Often the educational data we collect violates the important assumption of independence that is required for the simpler statistical procedures. Students are often groups (nested) in classrooms. Those classrooms are grouped (nested) in schools. The schools are grouped (nested) in districts. This nesting violates the assumption of independence. Hierarchical Linear Modeling (HLM) was designed to work with nested data. HLM allows researchers to measure the effect of the classroom, as well as the effect of attending a particular school, as well as measuring the effect of being a student in a given district on some selected variable, such as mathematics achievement.
Thank you very much for your reply!
1) For experiment 1, both data sets that failed the normality test (p= and p=) are not symmetric, according to the box plot. Therefore, a nonparametric test should be used for the analysis, right?
2) For experiment 2, there are two experimental groups. I only have three values for each group. The data for group A are: , , (normality test P<). The data for group B are: , , (normality test P=). The results from t-test (p=) and Mann-Whitney Rank sum test (p=) are very different.