 193.4 10 Models 1 vs 2 1 vs 3 1 vs 4 2 vs 3 2 vs 4 3 vs 4 Front diff 48.5 309.1 -56.7 260.6 -105.2 -365.8 Back Diff -47.6 -401.8 -522 -354.2 -474.4 -120.2 Front 3 2 1 4 Back 1234 ...
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lacrosse - 2-Factor ANOVA Impact on Lacrosse Helmets S.V....

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