1 Methodology
1.1 Overview
Using the R programming language, the methods used were frequency distributions, means and standard deviations (SDs), ANOVA, and the Tukey HSD method. The frequency distributions are used to compare the spread of points across each DDLC character that receives points in the Poem Minigame: Natsuki, Sayori, and Yuri. This method allows the detection of outliers or general patterns of the distribution among these characters. The means and SDs would reveal the central tendencies of the distributions, complimenting the ANOVA and Tukey HSD analysis that test whether there exists statistically significant differences among and between the average number of points of the characters. If a statistically significant difference exists, it would indicate that there is “bias” in the distribution of points, since one would presume a uniform distribution of points in a fair game. However, ANOVA assumes a normal distribution of the residuals: if this condition is not met, then the Kruskal-Wallis6 and Dunn Tests7 will be conducted, as they do not assume normally distributed residuals.8
1.2 Models
The models are defined as follows: \[Model1:Value = \mu_1 + Character_{1i} + \epsilon_{1ij}\] \[Model2:log(Value) = \mu_2 + Character_{2i} + \epsilon_{2ij},\] where \(\mu_1\) and \(\mu_2\) are the common effects; \(Character_{1i}\) and \(Character_{2i}\) are the treatment variables (which represent the DDLC characters in the Poem Minigame); and epsilons are the error terms for their respective models. These models will be estimated by ANOVA and the Kruskal Wallis Test; however, for the latter, only Model 1 will be estimated, as Model 2 is an attempt to normalize the residuals without resorting to a non-parametric test: if its residuals are not normally distributed, then the Kruskal Wallis test is necessary.
1.3 Hypotheses
The following are the hypotheses: \[H_0: \mu_{Natsuki} = \mu_{Sayori} = \mu_{Yuri}\] \[H_1: \mu_{Natsuki} \neq \mu_{Sayori} \neq \mu_{Yuri},\] where each of the \(\mu\)’s represents the means for a particular character. If the means are relatively similar, then we cannot make a case that there is bias in the distribution of points in the Poem Minigame. Otherwise, the mean points among the characters are not equal and thus the distribution of points may be biased towards a particular character, where we define a statistically significant difference when p < 0.05. So, in this paper, I expect that the minigame gears the player toward Sayori based on the events leading to the end of Act 1.9