Final answer:
One-Way ANOVA is the statistical test used to compare the means among three or more levels of a categorical variable when certain assumptions are met.
Step-by-step explanation:
The appropriate statistical method for comparing differences in means in a continuous outcome among 3 or more levels of a categorical variable is the One-Way ANOVA test. This test is used to determine if there are statistically significant differences between the means of three or more independent groups. In conducting a One-Way ANOVA, certain assumptions must be met, including that the samples are drawn from normally distributed populations with equal variances, and that the samples are randomly selected and independent. The null hypothesis states that all group means are equal, and this is tested against the alternative hypothesis that at least one group mean is different.