Welcome to Statistics using Catapults€¦ · 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

1 1 ©2012 Micron Foundation, Inc. |

Welcome to Statistics using Catapults

September 25, 2015


Linear Equation

What do m and b represent in the equation y=mx+b?

Will you ever use this in the “real” world?

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y = 2x + 12

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-5 -4 -3 -2 -1 0 1 2 3 4 5

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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 Conclusions

8. Report Your Results and Conclusion

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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 experiment

Run fewer number of experiments (less resources, less time, less chaos)

Provides a statistical model showing the relationship between the

input variables (x factors) and output variable (y response)

y= mx + b y = b + m1x1 + m2x2 + … + mixi

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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

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6 ©2012 Micron Foundation, Inc. |

Catapult Variables

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How many variables/factors?

How many settings per variable/factor?

How many possible combinations of settings?


Catapult Variables

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How many variables/factors?

5

How many settings per variable/factor?

3

How many possible combinations of settings?

35 =243


Catapult Variables

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Do we need to use all 3 settings in our first experiment?

Make TWO of the variables constant - Arm Tension - Upright Tension

Now there are just THREE variables – how many combinations?


Catapult Variables

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Do we need to use all 3 settings in our first experiment?

Make TWO of the variables constant - Arm Tension - Upright Tension

Now there are just THREE variables – how many combinations? 33 =27


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

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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

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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 low HIGH

8 low low low


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

(OPTIONAL E-RECORDER – Record data on iPad ‘Numbers’ App)

▶ Rotate roles or not?

What is the benefit to keeping people in the same role?

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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

• Note how each of the settings [Elevator Height, Turntable Height,

Ball Seat] influence how the ping pong balls travel

• Record your observations on your team Data Sheet

• DO NOT record measurement data YET

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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 (1-8)

Identify who will take each role for the team

• Step #4 – Perform an Experiment

• Step #5 – Gather and Record Data

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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

centimeters

(OPTIONAL E-RECORDER – Record data on iPad

‘Numbers’ App)

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Analyze the Results

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Questions

1. Which combination gave you the longest distance?

Elevator L/H * Ball Seat L/H * Turn Table L/H

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 effect? Can you quantify it?

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Class Session

A B C D E F

Team 1

Team 2

Team 3

Team 4

Team 5


Can we model the results?

▶ Example ONE

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Small differences in the 3 trials



▶ Example TWO

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Large differences in the 3 trials

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1 - HHH 2 - HHL 3 - HLH 4 - HLL 5 - LHH 6 - LHL 7 - LLH 8 - LLL

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Catapult Experiment

Trial 1

Trial 2

Trial 3

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1 - HHH 2 - HHL 3 - HLH 4 - HLL 5 - LHH 6 - LHL 7 - LLH 8 - LLL

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Trial 1

Trial 2

Trial 3


How much did one factor affect the distance?

▶ Changing the turntable from Low to High reduced the distance

by 27.4 inches on average!

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Interaction Effect

▶ Distance depends on the combination of different factors

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TT = High

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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 products and processes

▶ If you become a scientist, engineer, etc., you will use algebra!

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More Details

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▶ 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)

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Can we model the results? Yes!!!

▶ The overall mean (intercept) and effects (1/2 of each effect) are

used to build the linear equation

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321123322331132112332211 xxxmxxmxxmxxmxmxmxmby

3213231213211 042.7958.12708.1542.3708.13042.2875.104.69 xxxxxxxxxxxxy

L or Low setting = -1 H or High setting = +1


Model Predictions for MMM Setting

▶ Elevator Height = M (middle), Ball Seat = M, and Turntable =M

▶ Actual distance values:

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L or Low setting = -1 H or High setting = +1 M or Middle setting = 0

Distance Shot Combo Elevator Ball Seat Turntable Trial 1 Trial 2 Trial 3 Average MMM 0 0 0 70 68 72 70


What about physics versus statistics?

▶ Angles? Trajectory? Velocity?

September 25, 2015

Documents

Welcome to Statistics using Catapults€¦ · 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