Slide 1: Welcome to Statistics using Catapults
Welcome to Statistics using Catapults September 25, 2015 ©2012 Micron Foundation, Inc. | 1
Slide 2: Linear Equation
Linear Equation What do m and b represent in the equation y=mx+b? 20 18 y = 2x + 12 16 14 12 y 10 8 6 4 2 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 x Will you ever use this in the “real” world? September 25, 2015 ©2012 Micron Foundation, Inc. | 2
Slide 3: Statistics
Statistics ▶ The science of collecting, analyzing, interpreting, and presenting data. ▶ Applied mathematics ▶ Utilizes the scientific method 1. State the Problem 2. Research Your Topic 3. Develop a Hypothesis 4. Perform an Experiment 5. Gather and Record Data 6. Analyze Your Results 7. Draw Conclusi
Slide 4: Statistically Designed Experiments
Statistically Designed Experiments ▶ A designed experiment is a series of tests Change input variables in an organized method Measure the effect on the output variables ▶ A statistically designed experiment Limits the number of experimental combinations (variables) Provides a more organized
Slide 5: The Catapult Experiment
The Catapult Experiment ▶ Learn about the catapult How many variables are on the Catapult? What other variables exist? We will ‘ignore’ some variables ▶ Launch and collect data Each team (4-5 students) has its own Catapult Record data ▶ Analyze & share results Numbers & Graphs September
Slide 6: Catapult Variables
Catapult Variables How many variables/factors? How many settings per variable/factor? How many possible combinations of settings? September 25, 2015 ©2012 Micron Foundation, Inc. | 6
Slide 7: Catapult Variables
Catapult Variables How many variables/factors? 5 How many settings per variable/factor? 3 How many possible combinations of settings? 35 =243 September 25, 2015 ©2012 Micron Foundation, Inc. | 7
Slide 8: Catapult Variables
Catapult Variables Make TWO of the variables constant - Arm Tension - Upright Tension Now there are just THREE variables – how many combinations? Do we need to use all 3 settings in our first experiment? September 25, 2015 ©2012 Micron Foundation, Inc. | 8
Slide 9: Catapult Variables
Catapult Variables Make TWO of the variables constant - Arm Tension - Upright Tension Now there are just THREE variables – how many combinations? 3 3 =27 Do we need to use all 3 settings in our first experiment? September 25, 2015 ©2012 Micron Foundation, Inc. | 9
Slide 10: Statistical Hypothesis
Statistical Hypothesis ▶ Two complementary hypotheses statements: Null Hypothesis: None of the 3 factors affect the distance the ball travels Alternative Hypothesis: At least one factor affects the distance the ball travels September 25, 2015 ©2012 Micron Foundation, Inc. | 10
Slide 11: Catapult Experiment Worksheet
Catapult Experiment Worksheet ▶ 3 variables at 2 levels each = 2 x 2 x 2 = 23 = 8 combos ▶ Perform the launch of each combination 3 times each Distance Shot Combo Elevator Ball Seat Turntable 1 2 3 1 HIGH HIGH HIGH 2 HIGH HIGH low 3 HIGH low HIGH 4 HIGH low low 5 low HIGH HIGH 6 low HIGH low 7 low l
Slide 12: The Catapult Experiment
The Catapult Experiment ▶ Team roles: LAUNCHER – Launches the ping pong balls from the catapult STABILIZER – Holds the catapult launch pad in place PROCESS LEAD – Guide the team through process SPOTTER – Note where ball first hits DATA COLLECTOR – record distance on paper in centimeters
Slide 13: Let’s Start the Experiment
Let’s Start the Experiment ▶ Following the Scientific Method: Step #1 – State your problem • Identify if there is a specific combination of settings that will launch the ping pong ball the longest distance Step #2 – Research your topic • Launch each of the 3 ping pong balls at different settings
Slide 14: Continuing with the Scientific Method
Continuing with the Scientific Method Step #3 – Develop a Hypothesis • You have been given the two Hypotheses, but can you make your own Hypothesis about which setting will send the ping pong ball the farthest? • Note that on your datasheet by putting a star next to the combo setting in the table
Slide 15: Quickly decide who will perform each team role
Quickly decide who will perform each team role LAUNCHER – Launches the ping pong balls from the catapult STABILIZER – Holds the catapult launch pad in place PROCESS LEAD – Guide the team through process SPOTTER – Note where ball first hits DATA COLLECTOR – record distance on paper in centi
Slide 16: Analyze the Results
Analyze the Results September 25, 2015 ©2012 Micron Foundation, Inc. | 16
Slide 17: Questions
Questions 1. Which combination gave you the longest distance? Class A Seat L/H Elevator L/H * Ball B * TurnCTable L/H D E F Session Team 1 Team 2 Team 3 Team 4 Team 5 2. Did the Elevator, Ball Seat OR Turn Table have the largest effect on the distances the ping pong ball flew? How much of an eff
Slide 18: Can we model the results?
Can we model the results? ▶ Example ONE Small differences in the 3 trials September 25, 2015 ©2012 Micron Foundation, Inc. | 18
Slide 19: Can we model the results?
Can we model the results? ▶ Example TWO 140 120 100 Trial 1 Distance 80 Trial 2 Large differences Trial 3 in the 3 trials 60 40 20 0 1 - HHH 2 - HHL 3 - HLH 4 - HLL 5 - LHH 6 - LHL 7 - LLH 8 - LLL Catapult Experiment 140 120 100 Distance 80 Trial 1 60 Trial 2 40 Trial 3 20 0 1 - HHH 2 - HHL 3 - HLH
Slide 20: How much did one factor affect the distance?
How much did one factor affect the distance? ▶ Changing the turntable from Low to High reduced the distance by 27.4 inches on average! 100.00 80.00 Distance (inches) 60.00 40.00 20.00 0.00 TT = Low TT = High September 25, 2015 ©2012 Micron Foundation, Inc. | 20
Slide 21: Interaction Effect
Interaction Effect ▶ Distance depends on the combination of different factors 100.00 100.00 Distance (inches) 80.00 Distance (inches) 80.00 60.00 TT = Low 60.00 40.00 TT = High 40.00 TT = Low 20.00 TT = High 20.00 0.00 EH = Low EH = High 0.00 BS = Low BS = High September 25, 2015 ©2012 Micron Founda
Slide 22: Conclusion
Conclusion ▶ You performed a statistically designed experiment Was this a better method than randomly trying different settings? ▶ Were we able to disprove the statistical hypothesis based on the experimental results? ▶ We perform statistically designed experiments at Micron to optimize our produc
Slide 23: More Details
More Details September 25, 2015 ©2012 Micron Foundation, Inc. | 23
Slide 24: Can we model the results?
Can we model the results? ▶ Example – 1 rubber band; Josie launch; DaRon measure ▶ Effect = average change in distance when going from L to H setting (negative values indicate lost distance) September 25, 2015 ©2012 Micron Foundation, Inc. | 24
Slide 25: Can we model the results? Yes!!!
Can we model the results? Yes!!! ▶ The overall mean (intercept) and effects (1/2 of each effect) are used to build the linear equation L or Low setting = -1 H or High setting = +1 y b m1 x1 m2 x2 m3 x3 m12 x1 x2 m13x1 x3 m23x2 x3 m123x1 x2 x3 y 69.04 1.8751 x1 2.042 x2 13.708
Slide 26: Model Predictions for MMM Setting
Model Predictions for MMM Setting ▶ Elevator Height = M (middle), Ball Seat = M, and Turntable =M L or Low setting = -1 H or High setting = +1 M or Middle setting = 0 ▶ Actual distance values: Distance Shot Combo Elevator Ball Seat Turntable Trial 1 Trial 2 Trial 3 Average MMM 0 0 0 70 68 72 70 Sept
Slide 27: What about physics versus statistics?
What about physics versus statistics? ▶ Angles? Trajectory? Velocity? September 25, 2015 ©2012 Micron Foundation, Inc. | 27