## Line Graphs: Relationship Between Statistical Parameters and Test Configurations
### Overview
The image contains two line graphs (① and ②) analyzing statistical properties across different test configurations. Chart ① examines the relationship between pre-defined alpha levels and Type I Error/Power, while Chart ② explores how the number of maximum tests affects Power and Type I Error rates.
### Components/Axes
**Chart ①:**
- **X-axis**: Pre-defined alpha (0.10 to 0.20, increments of 0.05)
- **Y-axis**: Type I Error (0.100 to 0.225, increments of 0.025)
- **Legend**:
- Solid line: Power
- Dashed line: Type I Error
- **Legend Position**: Top-right corner of the chart
**Chart ②:**
- **X-axis**: Number of maximum tests (1, 3, 5, 7)
- **Y-axis**: Rate (0.0 to 0.6, increments of 0.1)
- **Legend**:
- Dashed line: Power
- Dotted line: Type I Error
- **Legend Position**: Top-right corner of the chart
### Detailed Analysis
**Chart ① Trends:**
1. **Type I Error (Dashed Line)**:
- At α=0.10: 0.100
- At α=0.15: 0.140
- At α=0.20: 0.225
- *Trend*: Linear increase with alpha (R²≈0.98)
2. **Power (Solid Line)**:
- At α=0.10: 0.100
- At α=0.15: 0.175
- At α=0.20: 0.225
- *Trend*: Accelerated increase, matching Type I Error at α=0.20
**Chart ② Trends:**
1. **Power (Dashed Line)**:
- At 1 test: 0.20
- At 3 tests: 0.60
- At 5 tests: 0.55
- At 7 tests: 0.65
- *Trend*: Non-linear increase with diminishing returns after 3 tests
2. **Type I Error (Dotted Line)**:
- At 1 test: 0.00
- At 3 tests: 0.15
- At 5 tests: 0.05
- At 7 tests: 0.15
- *Trend*: Bimodal pattern with mid-test dip
### Key Observations
1. **Chart ① Convergence**: Both Power and Type I Error reach identical values (0.225) at α=0.20, suggesting a critical threshold where statistical power maximizes at the cost of maximum Type I Error.
2. **Chart ② Power Tradeoff**: Increasing tests from 1→3 dramatically boosts Power (0.20→0.60), but additional tests yield smaller gains (0.60→0.65 between 3→7 tests).
3. **Type I Error Volatility**: The mid-test dip (0.05 at 5 tests) in Chart ② suggests potential correction mechanisms or methodological adjustments affecting error rates.
### Interpretation
These graphs demonstrate fundamental statistical tradeoffs:
- **Alpha Sensitivity**: Chart ① reveals that Type I Error scales linearly with alpha, while Power exhibits nonlinear growth, indicating diminishing returns at higher significance levels.
- **Multiple Testing Impact**: Chart ② shows that increasing test iterations improves Power but introduces erratic Type I Error patterns, likely due to Bonferroni-style corrections or adaptive testing protocols.
- **Practical Implications**: The convergence at α=0.20 in Chart ① suggests a potential optimal operating point for high-stakes testing scenarios where maximum power is required without exceeding critical error thresholds. The bimodal Type I Error pattern in Chart ② warrants investigation into whether the mid-test dip represents a methodological artifact or intentional design feature.
*Note: All values are approximate based on visual estimation from the chart scales.*
