6.43

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:

Total: 99 plays

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.

Question If players are playing against one another, does it make sense to count each throw as independent? For instance, if one person only throws paper, you will be more likely to try scissors?

Are we trying to determine if there’s a preference for one option over another, or if the throws are affected by one another?

Can use a chi-squared goodness of fit to test these hypotheses:

  • Null hypothesis: Each option was equally likely to have been thrown.

  • Alternative hypothesis: There was a difference in preference between options.

If each option was equally likely, the expected count for each would be: (1/3) * 99 = 33

The formula for chi-square goodness of fit is: \(\sum(O_i - E_1)^2/E_i\)

(43 - 33)^2/33 + (21 - 33)^2/33 + (35 - 33)^2/33
## [1] 7.515152

Three options, so df = 3 - 1 = 2.

Looking at the Chi-Square Probability Table:

Chi-Square Probability Table

Chi-Square Probability Table

The p-value is: 0.02 < p-value < 0.05. At a confidence level of 95%, we have evidence to reject the null hypothesis of no preference between options for rock-paper-scissor.