# Analysis Summary: Distance Between Flies

## Key Findings

### Overall Statistics
- Trained flies (aligned to barrier opening):
  - Data points: 46,613
  - Mean distance: 92.72
  - Std distance: 111.86

- Untrained flies (aligned to barrier opening):
  - Data points: 46,866
  - Mean distance: 78.67
  - Std distance: 102.86

### Pre-Opening Period (t < 0)
During this period, flies are physically separated by a barrier:
- Trained mean distance: 155.27
- Untrained mean distance: 147.19

### Post-Opening Period (t > 0)
After the barrier is removed and flies can interact:
- Trained mean distance: 77.44
- Untrained mean distance: 61.87

## Statistical Tests

### Pre-opening period comparison:
- Trained mean: 155.27, Untrained mean: 147.19
- T-statistic: 4.4024, P-value: 1.08e-05
- Cohen's d: 0.0654

### Post-opening period comparison:
- Trained mean: 72.52, Untrained mean: 63.86
- T-statistic: 30.4693, P-value: 1.08e-203
- Cohen's d: 0.0914

### Within-group changes:
- Trained flies - Pre vs Post:
  - Mean change: -82.75
  - T-statistic: 77.2805, P-value: 0.00e+00
  - Cohen's d: -0.8313

- Untrained flies - Pre vs Post:
  - Mean change: -83.33
  - T-statistic: 84.4719, P-value: 0.00e+00
  - Cohen's d: -0.9022

## Interpretation

1. **Pre-opening**: Both groups show high distances as expected since flies are separated by a barrier. There is a statistically significant difference between groups (p < 0.001), but the effect size is very small (Cohen's d = 0.0654).

2. **Post-opening**: Both groups show reduced distances after the barrier is removed, indicating interaction between flies. There is a statistically significant difference between groups (p < 0.001) with a small effect size (Cohen's d = 0.0914).

3. **Within-group changes**: Both trained and untrained flies show significant decreases in distance after the barrier opens (p < 0.001). The effect sizes are large for both groups (Cohen's d = -0.8313 for trained, -0.9022 for untrained).

4. **Group Differences**: 
   - Trained flies maintain slightly higher distances than untrained flies both before and after barrier opening.
   - This could indicate different behavioral patterns between trained and untrained flies, though the effect sizes are small.

## Visualization

The plot "avg_distance_aligned_to_opening.png" shows:
- Blue line: Average distance for trained flies (smoothed)
- Red line: Average distance for untrained flies (smoothed)
- Black dashed line: Time of barrier opening (t=0)

The visualization clearly shows the transition from high distances (pre-opening) to lower distances (post-opening) for both groups, with trained flies consistently maintaining slightly higher distances than untrained flies.