The phrase "based on a small sample" is correct and can be used in written English.
It is typically used to indicate that a conclusion or statement is drawn from a limited amount of data or evidence. Example: The study's findings should be taken with caution as they are based on a small sample of only 50 participants.
Unfortunately, as both studies were based on a small sample from one medical school they are therefore of limited generalisability.
Moreover, our results were based on a small sample of mostly well-educated women from one large city.
The findings are tentative, being based on a small sample of cases in Hong Kong.
Some doctors say there is insufficient evidence – Foldès' results were based on a small sample, tested with a self-devised scale of pleasure and pain.
The census data was collected before the real estate market began softening over the last year, and it was based on a small sample size, experts cautioned.
They all said the paper, while based on a small sample, pointed to a new area worthy of more research.
Other professors of cognitive psychology thought the study was well done, although based on a small sample, with results that have yet to be replicated.
This conclusion, based on a small sample, runs counter to the general presumption, backed by empirical findings in America, that immigration lowers wages.
All of these conclusions are based on a small sample size, and so they ought to be interpreted with some caution.
The economist who analyzed the data for the society, Mark K. Levitan, said there were many possible explanations for the trends that emerged from the numbers, which were based on a small sample.
The study (peer-reviewed but based on a small sample) is the latest in a growing scientific literature suggesting that sexual preferences may be not simply a matter of personal preference but part of our ingrained biology.
