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Based on the information that was given, I concluded that there are inconsistencies in the scores, but there is no evidence to proof that these scores were given based on preference.

Looking at the boxplots,  I can see that judges  1,2,3,4,5,and 6 medians scores were not consistent with judges 7,8,and 9. The other set of boxplots shows substantial differences in the medians scores of the 5 skaters. The skater is considered to be a blocking factor.

The parallel traces indicates the existence of interaction between judge's scores and skaters. As a result, we can say there are inconsistencies in the scores.

The ANOVA output

The skater is considered a blocking factor in order to reduce the SSE which leads to a larger value of F. Using the significant level 0.5, the critical value of is 3.592. The null hypothesis that mean score for all skaters are the same is rejected if the F ratio is exceeds 3.592. Therefore, the null hypothesis is rejected and the alternate accepted. We conclude that the mean score is not the same for all skaters. In addition, p-value for the null hypothesis regarding the skaters is 0.004. The p-value confirms that the null hypotheses for treatments and blocks should be rejected because the p-values is less than significant level.  

Based on the ANOVA output, we conclude that there is evidence of inconsistencies among the judges.

MMC shows the difference between means include 0 which shows no evidence of significant difference in scores.  However, the difference in mean scores between judge 1 and 3 are significant which led us to believe that unfair judging were committed by judge and 3.

Based on the information that was given, my conclusion is that there are inconsistencies in thescores, although there is no evidence to proof that these scores were given based on preference....