6.43 Rock-paper-scissors.

Problem:

Rock-paper-scissors is a hand game played by two or more people where players choose to sign either rock, paper, or scissors with their hands. For your statistics class project, you want to evaluate whether players choose between these three options randomly, or if certain options are favored above others. You ask two friends to play rock-paper-scissors and count the times each option is played. The following table summarizes the data:

Use these data to evaluate whether players choose between these three options randomly, or if certain options are favored above others. Make sure to clearly outline each step of your analysis, and interpret your results in context of the data and the research question.

Manual Solution:

Rock Paper Scissor

Actual

43

21

35

Expected

33

33

33

Z Score Equation

(43-33)/sqrt(33)

(21-33)/sqrt(33)

(35-33)/sqrt(33)

Z Score Value

1.74

-2.09

0.35

Z^2 Value

3.03

4.37

0.12

Sum of Z-Scores-Squared: 3.03+4.37+0.12 = 7.52

If the Null Hypothesis is TRUE, then X^2 = 7.52 follows a Chi-Squared Distribution.

K = 3 Categories (Rock, Paper, Scissor), so allow k-1 degrees of freedom.

Table on P.432 says that for degrees of freedom df=2, that 7.52 means a little over a 2% chance this is due to chance.

R Package Solution:

library(MASS)
library(knitr)

null.probs = c(1/3,1/3,1/3)
freqs = c(43,21,35)
chisq.test(freqs, p=null.probs)
## 
##  Chi-squared test for given probabilities
## 
## data:  freqs
## X-squared = 7.5152, df = 2, p-value = 0.02334

Confirmed:

2% chance that this Rock Paper Scissors uneven distribution was due to chance.