The phrase "a substantially smaller sample" is correct and usable in written English.
It can be used when comparing the size of a sample to another sample, indicating that it is significantly reduced in size.
Example: "In our study, we found that a substantially smaller sample was sufficient to achieve reliable results."
Alternatives: "a significantly reduced sample" or "a notably smaller sample".
Compared to the conservative method of treating all hypotheses as two-sided, the proposed procedure requires a substantially smaller sample, as all useful information on the direction of the alternatives is utilized in an optimal way.
Because the 'Meat and alcohol' cluster had a substantially smaller sample size than the other clusters, however, these findings may not be highly meaningful.
By contrast, fewer than 40% had reached the 10-year assessment of HRQoL when the study was halted, resulting in a substantially smaller sample of participants at this time, compared with year 8. (The same was true of the 9-year assessment of HRQoL).
They analyzed only one season of data with a substantially smaller sample size; and their study sample contained several populations not included in our study such as Medicaid-insured infants, second-season infants, and in-season births, in whom compliance is more difficult to assess.
This latter finding contrasts somewhat with the significant albeit small (r = 0.18) sibling cross-correlations for ADHD and ASD reported by Mulligan et al. yet may be explained by the substantially smaller sample size and use of a qualitatively different questionnaire in the Nijmeijer et al. study.
Even though the effect sizes showed slightly larger differences in magnitude compared to the less than 80 group they were highly imprecise due to substantially smaller sample size, hence they have not been reported here.
The results may not be broadly applicable to the full spectrum of patients with schizophrenia due to the specific recruitment criteria for the study, and substantially smaller sample size for the underweight group.
In this case, the results using the substantially smaller samples within 5 miles of a pollution monitor were remarkably similar to the primary results presented.
Despite these weaknesses, our study surveyed a large number of adolescents, whereas much of the available literature is based on substantially smaller samples of undergraduate students [ 11- 13, 26].
The graph induced by the subset of nodes has a substantially smaller number of edges than the sampling fraction, p (see Table 1).
We were unable to assess the association between sugar and total energy intake in the complete study sample; however, in a substantially smaller subset of participants with self-reported dietary data (n = 230), we found no association between our measure of sugar intake and reported total energy intake.
