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The phrase "are based on smaller" is correct and usable in written English.
It can be used when discussing concepts, theories, or systems that derive from or are influenced by smaller components or elements.
Example: "The findings of this study are based on smaller sample sizes, which may affect the overall validity of the results."
Alternatives: "are derived from smaller" or "are founded on smaller".
Exact(11)
"All the planning assumptions are based on smaller population projections".
Quantitative nation comparisons usually are based on smaller N's.
Treatment recommendations are based on smaller case series, with selection bias towards symptomatic patients.
However, these studies are based on smaller series of men and women with specific CHD diagnoses.
These rates fluctuate somewhat, as they are based on smaller numbers than the all-ages death rates.
The sex-specific meta-analyses are noticeably less powerful than these two strategies because they are based on smaller sample sizes.
Similar(49)
Sometimes big-scale will provide exports, but local markets are based on small-scale agriculture".
MANY of the claims for other estrogens are based on small studies, some without control groups.
These results nonetheless are based on small sample size and a cross-sectional design.
Current follow-up recommendations for patients with penile carcinoma are based on small numbers of patients.
Yet, most of the FDA-approved theranostic approaches are based on small molecules.
More suggestions(3)
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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