Executive Summary
This study analyzes ping pong serve precision through a controlled experiment with 309 observations. We validated a Negative Binomial model (k=3, p=0.3) and found significant patterns in participant performance.
Key Finding
The data fits the proposed model with p-value = 0.660, validating the Negative Binomial distribution hypothesis.
Study Objectives
General Objective
Analyze the statistical behavior of ping pong serve precision using a Negative Binomial model.
Specific Objectives
- Validate the Negative Binomial model fit (k=3, p=0.3)
- Evaluate differences in average serve time
- Analyze relationships between categorical variables
- Quantify correlation between attempts and time
Descriptive Analysis
General Statistics
| Metric | Value | Description |
|---|---|---|
| Total Observations | 309 | Total number of experiments conducted |
| Mean Attempts | 3.2 | Average attempts until success |
| Mean Serve Time (s) | 1.945 | Average serve time in seconds |
| Std Dev Attempts | 2.1 | Variability in number of attempts |
| Std Dev Time | 0.32 | Variability in serve time |
Categorical Variable Distribution
Dominant Hand
Serve Height
Data Visualizations
Charts generated automatically by the R analysis pipeline
Attempts Distribution
Histogram showing the distribution of attempts until success. The red dashed line indicates the mean.
Serve Time Distribution
Distribution of serve time in seconds. Mean is significantly lower than the theoretical value of 2 seconds.
Attempts vs Time Correlation
Scatter plot showing the relationship between number of attempts and serve time. Moderate positive correlation suggests a fatigue effect.
Serve Time by Handedness
Comparison of time distribution between right-handed and left-handed players.
Inferential Statistics
Statistical Test Results
| Test | Statistic | P-Value | Conclusion | Significance |
|---|---|---|---|---|
| Goodness of Fit (Chi²) | χ² = 0.193 | 0.660 | Fits the model | Not Significant |
| Time vs 2 seconds | t = -3.18 | 0.002 | Significantly less than 2s | Significant |
| Attempts-Time Correlation | r = 0.65 | < 0.001 | Significant correlation | Very Significant |
Conclusions
Key Findings
Model Validated
Data fits the Negative Binomial model (k=3, p=0.3) with p = 0.660
Temporal Efficiency
Average serve time (1.945s) is significantly lower than theoretical 2 seconds
Positive Correlation
Moderate correlation (r = 0.65) between attempts and serve time
Natural Distribution
Right-handed player proportion (64.4%) is consistent with population distribution
Practical Implications
- Players tend to be more temporally efficient than expected
- Fatigue or technique adjustment influences time as attempts increase
- The Negative Binomial model is appropriate for predicting success patterns in this context