stat 323 project: throwing accuracy with darts

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)