The relationship between sample size and sample error is inverse. As the sample size increases, the sample error decreases.
This is because larger sample sizes provide more data points, which allows for more accurate estimates of population parameters. In contrast, smaller sample sizes are associated with higher sample errors, as they provide fewer data points and are more susceptible to random fluctuations[1][6].
The correlation between sample size and sample error can be approximated as -0.31, indicating a negative relationship. This means that as sample size increases, the error decreases, and vice versa[1]. The sample correlation converges to the population value with increasing sample size, but the estimates are less stable in small samples[1].
In summary, the larger the sample size, the lower the sample error, and the more accurate the estimate of the population parameter will be.
Conversely, smaller sample sizes are associated with higher sample errors and less accurate estimates.
Citations:
[1] https://www.cfholbert.com/blog/sample-size-correlation/
[2] https://forms.app/en/blog/correlation-between-research-type-and-sample-size
[3] https://towardsdatascience.com/how-is-sample-size-related-to-standard-error-power-confidence-level-and-effect-size-c8ee8d904d9c
[4] https://www.universalcpareview.com/ask-joey/why-is-there-a-direct-relationship-between-sample-size-and-expected-error-rate/
[5] http://users.sussex.ac.uk/~grahamh/RM1web/Eight%20things%20you%20need%20to%20know%20about%20interpreting%20correlations.pdf
[6] https://www.dummies.com/article/academics-the-arts/math/statistics/how-sample-size-affects-the-margin-of-error-169723/
[7] https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_power/bs704_power_print.html
[8] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2993974/
[9] https://www.r-bloggers.com/2020/01/on-the-relationship-of-the-sample-size-and-the-correlation/
[10] https://www.statology.org/sample-size-and-margin-of-error/
[11] https://online.stat.psu.edu/stat100/lesson/2/2.3
[12] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7745163/
[13] https://www.appinio.com/en/blog/market-research/margin-of-error-and-sample-size
[14] https://www.statalist.org/forums/forum/general-stata-discussion/general/1585885-what-is-the-relationship-between-sample-size-and-type-i-error
[15] https://sample-size.net/correlation-sample-size/
[16] https://www.sciencedirect.com/science/article/pii/S0092656613000858
