A survey is conducted on 398 people that are either of type A (198) or type B (200) and answer 1 question on a 5 point scale 1=strongly agree, 2= agree,...5=strongly disagree.
What is the correct summary statistic and what hypothesis test should be used in answering: if the 2 types of people have differing opinions regarding the question?
attempt
Summarize using a 2 way table of type vs response (1,2,...,5), with a vector $\hat p = \begin{pmatrix}p_1 \\ p_2\\ p_3 \\p_4 \\p_5 \end{pmatrix}$ as the summary statistic
This seems like a test of homogeneity is appropriate to answer the question but these people are drawn from the same population and cross-classified (right?) so then a test of independence (however a test of indep is unrelated to the question?)
I would use the level of dispersion for categorical variables which is equivalent to $1-\sum_{i=1}^n P^2_i$ where $P_i$ es the proportion of people who provided answer $i$. See Budescu and Budescu (2012) How to measure diversity when you must. This summary statistic will tell you the difference in opinion disagreement between groups.
Also, if you had data that explains to some extent people's opinions, an ordered probit (logit) would show you the differences between groups, in the probability of getting one specific answer.