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I am looking for an approach to calculate and assess the positional accuracy of POIs in QGIS.

I have two layers that show the locations of supermarkets:

One is from a commercial database and the other is made by hand based on the addresses given on the websites, I want to see how accurate the commercial data are in the relation to the hand-made as reference data.

How can I measure positional accuracy of points in QGIS?

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Depending on how your data is structured you can use the tool "Distance Matrix" from the menue "Vector-Analysis". It compares two point datasets point-by-point for their distances. Necessary is a key-attribut to compare both datasets. If you have a column with related values in both tables it is the fastest way.

By default the tool calculates the distances for each point to all other points in the belonging dataset. That is in you case unnecessary. There is an option to use "only(k) next points" that you can set to 1. Then only the distance to the closest point is written into the output file.

The output .csv file can then joined back to the original table quite easily(as you have the related column).

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