Qualitative methods are effective at assessing community engagement at a project or program level; however, they are time consuming, do not easily scale up for the evaluation of large-scale or multi-community projects.

Qualitative research methods use different techniques to project divergent assumptions about the world and different means to persuade the reader’s assumptions.

Qualitative research may be useful (like Focussed group discussion)which is a method in which the study participants are observed .Different data collection tools like tape recorder , field notes are used . Even non verbal clues (memos) can be used . These information can then be written (Transcribed) into word document with preformed codes (inductive analysis).Codes can be further joined as narrative analysis. Theme analysis can also be carried out if interesting theme emerges. Even mixed method approach may be useful.

The advice provided by Suraj Kapoor above should be really useful, especially the initial comment regarding qualitative methods. I would add a couple of observations, partly in support of the need for mixed methods:

1. your methods of choice ought to be driven by the aims and objectives of the project you are examining and the population expected to be 'impacted'. Depending on your involvement with the project (planner, implementer, evaluator) you may need to collect and analyse the initiating documentation (document analysis/ thematic analysis). Community engagement projects run from superficial (PR jobs) to deep learning (democratic governance). You should have a feel for this in the project under investigation before developing questions on 'impact'. Qualitative data collection and analysis from people involved should then provide the nuance and any meaning.

2. in any case, you should include some kind of quantitative data collection around the 'engagement 'element. For instance, how many different people in 'the community' actually engaged in the various activities promoted by the project? How far did they travel to participate? What was the cost for them of participating? Did they benefit in any economic, political or social manner? and so forth. The last question on benefits probably needs the specification of quantifiable indicators.

There are quite a lot of good articles relating to these issues in the World Bank archives from 2000-2015 at least.