descriptive-and-statistical-analysis

# Skill: descriptive and statistical analysis ## 1. Capability Definition & Real Case * **Professional Definition**: This capability is the ability to compute and interpret descriptive statistics, classical statistical relationships, formal hypothesis tests (t-tests, ANOVA, Chi-square), and unsupervised pattern extractions (Clustering, Dimensionality Reduction) once the relevant variables are available. It encompasses the mapping of numerical or latent results (p-values, R-squared, PCA loadings, cluster labels) to qualitative biological or business insights, while ensuring the analysis is calibrated for the specific data modality and platform context. * **Dimension Hierarchy**: Analytical Transformation->Analytical Inference->descriptive and statistical analysis ### Real Case **[Case 1]** * **Initial Environment**: A high-dimensional data environment (such as an AnnData object or a matrix) is provided, containing feature measurements and observation labels. The environment supports dimensionality reduction tools like PCA. * **Real Question**: After performing dimensionality reduction, which cell populations are primarily separated along the first principal component (PC1)? * **Real Trajectory**: Load the dataset; compute principal components (PCA); extract the loadings for PC1 to identify top contributing features; examine the distribution of existing labels along the PC1 axis; identify that Category A has high positive scores while Category B has negative scores; conclude that PC1 separates Category A from Category B. * **Real Answer**: PC1 primarily separates Category A and Category B. * **Why this demonstrates the capability**: The agent must go beyond simple calculation by interpreting a latent statistical axis and grounding it in known metadata categories. Success requires relating mathematical variance to descriptive labels, which is a core part of advanced statistical analysis. --- **[Case 2]** * **Initial Environment**: A spatial data sandbox is provided, containing coordinate-aware measurements (x, y) and estimated sub-population abundances. The task requires identifying localized tissue structures. * **Real Question**: Identify the bone-formation niche (area of active growth) and determine which 5 marker genes are most significantly enriched there. * **Real Trajectory**: Cluster the data based on local sub-population composition; identify the cluster that corresponds to the 'bone-formation' signature; perform a differential expression test (e.g., t-test or Wilcoxon) comparing this cluster to all others; rank genes by significance and fold-change; return the top 5 genes. * **Real Answer**: The bone-formation niche is enriched for COL1A1, SPP1, SPARC, BGLAP, and IBSP. * **Why this demonstrates the capability**: This case demonstrates clustering-based inference and comparative differential analysis. The agent must identify an unsupervised group (niche) and derive a statistical signature (markers) that defines its unique characteristics relative to the rest of the data. --- **[Case 3]** * **Initial Environment**: A longitudinal or multi-condition dataset is provided with pre-annotated groups. The agent has access to statistical comparison tools in Python. * **Real Question**: How does the proportion of 'Injured' cells relative to 'Healthy' cells change across the 12-hour, 24-hour, and 48-hour time points? * **Real Trajectory**: Filter the dataset for the relevant sub-populations; aggregate the cell counts for each category at each temporal index; compute the percentage of 'Injured' cells relative to the total for each time point; identify the trend (e.g., peak at 24h); report the final distribution. * **Real Answer**: The proportion of 'Injured' cells is 15% at 12h, 45% at 24h, and 30% at 48h. * **Why this demonstrates the capability**: The agent performs distributional comparison over a specific metadata index (time). This shows the ability to conduct descriptive trend analysis and derive comparative metrics from structured partitions of a larger dataset. ## Pipeline Execution Instructions To synthesize data for this capability, you must strictly follow a 3-phase pipeline. **Do not hallucinate steps.** Read the corresponding reference file for each phase sequentially: 1. **Phase 1: Environment Exploration** Read the exploration guidelines to discover raw knowledge seeds: `references/EXPLORATION.md` 2. **Phase 2: Trajectory Selection** Once Phase 1 is complete, read the selection criteria to evaluate the trajectory: `references/SELECTION.md` 3. **Phase 3: Data Synthesis** Once a trajectory passes Phase 2, read the synthesis instructions to generate the final data: `references/SYNTHESIS.md`