In the past three months we helped a small history museum in a data analysis project and answered a question exactly you are asking. The way we dealt with this question had an important assumption: segmenting donors is a separate analysis from segmenting your visitors. What this means is that we needed separate datasets to answer the same question for these two different stakeholder groups.
Then we went on to segment the visitors and donors based on data (of course in the process there were lots of debates about what way would be more meaningful than others). One principle when segmenting is to reduce overlapping between segments (e.g. K-5 students v.s. Weekend families has a clear overlap on the young audience). But if you are sure that some segmentations that might seem having overlapping with each other actually don't, you should certainly go ahead and segment that way.
Also, when we did the segmentation, we always wanted to ensure that we can use future data to test the quality of future decision. To do this, we also modified some internal operating procedures to ensure that there is a link between operating results, namely earned income, # of visitors, or membership, and their internal projects, including marketing campaigns, special exhibitions, outreach programs, etc. So that we can use the segmentation to verify whether investments on the projects generate returns (not necessarily income, it can be visitor increase or membership renewal ratio increase) as expected in some specific segments. As you may have come to an idea about your segmentation strategy, in the end we actually did very simple segmentation- for visitors we segmented by admission ticket types and some demographic information including ZIP, gender, and age, and for for members, we did it by member types and demographic figures as well. We found this way to be the most effective because you can easily use transactional data to test and to verify your marketing campaigns, among other projects.
What we did not do and agreed not to do from the beginning was to stereotype visitors and members, simply because you would have difficulty verifying results against those assumptions.
Good luck segmenting your visitors.
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