Analysis of Variance (ANOVA) for Actuarial Applications
Apply ANOVA methods to compare group means in actuarial data analysis for Exam MAS-I.
One-Way ANOVA
One-way ANOVA tests whether the means of k groups are equal: H0: mu_1 = mu_2 = ... = mu_k. The total sum of squares (SST) decomposes into between-group (SSB) and within-group (SSW): SST = SSB + SSW. The F-statistic is (SSB/(k-1)) / (SSW/(N-k)). Under H0, F follows an F-distribution with k-1 and N-k degrees of freedom. Rejecting H0 means at least one group mean differs but does not identify which ones. Multiple comparison procedures (Tukey, Bonferroni, Scheffe) control family-wise error rate when making pairwise comparisons.
Two-Way ANOVA and Applications
Two-way ANOVA examines two factors simultaneously and their interaction. The model is Y_{ijk} = mu + alpha_i + beta_j + (alpha*beta)_{ij} + epsilon_{ijk}. The interaction term captures effects that depend on the combination of factor levels. In actuarial applications, ANOVA can compare claim costs across territories and coverage types, test whether mortality rates differ by rating class, or evaluate the effectiveness of different risk management strategies. Exam MAS-I tests ANOVA table construction, F-test execution, and interpretation of main effects and interactions.