Bears In Space
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BEARS IN SPACE Marshall Jiang 3rd Period
1
Design of Experiment The purpose of this experiment was to determine how far a GummiBear can be sent into space by a launcher and the effect on the launch distance by the angle and the position of the launch pad. An experiment was chosen as the method of study for this question due to the fact that our group cannot just observe GummiBears launching into space, thus we have to deliberately create an experiment. The nature of this experiment dictates us that GummiBears are to be used as the experimental units of this experiment. Our explanatory variables would be the launch angle (determined by the number of books) and the launch position (determined by the position of the launcher on the ruler). The response variable is the length the GummiBear after it was at rest from the end of the ruler. Treatment is as follows where top is the top of the ruler and bottom at the bottom of the ruler: Group 1: 5 subjects
Treatment 1: 1 book, top
Group 2: 5 subjects
Treatment 2: 1 book, bottom
Group 3: 5 subjects
Treatment 3: 3 book, top
Group 4: 5 subjects
Treatment 4: 3 book, bottom
Group 5: 5 subjects
Treatment 5: 5 book, top
Group 6: 5 subjects
Treatment 6: 5 book, bottom
Random allocation
Compare length of launch
Blocking in this experiment was determined to be of no use as our group determined that outside variables are to their minimal. This was determined due to the fact that most of the GummiBears looked like they are similar in almost every physical aspect with the exception of colors and slight variations of the shape. Blinding is only single blinding as the bears are not conscious of the treatments they are receiving. The reason it is not double-blind is because the measurer, our group, was fully aware the treatment the bear received.
2
Description of Set Up First of all, get a pack of GummiBears with at least 30 bears in it too ensure that enough bears are launched for replication and to ensure control as they should be of the same type. Create the launcher with two popsicle sticks and two rubber bands by wrapping one rubber band around both sticks and the other rubber band around only one stick. Now gather 5 “The Practice of Statistics: 3rd Edition” textbooks and a meter stick. Place the meter stick on the book as shown in the picture below with around half an inch at the top:
Now follow the experiment by random allocating the 30 GummiBears into 6 groups of 5 GummiBears each. To create the treatment group, just stack the textbooks on top of each other by the amount indicated in the diagram drawn under Design of Experiment. The position of the launcher is either at the very top with the back parallel to the back of the ruler, or at the bottom with the front parallel to the front of the ruler. Now just place the GummiBear on top of the launcher and pull back the the popsicle stick and let go quickly. When the GummiBear finally stops bouncing around, measure the distance the GummiBear went by only measuring how far the GummiBear went forward, not sideways, starting from the end of the ruler at the ground. This way we could implement, as best as we could, the three principles of experimental design: control and replication was gained by purchasing the GummiBears in one large pack of the same types of bears (large amounts of bears and the same types of bears), and randomness was gained by the random allocation of the bear into the groups.
Data and Analysis Table (The format of the column is “number of books: position”; all measurements are in inches):
3
T R I A L 1 T R I A L 2 T R I A L 3 T R I A L 4 T R I A L 5 AVERAGE 1: Top
-5.5
-7.5
-11
-2
-10
-7.2
1: Bottom
18
21
21
17.5
15
18.5
3: Top
-3
-7
-6
-3
-8
-5.4
3: Bottom
23
24
26
23
18.5
22.9
5: Top
5
-1
1
-2
0
0.6
5: Bottom
29
33
23
37
17
27.8
Average Distance Launched in Inches 30.0
Launch Lenght in Inches
22.5 15.0 7.5 0 -7.5 -15.0 1: Top
1: Bottom
3: Top
3: Bottom
5: Top
5: Bottom
Treatment
As you can see by the graph (5 books, top position cannot be seen that well due to a hard scale), there is clearly a great improvement (statistically significant) if you move from top to bottom or increase the book height. Accordingly, the maximum distance seems to be with 5 books at the bottom of the meter stick. I think it is quite reasonable for me to say that there’s a strong correlation between either increasing the book height, or moving the launcher to the bottom, with increased distance launched. But the data from two groups of my classmates seems to somewhat disagree with me.
4
Group 2 seems to have more data resembling mine, as the general shape of the bar histogram looks like mine but both Group 1 and Group 2 have the same conclusion in terms of book angle: the more the better. The placement of the launcher differs though, as Group 2 suggests the bottom of the 5 book one while Group 1 suggests the top of the 5 book stack.
AVERAGE
AVERAGE
1: Top
14.6
6.8
1: Bottom
45.5
70.5
3: Top
45.1
18.7
3: Bottom
42.6
68.2
5: Top
65.7
38.3
5: Bottom
60.8
82.3
Group 1
Group 2
Other Group’s Launch Data in Inches
Launch Lenght in Inches
90.0
67.5
45.0
22.5
0 1: Top
1: Bottom
3: Top
3: Bottom
5: Top
5: Bottom
Treatment
5
After analyzing the design after doing it, there’s a few places where it could be improved upon. First of all, the lurking variable of measuring the GummiBear after it bounced probably proved to be a bit of a bad judgement. The second possible lurking variable is that the human launcher got better at launching the bears as time went on (this is what happened to Group 1 as I consulted their group why their data are like that). I would fix the first one by measuring the distance at the point where the GummiBear first hit the ground and the second one could be fix by either creating a mechanical launcher that doesn’t need a human operator or use a new person for every launch. There was also significant bias in where we measured the distance from as then the launchers from the bottom of the ruler gets a some 35ish inches of advantage over the ones in the back. To correct this, we could measure the distance from where we launched instead to correct for this bias.
6
1
Design of Experiment The purpose of this experiment was to determine how far a GummiBear can be sent into space by a launcher and the effect on the launch distance by the angle and the position of the launch pad. An experiment was chosen as the method of study for this question due to the fact that our group cannot just observe GummiBears launching into space, thus we have to deliberately create an experiment. The nature of this experiment dictates us that GummiBears are to be used as the experimental units of this experiment. Our explanatory variables would be the launch angle (determined by the number of books) and the launch position (determined by the position of the launcher on the ruler). The response variable is the length the GummiBear after it was at rest from the end of the ruler. Treatment is as follows where top is the top of the ruler and bottom at the bottom of the ruler: Group 1: 5 subjects
Treatment 1: 1 book, top
Group 2: 5 subjects
Treatment 2: 1 book, bottom
Group 3: 5 subjects
Treatment 3: 3 book, top
Group 4: 5 subjects
Treatment 4: 3 book, bottom
Group 5: 5 subjects
Treatment 5: 5 book, top
Group 6: 5 subjects
Treatment 6: 5 book, bottom
Random allocation
Compare length of launch
Blocking in this experiment was determined to be of no use as our group determined that outside variables are to their minimal. This was determined due to the fact that most of the GummiBears looked like they are similar in almost every physical aspect with the exception of colors and slight variations of the shape. Blinding is only single blinding as the bears are not conscious of the treatments they are receiving. The reason it is not double-blind is because the measurer, our group, was fully aware the treatment the bear received.
2
Description of Set Up First of all, get a pack of GummiBears with at least 30 bears in it too ensure that enough bears are launched for replication and to ensure control as they should be of the same type. Create the launcher with two popsicle sticks and two rubber bands by wrapping one rubber band around both sticks and the other rubber band around only one stick. Now gather 5 “The Practice of Statistics: 3rd Edition” textbooks and a meter stick. Place the meter stick on the book as shown in the picture below with around half an inch at the top:
Now follow the experiment by random allocating the 30 GummiBears into 6 groups of 5 GummiBears each. To create the treatment group, just stack the textbooks on top of each other by the amount indicated in the diagram drawn under Design of Experiment. The position of the launcher is either at the very top with the back parallel to the back of the ruler, or at the bottom with the front parallel to the front of the ruler. Now just place the GummiBear on top of the launcher and pull back the the popsicle stick and let go quickly. When the GummiBear finally stops bouncing around, measure the distance the GummiBear went by only measuring how far the GummiBear went forward, not sideways, starting from the end of the ruler at the ground. This way we could implement, as best as we could, the three principles of experimental design: control and replication was gained by purchasing the GummiBears in one large pack of the same types of bears (large amounts of bears and the same types of bears), and randomness was gained by the random allocation of the bear into the groups.
Data and Analysis Table (The format of the column is “number of books: position”; all measurements are in inches):
3
T R I A L 1 T R I A L 2 T R I A L 3 T R I A L 4 T R I A L 5 AVERAGE 1: Top
-5.5
-7.5
-11
-2
-10
-7.2
1: Bottom
18
21
21
17.5
15
18.5
3: Top
-3
-7
-6
-3
-8
-5.4
3: Bottom
23
24
26
23
18.5
22.9
5: Top
5
-1
1
-2
0
0.6
5: Bottom
29
33
23
37
17
27.8
Average Distance Launched in Inches 30.0
Launch Lenght in Inches
22.5 15.0 7.5 0 -7.5 -15.0 1: Top
1: Bottom
3: Top
3: Bottom
5: Top
5: Bottom
Treatment
As you can see by the graph (5 books, top position cannot be seen that well due to a hard scale), there is clearly a great improvement (statistically significant) if you move from top to bottom or increase the book height. Accordingly, the maximum distance seems to be with 5 books at the bottom of the meter stick. I think it is quite reasonable for me to say that there’s a strong correlation between either increasing the book height, or moving the launcher to the bottom, with increased distance launched. But the data from two groups of my classmates seems to somewhat disagree with me.
4
Group 2 seems to have more data resembling mine, as the general shape of the bar histogram looks like mine but both Group 1 and Group 2 have the same conclusion in terms of book angle: the more the better. The placement of the launcher differs though, as Group 2 suggests the bottom of the 5 book one while Group 1 suggests the top of the 5 book stack.
AVERAGE
AVERAGE
1: Top
14.6
6.8
1: Bottom
45.5
70.5
3: Top
45.1
18.7
3: Bottom
42.6
68.2
5: Top
65.7
38.3
5: Bottom
60.8
82.3
Group 1
Group 2
Other Group’s Launch Data in Inches
Launch Lenght in Inches
90.0
67.5
45.0
22.5
0 1: Top
1: Bottom
3: Top
3: Bottom
5: Top
5: Bottom
Treatment
5
After analyzing the design after doing it, there’s a few places where it could be improved upon. First of all, the lurking variable of measuring the GummiBear after it bounced probably proved to be a bit of a bad judgement. The second possible lurking variable is that the human launcher got better at launching the bears as time went on (this is what happened to Group 1 as I consulted their group why their data are like that). I would fix the first one by measuring the distance at the point where the GummiBear first hit the ground and the second one could be fix by either creating a mechanical launcher that doesn’t need a human operator or use a new person for every launch. There was also significant bias in where we measured the distance from as then the launchers from the bottom of the ruler gets a some 35ish inches of advantage over the ones in the back. To correct this, we could measure the distance from where we launched instead to correct for this bias.
6
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