6.47 Rock-paper-scissors

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:

Rock Paper Scissors
 43    21     35

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.

Chi Squared Goodness of Fit

The Chi Squared Goodness of Fit examines all bins at the same time to determine if the options are chosen randomly.

Conditions

  • Independence
    • Each case must be independent of all the other cases
  • Sample size / distribution
    • At least 5 expected cases

Contingency Table

Outcome Observed Expected
Rock 43 33
Paper 21 33
Scissors 35 33
Total 99 99

Hypothesis Testing

\(H_0:\) All Rock-Paper-Scissors outcomes are equally favored

\(H_A:\) Rock-Paper-Scissors outcomes are not equally favored, i.e. there is a preference for a particular option.

\(Signficance: \; .05\)

rps <- c(43,21,35)

rps_equal <- c(1/3,1/3,1/3)

res <- chisq.test(rps,p = rps_equal)

## 
##  Chi-squared test for given probabilities
## 
## data:  rps
## X-squared = 7.5152, df = 2, p-value = 0.02334

Conclusion

Using a significance p-value of .05, we can reject the null hypothesis since our Chi-Squared test returns a p-value of .023 which is less than .05.

Our test shows there is statistically significant evidence that Rock-Paper-Scissors outcomes are not equally favored.