A THREE FACTOR EXAMPLE and ANOVA analysis
1. Name(s) – Luke Skywalker (002)
Darth Vader (005)
Yoda (601)
2. Title and Brief description of experiment:
Title – “It’s Nerf or Nothing”
Description – This experiment will attempt to measure the accuracy of Nerf darts shot from Nerf guns. Three different types of darts will be shot from three different types of Nerf guns at three different distances. The types of darts are unique in their design. The first type is foam bodied with a hard plastic tip. The second type is foam bodied with a suction cup end, used for sticking to glass. The third type is foam bodied with a Velcro tip, used for sticking to Velcro. The Nerf guns will be mounted level to a saw horse. A laser pointer will be inserted into the barrel to identify the true center of the target. The saw horse will be set 5, 10, and 15 ft from the target. The first target will be made from glass covered in whipped cream in order to identify where the plastic tip darts will hit. The second target will be plain glass to allow the suction cup darts to stick. The third target will be Velcro to allow the Velcro darts to stick. The distance from the dart impact to the center of the target will be measured in inches.
3. The response variable is accuracy of the darts(The measured distance from dart impact to center of target) and is measured in units of inches.
4. Factors:
Factor 1 is: Darts
Its levels are:Dart 1: Plastic tip
Dart 2: Suction tip
Dart 3: Velcro tip
Factor 2is : Distance
Its levels are: 5 ft from target
10 ft from target
15 ft from target
Factor 3 is: Nerf Gun
Its levels are: Nerf Gun 1
Nerf Gun 2
Nerf Gun 3
DESIGN MATRIX
5’ / 10’ / 15’ / 5’ / 10’ / 15’ / 5’ / 10’ / 15’
Nerf Dart 1 / 22,5 / 6,13 / 3,7 / 16,8 / 11,27 / 7,3 / 17,18 / 14,24 / 8,6
Nerf Dart 2 / 5,11 / 21,15 / 25,1 / 27,14 / 26,20 / 19,19 / 15,21 / 1,26 / 23,2
Nerf Dart 3 / 2,25 / 4,10 / 18,4 / 24,22 / 13,23 / 9,16 / 20,17 / 10,9 / 12,12
5. How will randomization and replication be used?
Randomization will be used in selecting the individual darts from each type. Randomization is again used to select which darts and at what distance get fired in random order, as shown in the design matrix. Replication is used by performing the randomizations as many times as possible (at minimum twice).
6. How will you analyze the data? means table and ANOVA (lm with class variables,
i.e., with qualitative explanatory variables) or regression (lm with quantitative
explanatory variables) or a mixture of the two?
Besides the mandatory mplot, side by side boxplots, mfit and stats;
The data collected is quantitative and will be modeled by ANOVA analysis using 2 models:
model accuracy =dist + darttype +nerfgun +dist*darttype +dist*nerfgun +darttype*nerfgun + dist*darttype*nerfgun
And
modelsqrt(accuracy) =dist + darttype +nerfgun +dist*darttype +dist*nerfgun +darttype*nerfgun + dist*darttype*nerfgun
usingsqrt rather than log since a possible value of accuracy could be zero.
also compare the models to see which has largest R^2
7. Briefly what do you expect to happen?
Having used Nerf guns on several occasions and observing the darts used, it is predicted that dart 1 (the plastic tip) will be the most accurate. This is based on the assumption that the suction dart and the Velcro dart both will experience additional forces from the weight and aerodynamics of the tip while traveling through the air.
8. Any additional comments:
This seems like it will be a fun experiment to participate in.