Upload
hubert-lo
View
55
Download
0
Embed Size (px)
DESCRIPTION
A group project that I and two other group members, Kyle and Cisco accomplished in winter quarter 2014 which focuses on Design of Experiments and ANOVA- Analysis of Variance.
Citation preview
Investigation: Throwing accuracy with darts
Cisco Bass Hubert Lo Kyle Beekman
Introduction
• The motivation for our experiment was to investigate what sort of different factors affect throwing accuracy. There was a multitude of factors that we considered, but we decided to narrow down to two factors, distance and blindfold-indicator.
Treatment Structure
• 3 x 2 Factorial Structure
• Two factors o Distance - 3 Levels - (Ordinal distances; 6, 8 10 ft)o Blindfold - 2 Levels – (Blindfold and No Blindfold)
Experimental Units/ Response variable
• Experimental Units: trials (60)
• Response variable: sum score of three dart throws
Design Structure
• Randomized Complete Block Design
• Block variable: Person Skillo Randomization: the order of treatment combinationso Replication: no replicationo Blocked: person
Discussion of randomization/direct controls
• Randomized the order of treatment combinations within block
• Confounding variable: order of trials o Throwers adaptation
• Assign order of treatment combinations with a six-sided die
ANOVA Table (Source & DF)
Source DFThrower & random 9
Distance 2
Blindfold 1
Distance * Blindfold 2
Error 45
Total 59
Assumptions
Normality:•Using Shapiro-Wilk Test,
p-value is 0.0090.
Assumptions
Equal Variance:
Independence:
Significant factors:
Analysis:•Blindfold : F ratio = 22.7245 P-value <0.0001
•Distance: F ratio = 0.6605 P-value = 0.5215
•Blindfold * Distance : F ratio = 0.8209 P-value = 0.4465
Main Effects Plots
Main Effects: Blindfold Main Effects: Distance
Interaction Plot
Interaction Plot: Distance & Blindfolded
Table of Means
Levels Mean Standard deviation
Not 35.733 12.66
Yes 17.233 14.60
Main Effect: Blindfolded
Table of Means
Levels Mean Standard deviation
10 23.40 18.34
6 28.60 14.05
8 27.45 17.05
Main Effect: Distance
Table of MeansLevels Mean Standard
deviation
not, 6ft. 37.10 14.06
not, 10ft. 36.00 16.28
not, 8ft. 34.10 16.01
yes, 8ft. 20.80 21.62
yes, 6ft. 20.10 7.60
yes, 10ft. 10.80 15.69
Interaction Effect: Distance & Blindfolded
Contrasts/ Tukey Method
•Not blindfolded 6ft vs blindfolded 10ft
F-ratio = 15.3088 P-value = 0.0003
•6ft vs 10 ft (regardless of blindfolded)
F-ratio = 1.1969 P-value = 0.2798
•Tukey Method not blindfolded blindfolded
Level Level P-Value
Not blindfolded Blindfolded Less than 0.0001
Conclusion
• Blindfolding a thrower will cause them to have less accuracy when throwing darts at any distance between 6 feet and 10 feet.
• This can be generalized to any person throwing darts regardless of skill.
Going Forward
• If we were to repeat this experiment, we would consider using more spread out distances (i.e. 10ft, 15ft, 20ft)
• We would also consider using other factors such as type of dart and room conditions
Appendix
Appendix
Appendix
Appendix
Appendix
Appendix
Appendix
Appendix
Appendix
• Contrast: not blinded 6ft vs blindfolded 10ft
• Contrast: 6ft vs 10 ft (regardless of blindfolded)