This study shows that the type of the analytical treatment that should be adopted for nonprobabilistic analysis of uncertainty depends on the available experimental data. The main idea is based on the consideration that the maximum structural response predicted by the preferred theory ought to be minimal, and the minimum structural response predicted by the preferred theory ought to be maximal, to constitute a lower overestimation. Prior to the analysis, the existing data ought to be enclosed by the minimum-volume hyper-rectangle $V1$ that contains all experimental data. The experimental data also have to be enclosed by the minimum-volume ellipsoid $V2$. If $V1$ is smaller than $V2$ and the response calculated based on it $R(V1)$ is smaller than $R(V2)$, then one has to prefer interval analysis. However, if $V1$ is in excess of $V2$ and $R(V1)$ is greater than $R(V2)$, then the analyst ought to utilize convex modeling. If $V1$ equals $V2$ or these two quantities are in close vicinity, then two approaches can be utilized with nearly equal validity. Some numerical examples are given to illustrate the efficacy of the proposed methodology.

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