An initial look at my two datasets, one collected randomly and one via stratified convenience sampling, indicates the tree species and abundance data are fairly similar. I want to compare them statistically (species and abundance, and also other metrics such as DBH and height) but am aware that the two sampling approaches renders them effectively two separate studies even though they are sampling the same population (a city's trees) and both cover the landtypes within the city equally well. A literature search has so far uncovered hardly any studies that compare the two different methodologies against each other. Am I wasting my time trying or are there some fancy stats tricks i can use?
I'm wondering whether the key here isn't the different data collection methods, but rather whether each method used an adequate sample size to effectively capture the range of tree species found in each city and for each land type (what are the land types? Street, park, green space? Are they all public trees?). It might be useful for you to create species accumulation curves for both sets of data, to ensure that sampling saturation has been reached in each. That could make using both data sets more defensible in statistical analyses. This was one of the methods I employed in my own work to defend the comparison of diversity indices among different sampling schemes in 2 cities. It is worth noting, however, that SAC were designed for naturally occurring communities, and will be influenced by the differences in tree establishment and planting practices in urban areas.
http://urbantreemanagement.teiep.gr/tree-map
http://urbantreemanagement.teiep.gr/scenario-map?municipality=ioan
For some time now, a model-based (prediction-based) approach has been used to estimate totals and means from finite populations as an alternative to a probability-of-selection-based approach, and regression is also used to compare various variables and predict one from others. But also some now look into psuedo-inclusion probabilities for nonprobability samples, also using covariates. See https://www.researchgate.net/publication/316867475_Inference_for_Nonprobability_Samples
There they have a link to this paper, open access, by Project Euclid:
https://projecteuclid.org/journals/statistical-science/volume-32/issue-2/Inference-for-Nonprobability-Samples/10.1214/16-STS598.full
That paper, and others by Valliant, and perhaps by J. Michael Brick and others, found on ResearchGate, might be useful to you.
It seems to me that a reason your two samples are similar are that you did stratify your nonprobability sample. I expect that sometimes that might help insure "representativeness" even more than a simple random sample.
Note that with the model-based approach, the need for "representativeness" may not be as strict, but you need to avoid leaving out important parts of the population. Each model needs to adequately apply to the portion of a population which it is purported to model, from a total survey error point-of-view. In your case, if you can assume the stratification and allocations therein were a good enough substitute for a "balanced sample," which achieves what a random sample hopes to achieve, then with those caveats spelled out, you could have a better than average combined sample from which you might estimate the variances of prediction errors.
I don't know exactly what your project was, and it was some time ago, but perhaps the reference above may be of future use to you, and others, but please use with care.
Best wishes - Jim
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