MOTIVATION: Mass spectrometry imaging (MSI) and single-cell RNA sequencing (scRNA-seq) offer high-resolution views into tissue and cellular heterogeneity. However, conventional statistical analyses often treat sub-measurements (pixels or cells) as independent, ignoring their nested origin from individual samples. This assumption inflates the effective sample size, increases false discoveries, and undermines biological interpretation. Pixel- or cell-level averaging avoids this but sacrifices spatial or cellular resolution. RESULTS: We evaluated block-SAM on both simulated and real-world datasets. In DESI-MSI data from kidney, lung, and ovarian tumors, block-SAM consistently identified fewer-but more reliable-differential features compared to traditional-SAM. For example, in the kidney dataset, traditional-SAM identified 569 features between tumor and normal tissue, while block-SAM identified 186-all overlapping but excluding 383 likely false positives. Applied to a metastatic RCC scRNA-seq dataset comparing immune checkpoint blockade (ICB)-treated versus untreated patients, traditional-SAM identified over 19,000 differentially expressed genes in malignant cells; block-SAM reduced this to 19. These results demonstrate block-SAM's ability to reduce false discoveries while retaining biologically meaningful signals across diverse high-dimensional datasets. AVAILABILITY AND IMPLEMENTATION: All code and data associated with this study are deposited on Zenodo (https://doi.org/10.5281/zenodo.18273497). The samr package is freely available on the Comprehensive R Archive Network (CRAN).