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analysis of variance noteshells 2

analysis of variance noteshells 2 - Multiple-sample...

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1 ANOVA 1 Multiple-sample Comparisons Analysis of Variance Chapter 11 ANOVA 2 Comparing three samples A sporting goods manufacturer is testing three "dimple" design patterns to see which one yields the longest distance.
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2 ANOVA 3 What do dimples do? head2right Different layouts control various aspects of ball flight. head2right Some dimple designs are even banned by the USGA. ANOVA 4 The experiment head2right Ten balls of each type were going to be used in the experiment. In the first trial, two different professional golfers were to hit half the balls each in a random order. head2right It didn’t quite work out when one pulled a muscle before finishing. head2right So, a second trial used a golf-ball hitting robot.
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3 ANOVA 5 GolfBallDesign.XLS Three golf ball dimple designs Asymmetric, Equal-Spaced and Oval Driven By Human Golfers Driven by Golf-Ball Hitting Robot Asymm EqSpc Oval AsymmR EqSpcR OvalR 216 217 224 221 225 231 217 218 227 222 226 233 218 222 231 222 226 235 219 224 232 223 228 237 223 229 236 224 229 237 225 235 241 224 231 238 234 237 245 225 232 238 236 239 247 226 233 239 237 240 248 229 233 244 249 232 233 245 ANOVA 6 Average distance travelled 1. Averages about the same in both trials. 2. “Oval” looks best, but we don’t know what difference is significant. 3. For that, we also need to consider the variation within each type of ball. Design Golfers Machine Asymmetric 225.0 224.8 EquiSpace 229.0 229.6 Oval 238.0 237.7
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4 ANOVA 7 Balls Driven By Human Golfers Asymm EqSpc Oval 210 215 220 225 230 235 240 245 250 255 260 Balls driven by golfers Lots of overlap ANOVA 8 Balls Driven By Golf-Ball Hitting Robot AsymmR EqSpcR OvalR 210 215 220 225 230 235 240 245 250 255 260 Balls driven by machine Much Less Overlap
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5 ANOVA 9 All together for comparison Both Data Sets Together Asymm EqSpc Oval AsymmR EqSpcR OvalR 210 215 220 225 230 235 240 245 250 255 260 Less variation with machine-driven balls ANOVA 10 Two samples: what’s significant? For significance, we need to have either T CALC > +2 or T CALC < -2. If we square the whole thing, 4 or more shows significance. + - = 2 1 2 2 1 1 1 n n s X X T p CALC
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6 ANOVA 11 A new procedure head2right How do we compare 3 means to each other to look for differences? head2right We can generalize the denominator (compute S p across more groups).
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