I need to prove that one method is statistically stronger than another method.

Compliance rates over a period of time in the Emergency Department setting. During Method 1, educational methods were used as a tool to improve compliance. During Method 2, data transparency methods were used as a tool to improve compliance. I need to prove that one method is statistically stronger than another method. When I simply use a heat map or run chart, it is evident that method 2 is stronger, however I need to show statistical significance, more than just a nice heat map or bar graph. I need to add a statistical analysis to my abstract. I need a detailed explanation of why the particular statistical tool was used, the excel depicting the raw data and how the conclusion was made. I also need a brief description of the analysis as to defend the abstract. I also am not sure if I should be making a hypothesis statement to prove one method over the other. I am told I should use a chi square test, another person told me I need to do Kruskal Wallis test. I tried a two tail test but I was told it did not make sense. I am a nurse manager, don't have much money, and need help.