How to value comparative Likert results

Question

I have absolutely no knowledge of statistics. My question is how to make sense of some evaluation results I received. The attached graph represents my results of a Likert question compared to my department, division, and college. My question is, how should I interpret these results? While I have more students who "strongly agree" on this question, I have fewer who merely "agree." What interpretations of my performance are authorized here? Am I performing better? Similarly? Is there some empirically valid way of making assertions about this data?

There are twelve other such graphs, and I have to write a summary of the findings. But it is hard for me to know what kind of claims I can make based on the data.

Answer 1

I believe what you should do is to compare your distribution with the distribution for college, department, etc. The null hypothesis (think of it as a baseline case you would stick to until proven otherwise) is that your results are from the same distribution, so while asking students you did not introduce some selection (for example asking only student before the first class started, so late-comers did not show up in your results). Tip for the future questions and for your report: always make clear how your data was collected.

To answer your question you should perform some visualizations and testing. For visualization I would opt for having 4 separate histograms on one graph: that would do visual comparison of distributions better. For testing you should perform a number of tests: Mann-Whitney's U, Wilcoxon signed-rank test and Sign test. Wikipedia are quite good on the limitations of these tests and assumptions behind them.