hypothesis

# Hypothesis Generation Command

Generate research hypotheses and experimental designs for dataset `$1` in domain `$2` using the hypothesis-generator subagent.

## Context
- Dataset location: @data_storage/$1
- Analysis domain: $2 (user-behavior, business-impact, technical-performance, custom)
- Current working directory: !`pwd`
- Output directory: ./hypothesis_reports/
- Available research methodologies and experimental designs
- Statistical analysis capabilities

## Your Task

Use the hypothesis-generator subagent to create rigorous, testable hypotheses:

### 1. Pattern Analysis
- Identify significant correlations and relationships
- Detect temporal patterns and trends
- Discover clusters and segments in the data
- Recognize anomalies and unusual patterns

### 2. Hypothesis Formulation
- Create clear, testable hypotheses
- Define null and alternative hypotheses
- Specify variables and their relationships
- Establish measurable outcomes and success criteria

### 3. Experimental Design
- Select appropriate research methodologies
- Design experimental approaches to test hypotheses
- Determine sample size and power requirements
- Plan data collection and measurement procedures

### 4. Validation Strategy
- Define statistical testing approaches
- Establish success criteria and metrics
- Plan for replication and verification
- Consider alternative explanations and approaches

## Analysis Domains

### User Behavior
- **Engagement Patterns**: User interaction and engagement hypotheses
- **Conversion Optimization**: Conversion rate and funnel analysis hypotheses
- **Retention and Churn**: User retention and churn prediction hypotheses
- **Segmentation**: User behavior segmentation hypotheses
- **Journey Analysis**: User journey and path analysis hypotheses

### Business Impact
- **Revenue Optimization**: Revenue generation and growth hypotheses
- **Cost Reduction**: Cost efficiency and optimization hypotheses
- **Market Expansion**: Market growth and expansion hypotheses
- **Customer Satisfaction**: Customer experience and satisfaction hypotheses
- **Operational Efficiency**: Process improvement and efficiency hypotheses

### Technical Performance
- **System Optimization**: Performance and scalability hypotheses
- **Reliability**: System stability and reliability hypotheses
- **Security**: Security vulnerability and protection hypotheses
- **User Experience**: Technical UX and performance hypotheses
- **Integration**: System integration and compatibility hypotheses

### Custom
- **Domain-Specific**: Custom domain-specific hypotheses
- **Research-Oriented**: Academic and research hypotheses
- **Experimental**: Novel experimental hypotheses
- **Predictive**: Predictive modeling hypotheses

## Hypothesis Types

### Descriptive Hypotheses
Describe patterns and relationships in the data without inferring causation.

**Example**: "There is a positive correlation between user engagement time and conversion rates."

### Explanatory Hypotheses
Explain underlying mechanisms and causal relationships.

**Example**: "Increased user engagement time leads to higher conversion rates due to improved product understanding."

### Predictive Hypotheses
Forecast future outcomes based on current patterns.

**Example**: "Users with engagement time > 5 minutes are 3x more likely to convert within 30 days."

### Prescriptive Hypotheses
Recommend optimal actions and interventions.

**Example**: "Implementing personalized recommendations will increase user engagement by 25%."

## Research Methodologies

### Experimental Designs
- **A/B Testing**: Randomized controlled experiments
- **Multivariate Testing**: Multiple variable experiments
- **Longitudinal Studies**: Time-series analysis
- **Cross-sectional Studies**: Point-in-time analysis
- **Quasi-experiments**: Non-randomized designs
- **Case Studies**: In-depth analysis of specific cases

### Statistical Approaches
- **Hypothesis Testing**: Statistical significance testing
- **Confidence Intervals**: Estimation of effect sizes
- **Bayesian Methods**: Bayesian hypothesis testing
- **Power Analysis**: Statistical power calculation
- **Effect Size Measurement**: Quantifying relationship strength

### Validation Methods
- **Cross-validation**: Model validation techniques
- **Bootstrapping**: Resampling validation
- **Sensitivity Analysis**: Testing robustness
- **Replication Studies**: Independent verification
- **Meta-analysis**: Synthesis of multiple studies

## Expected Output

### Hypothesis Documentation
- `hypothesis_reports/$1_$2_hypotheses.md` - Hypothesis documentation
- `hypothesis_reports/$1_$2_experimental_design.md` - Experimental design
- `hypothesis_reports/$1_$2_validation_plan.md` - Validation strategy
- `hypothesis_reports/$1_$2_research_proposal.md` - Research proposal

### Hypothesis Structure
Each hypothesis includes:
- **Clear Statement**: Testable hypothesis statement
- **Rationale**: Justification and theoretical foundation
- **Variables**: Independent and dependent variables
- **Methodology**: Proposed testing approach
- **Success Criteria**: Metrics for validation
- **Expected Outcomes**: Predicted results
- **Alternative Explanations**: Other possible explanations

### Experimental Design
Comprehensive experimental design including:
- **Research Questions**: Clear research questions
- **Methodology**: Detailed experimental approach
- **Sample Size**: Power analysis and justification
- **Variables**: Measurement and operationalization
- **Procedure**: Step-by-step experimental process
- **Analysis Plan**: Statistical analysis approach
- **Timeline**: Project schedule and milestones
- **Resources**: Required resources and budget

## Working Process

### 1. Data Pattern Discovery
```python
import pandas as pd
import numpy as np
from scipy import stats
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler

def discover_research_patterns(data):
    """Discover patterns that suggest research hypotheses"""
    patterns = {