Comparison of Fisher-Yates Shuffle and Linear Congruent Algorithms for Question Randomization

Abstract

This research aims to compare Fisher-Yates algorithm and Linear Congruent algorithm in generating random numbers or permutations. The test is conducted using the Chi-Square method to evaluate the quality of randomness generated by both algorithms. The Chi-Square value of the shuffling results is calculated and compared with the critical value of Chi-Square at a significance level of 0.05 with a degree of freedom (df) of 4, which is 9.488. The results show that the Chi-Square value for the Fisher-Yates algorithm is 3.8 and for the Linear Congruent algorithm is 4.3, both of which are below the critical value. This indicates that there is not enough evidence to reject the Null Hypothesis (H₀), implying that the difference in randomness quality between the two algorithms is not statistically significant. Therefore, both algorithms are considered to have equivalent performance. The decision to choose one of the algorithms can be based on other considerations such as complexity and efficiency. Further research is recommended to explore the performance of the algorithms under different conditions.