<s>[INST] A researcher is studying the effects of three different teaching methods on student performance. The methods are denoted by A, B, and C, and the performance of the students are ranked via three different parameters, denoted by 1, 2, and 3. The researcher has a list of the average ranks for students taught by each method, as follows:
- A: (3.4, 2.2, 1.9)
- B: (3.1, 2.5, 2.3)
- C: (3.0, 2.8, 2.2)
The researcher wants to use a statistical method to determine which teaching method is the most effective. Assuming a normal distribution of scores and homogeneity of variance, which method is most effective based on the data provided?[/INST]