# Descriptive And Statistical Analysis

> Skill: descriptive and statistical analysis

- Skill: `dingxingdi/descriptive-and-statistical-analysis` (Agent Skill, multi-file: 5 files)
- Install (CLI): `npx skillmds@latest add dingxingdi/descriptive-and-statistical-analysis`
- Raw SKILL.md: https://api.skillmd.com/api/skills/dingxingdi/descriptive-and-statistical-analysis/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: dingxingdi (https://skillmd.com/u/dingxingdi)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/dingxingdi/descriptive-and-statistical-analysis

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# 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.
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**[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.
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**[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`