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The phrase "assignment was based on" is correct and usable in written English.
You can use it when explaining the foundation or criteria upon which an assignment or task was created or structured.
Example: "The assignment was based on the principles of sustainable development and aimed to encourage critical thinking among students."
Alternatives: "assignment was derived from" or "assignment was founded on".
Exact(55)
For ED visits with more than one E-code of the same specificity level, assignment was based on the first-listed E-code cFor each category header, the level of specificity is the mode for that category.
Group assignment was based on participants' availability.
Cell type assignment was based on cell type-specific marker genes expressions and validated using functional enrichment of cluster-specific differentially expressed genes.
Anonymous officials sought to discredit Wilson's findings by claiming his selection for the assignment was based on nepotism, exposing his wife's identity in the process.
Peak assignment was based on a comparison with library mass spectra (NIST 1.7, WILEY275).
Although assignment was based on consensus between two of the authors, it cannot be excluded that different responses of the students could be assigned to other categories.
Class assignment was based on posterior probabilities.
Country assignment was based on automated detection of the country, city, or institution in the first author's affiliation field.
Gene assignment was based on the levels of naming specificity used by the Manetee project (The Institute for Genomic Research TIGRR) http://manatee.sourceforge.net).net
Sequence type (ST) assignment was based on the sequence of the alleles at each locus of seven housekeeping genes using the MLST database (www.mlst.net).net
Similar(1)
The chromosomal/transcript assignment was based on the sequence alignment of the cloned sequences against the entire human genome and EST, which overlapped with the HERV-W env sequence.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com