Single-cell RNA sequencing (scRNA-seq) enables high-resolution analysis of cellular heterogeneity, yet accurate and consistent cell-type annotation remains a crucial challenge. Numerous automated tools exist, but their complex modeling assumptions can hinder reliability across varied datasets and protocols. We propose PCLDA, a pipeline composed of three modules: t-test-based gene screening, principal component analysis (PCA) and linear discriminant analysis (LDA), all built on simple statistical methods. An ablation study shows that each module in PCLDA contributes significantly to performance and robustness, with two novel enhancements in the second module yielding substantial gains. Despite these additions, the model retains its original assumptions, computational efficiency, and interpretability. Benchmarking against nine state-of-the-art methods across 22 public scRNA-seq datasets and 35 distinct evaluation scenarios, PCLDA consistently achieves top-tier accuracy under both intra-dataset (cross-validation) and inter-dataset (cross-platform) conditions. Notably, when reference and query data are generated via different protocols, PCLDA remains stable and often outperforms more complex machine-learning approaches. Furthermore, PCLDA offers strong interpretability, attributed to the linear nature of its PCA and LDA modules. The final decision boundaries are linear combinations of the original gene expression values, directly reflecting the contribution of each gene to the classification. Top-weighted genes identified by PCLDA better capture biologically meaningful signals in enrichment analyses than those selected via marginal screening alone, offering deeper functional insights into cell-type specificity. In conclusion, our work underscores the utility of carefully enhanced simple statistics methods for single-cell annotation. PCLDA's simplicity, interpretability, and consistently high performance make it a practical, reliable alternative to more complex annotation pipelines. Code is available on GitHub:https://github.com/kellen8hao/PCLDA.