Final answer:
The Games-Howell post-hoc test is the best choice for sample sizes of 9, 10, and 11, particularly when the assumption of equal variances is violated.
Step-by-step explanation:
The best post-hoc test to use after analyzing variance (ANOVA) when dealing with sample sizes of 9, 10, and 11. For samples of these sizes that may also have unequal variances, the Games-Howell post-hoc test is often a good choice. The Games-Howell test does not assume equal variances, making it appropriate when the homogeneity of variance assumption is violated. The other options, such as Holm's method, LSD (Least Significant Difference), and Dunnett's test, have different scenarios where they are best applied; for example, LSD is used when equal variances can be assumed, Dunnett's test is for comparing a control group against several treatment groups, and Holm's method is a stepwise approach to control for the family-wise error rate, typically used when variances are equal and sample sizes are similar.