tpmjs/packages/tools/official/STATISTICS_TOOLS.md

# Statistics Tools Implementation Summary

Successfully implemented 3 statistical analysis tools for the TPMJS official tools collection.

## Tools Implemented

### 1. Permutation Test (`@tpmjs/tools-permutation-test`)
**Path:** `/Users/ajaxdavis/repos/tpmjs/tpmjs/packages/tools/official/permutation-test`

**Purpose:** Performs a permutation test to assess the statistical significance of the difference in means between two groups.

**Features:**
- Non-parametric hypothesis testing
- Configurable iterations (100-100,000)
- Returns p-value, observed difference, significance status
- No assumptions about distribution

**Example:**
```typescript
const result = await permutationTestTool.execute({
  group1: [23, 25, 27, 29, 31],
  group2: [18, 20, 22, 24, 26],
  iterations: 10000
});
// Returns: pValue, observedDiff, significant, metadata
```

### 2. Multiple Testing Adjustment (`@tpmjs/tools-multiple-testing-adjust`)
**Path:** `/Users/ajaxdavis/repos/tpmjs/tpmjs/packages/tools/official/multiple-testing-adjust`

**Purpose:** Adjusts p-values for multiple comparisons using Bonferroni, Benjamini-Hochberg (BH), or Holm methods.

**Features:**
- Three adjustment methods:
  - **Bonferroni**: Most conservative, controls FWER
  - **Benjamini-Hochberg (BH)**: Controls FDR, less conservative
  - **Holm**: Step-down procedure, more powerful than Bonferroni
- Returns adjusted p-values and indices of significant tests
- Handles monotonicity constraints correctly

**Example:**
```typescript
const result = await multipleTestingAdjustTool.execute({
  pValues: [0.001, 0.02, 0.03, 0.15, 0.8],
  method: 'bh',
  alpha: 0.05
});
// Returns: adjusted[], significant[], method, alpha, metadata
```

### 3. Linear Regression OLS (`@tpmjs/tools-linear-regression-ols`)
**Path:** `/Users/ajaxdavis/repos/tpmjs/tpmjs/packages/tools/official/linear-regression-ols`

**Purpose:** Performs simple linear regression using Ordinary Least Squares (OLS) method.

**Features:**
- Calculates slope and intercept
- Computes R-squared (coefficient of determination)
- Returns residuals and predictions
- Handles edge cases (identical x or y values)

**Example:**
```typescript
const result = await linearRegressionOLSTool.execute({
  x: [1, 2, 3, 4, 5],
  y: [2, 4, 5, 4, 5]
});
// Returns: slope, intercept, rSquared, residuals[], predictions[], metadata
```

## Implementation Details

### Architecture
- Each tool follows the TPMJS pattern using AI SDK v6
- Uses `import { tool, jsonSchema } from 'ai'`
- TypeScript with strict type checking
- No external statistical libraries - implemented from scratch
- Comprehensive input validation

### File Structure (each tool)
```
tool-name/
├── src/
│   └── index.ts          # Main implementation
├── dist/                 # Built output (ESM + TypeScript declarations)
│   ├── index.js
│   └── index.d.ts
├── package.json          # Package configuration with tpmjs metadata
├── tsconfig.json         # TypeScript configuration
├── tsup.config.ts        # Build configuration
└── README.md            # Documentation with examples
```

### Build Status
✅ All tools build successfully
✅ All tools pass TypeScript type-check
✅ All tools tested and working correctly

### Statistical Algorithms Implemented

**Permutation Test:**
- Fisher-Yates shuffle algorithm
- Monte Carlo permutation sampling
- Two-tailed p-value calculation

**Multiple Testing Adjustment:**
- Bonferroni correction: p_adj = min(1, p × n)
- Benjamini-Hochberg: Monotonic FDR control
- Holm step-down: Sequential rejection procedure

**Linear Regression:**
- OLS slope: β₁ = Σ((x-x̄)(y-ȳ)) / Σ((x-x̄)²)
- OLS intercept: β₀ = ȳ - β₁x̄
- R-squared: R² = 1 - (SSE/SST)

## Package Metadata

Each tool includes proper `tpmjs` metadata in package.json:
- Category: `statistics`
- Framework: `vercel-ai`
- Tool documentation with parameters and returns
- Published to npm under `@tpmjs` scope

## Testing Results

All three tools have been tested and verified working:

```
✅ Permutation Test: Correctly identifies significance with p-values
✅ Multiple Testing Adjust: Properly adjusts p-values with BH method
✅ Linear Regression: Accurately calculates slope, intercept, and R²
```

## Next Steps

The tools are ready to be:
1. Added to `blocks.yml` (to be done by user)
2. Published to npm
3. Documented on tpmjs.com

## Dependencies

- `ai`: ^6.0.0-beta.124 (AI SDK v6)
- No external statistical libraries required
- All algorithms implemented from scratch for transparency and control