Which statistical measure cannot be reliably derived with a very small sample size during analysis?

The Root Mean Square Error (RMSE) is a statistical measure that quantifies the difference between values predicted by a model or an estimator and the values observed. It is calculated by taking the square root of the average of squared differences between predicted and observed values. This measure relies on the validity of having multiple data points to provide a meaningful error estimation.

When the sample size is very small, the RMSE can be significantly affected by outliers or extreme values, leading to a potentially misleading representation of model performance. Small sample sizes do not provide enough data to capture the underlying variability and can distort the estimated error, resulting in lack of reliability.

In robust statistical analysis, larger samples have the advantage of reducing the impact of individual data points, allowing for a more accurate and stable estimate of performance measurement like RMSE. In contrast, other measures, such as the mean or median, can yield meaningful values even with smaller sample sizes, as they are less sensitive to the overall distribution and can give insights into central tendency with limited data. Standard deviation may also be informative, but its variability would still reflect the small sample constraints. Therefore, RMSE is particularly limited in reliability when derived from very small samples.