statistical-analysis

# Statistical Analysis Skill

Descriptive statistics, trend analysis, outlier detection, hypothesis testing, and guidance on when to be cautious about statistical claims.

## Descriptive Statistics Methodology

### Central Tendency

Choose the right measure of center based on the data:

| Situation | Use | Why |
|---|---|---|
| Symmetric distribution, no outliers | Mean | Most efficient estimator |
| Skewed distribution | Median | Robust to outliers |
| Categorical or ordinal data | Mode | Only option for non-numeric |
| Highly skewed with outliers (e.g., revenue per user) | Median + mean | Report both; the gap shows skew |

**Always report mean and median together for business metrics.** If they diverge significantly, the data is skewed and the mean alone is misleading.

### Spread and Variability

- **Standard deviation**: How far values typically fall from the mean. Use with normally distributed data.
- **Interquartile range (IQR)**: Distance from p25 to p75. Robust to outliers. Use with skewed data.
- **Coefficient of variation (CV)**: StdDev / Mean. Use to compare variability across metrics with different scales.
- **Range**: Max minus min. Sensitive to outliers but gives a quick sense of data extent.

### Percentiles for Business Context

Report key percentiles to tell a richer story than mean alone:

```
p1:   Bottom 1% (floor / minimum typical value)
p5:   Low end of normal range
p25:  First quartile
p50:  Median (typical user)
p75:  Third quartile
p90:  Top 10% / power users
p95:  High end of normal range
p99:  Top 1% / extreme users
```

**Example narrative**: "The median session duration is 4.2 minutes, but the top 10% of users spend over 22 minutes per session, pulling the mean up to 7.8 minutes."

### Describing Distributions

Characterize every numeric distribution you analyze:

- **Shape**: Normal, right-skewed, left-skewed, bimodal, uniform, heavy-tailed
- **Center**: Mean and median (and the gap between them)
- **Spread**: Standard deviation or IQR