// Apply statistical methods including descriptive stats, trend analysis, outlier detection, and hypothesis testing. Use when analyzing distributions, testing for significance, detecting anomalies, computing correlations, or interpreting statistical results.
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| name | statistical-analysis |
| description | Apply statistical methods including descriptive stats, trend analysis, outlier detection, and hypothesis testing. Use when analyzing distributions, testing for significance, detecting anomalies, computing correlations, or interpreting statistical results. |
| user-invocable | false |
Descriptive statistics, trend analysis, outlier detection, hypothesis testing, and guidance on when to be cautious about statistical claims.
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.
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."
Characterize every numeric distribution you analyze:
Moving averages to smooth noise:
# 7-day moving average (good for daily data with weekly seasonality)
df['ma_7d'] = df['metric'].rolling(window=7, min_periods=1).mean()
# 28-day moving average (smooths weekly AND monthly patterns)
df['ma_28d'] = df['metric'].rolling(window=28, min_periods=1).mean()
Period-over-period comparison:
Growth rates:
Simple growth: (current - previous) / previous
CAGR: (ending / beginning) ^ (1 / years) - 1
Log growth: ln(current / previous) -- better for volatile series
Check for periodic patterns:
For business analysts (not data scientists), use straightforward methods:
Always communicate uncertainty. Provide a range, not a point estimate:
When to escalate to a data scientist: Non-linear trends, multiple seasonalities, external factors (marketing spend, holidays), or when forecast accuracy matters for resource allocation.
Z-score method (for normally distributed data):
z_scores = (df['value'] - df['value'].mean()) / df['value'].std()
outliers = df[abs(z_scores) > 3] # More than 3 standard deviations
IQR method (robust to non-normal distributions):
Q1 = df['value'].quantile(0.25)
Q3 = df['value'].quantile(0.75)
IQR = Q3 - Q1
lower_bound = Q1 - 1.5 * IQR
upper_bound = Q3 + 1.5 * IQR
outliers = df[(df['value'] < lower_bound) | (df['value'] > upper_bound)]
Percentile method (simplest):
outliers = df[(df['value'] < df['value'].quantile(0.01)) |
(df['value'] > df['value'].quantile(0.99))]
Do NOT automatically remove outliers. Instead:
Report what you did: "We excluded 47 records (0.3%) with transaction amounts >$50K, which represent bulk enterprise orders analyzed separately."
For detecting unusual values in a time series:
Use hypothesis testing when you need to determine whether an observed difference is likely real or could be due to random chance. Common scenarios:
| Scenario | Test | When to Use |
|---|---|---|
| Compare two group means | t-test (independent) | Normal data, two groups |
| Compare two group proportions | z-test for proportions | Conversion rates, binary outcomes |
| Compare paired measurements | Paired t-test | Before/after on same entities |
| Compare 3+ group means | ANOVA | Multiple segments or variants |
| Non-normal data, two groups | Mann-Whitney U test | Skewed metrics, ordinal data |
| Association between categories | Chi-squared test | Two categorical variables |
Statistical significance means the difference is unlikely due to chance.
Practical significance means the difference is large enough to matter for business decisions.
A difference can be statistically significant but practically meaningless (common with large samples). Always report:
When you find a correlation, explicitly consider:
What you can say: "Users who use feature X have 30% higher retention" What you cannot say without more evidence: "Feature X causes 30% higher retention"
When you test many hypotheses, some will be "significant" by chance:
A trend in aggregated data can reverse when data is segmented:
You can only analyze entities that "survived" to be in your dataset:
Aggregate trends may not apply to individuals:
Be wary of false precision: