Statistical Analysis

AnthropicOfficialPublished by Anthropic

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Data and AI
Apache-2.0
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From the author

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.

— the description by Anthropic

AutoGineer summary

Written by AutoGineer from the skill’s own files, not by the author

This skill provides a structured framework for performing statistical analysis, emphasizing practical application over theoretical complexity. It covers descriptive statistics, trend analysis, outlier detection, and hypothesis testing, while offering critical guidance on interpreting results and avoiding common statistical pitfalls like correlation-causation fallacies and Simpson's Paradox. It is designed to help analysts communicate data insights with appropriate nuance and rigor.

What it does

Provides methodologies for descriptive statistics, including central tendency and variability measures.
Offers techniques for trend analysis, seasonality detection, and simple forecasting.
Outlines statistical approaches for identifying and handling outliers and anomalies.
Explains the framework for hypothesis testing, including common tests and significance interpretation.
Highlights common statistical traps such as survivorship bias and the multiple comparisons problem.
Advises on how to communicate uncertainty and practical significance to stakeholders.

When to use it

When analyzing data distributions to determine the best metrics for reporting.
When identifying trends or seasonal patterns in time-series data.
When evaluating whether observed differences in A/B tests are statistically significant.
When cleaning datasets and deciding how to treat extreme values or anomalies.
When interpreting business metrics to ensure claims are supported by evidence.

Advantages

Promotes rigorous data interpretation by balancing statistical and practical significance.
Encourages transparent reporting by recommending ranges instead of false precision.
Provides clear guidance on choosing the right statistical tests for different data types.
Helps prevent common analytical errors through awareness of cognitive and statistical biases.

Usage examples

“How should I report the average revenue per user if my data is highly skewed?”: The skill advises reporting both the mean and the median, noting that the gap between them illustrates the skew, and suggests using the median as a robust measure of the typical user.
“Is my A/B test result statistically significant?”: The skill provides a framework to define null and alternative hypotheses, choose a significance level, select the appropriate test (e.g., t-test or z-test), and evaluate both statistical and practical significance.
“How do I handle outliers in my dataset?”: The skill recommends investigating the cause of outliers (errors vs. genuine extremes) and suggests using robust statistics like the IQR method or segmenting the data rather than automatically deleting records.
“What is the best way to forecast next month's signups?”: The skill suggests using simple methods like seasonal naive or moving averages as a baseline, while emphasizing the importance of providing a range of outcomes rather than a single point estimate.

Install

Download the skill as a ZIP:
https://autogineer.com/agent-skills/anthropics/statistical-analysis/download

Unzip it into the cross-client skills folder of your project:

mkdir -p .agents/skills && unzip statistical-analysis.zip -d .agents/skills

Documentation by Anthropic

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
Outliers: How many and how extreme
Bounds: Is there a natural floor (zero) or ceiling (100%)?

Trend Analysis and Forecasting

Identifying Trends

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:

Week-over-week (WoW): Compare to same day last week
Month-over-month (MoM): Compare to same month prior
Year-over-year (YoY): Gold standard for seasonal businesses
Same-day-last-year: Compare specific calendar day

Growth rates:

Simple growth: (current - previous) / previous
CAGR: (ending / beginning) ^ (1 / years) - 1
Log growth: ln(current / previous)  -- better for volatile series

Seasonality Detection

Check for periodic patterns:

Plot the raw time series -- visual inspection first
Compute day-of-week averages: is there a clear weekly pattern?
Compute month-of-year averages: is there an annual cycle?
When comparing periods, always use YoY or same-period comparisons to avoid conflating trend with seasonality

Forecasting (Simple Methods)

For business analysts (not data scientists), use straightforward methods:

Naive forecast: Tomorrow = today. Use as a baseline.
Seasonal naive: Tomorrow = same day last week/year.
Linear trend: Fit a line to historical data. Only for clearly linear trends.
Moving average forecast: Use trailing average as the forecast.

Always communicate uncertainty. Provide a range, not a point estimate:

"We expect 10K-12K signups next month based on the 3-month trend"
NOT "We will get exactly 11,234 signups next month"

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.

Outlier and Anomaly Detection

Statistical Methods

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))]

Handling Outliers

Do NOT automatically remove outliers. Instead:

Investigate: Is this a data error, a genuine extreme value, or a different population?
Data errors: Fix or remove (e.g., negative ages, timestamps in year 1970)
Genuine extremes: Keep them but consider using robust statistics (median instead of mean)
Different population: Segment them out for separate analysis (e.g., enterprise vs. SMB customers)

Report what you did: "We excluded 47 records (0.3%) with transaction amounts >$50K, which represent bulk enterprise orders analyzed separately."

Time Series Anomaly Detection

For detecting unusual values in a time series:

Compute expected value (moving average or same-period-last-year)
Compute deviation from expected
Flag deviations beyond a threshold (typically 2-3 standard deviations of the residuals)
Distinguish between point anomalies (single unusual value) and change points (sustained shift)

Hypothesis Testing Basics

When to Use

Use hypothesis testing when you need to determine whether an observed difference is likely real or could be due to random chance. Common scenarios:

A/B test results: Is variant B actually better than A?
Before/after comparison: Did the product change actually move the metric?
Segment comparison: Do enterprise customers really have higher retention?

The Framework

Null hypothesis (H0): There is no difference (the default assumption)
Alternative hypothesis (H1): There is a difference
Choose significance level (alpha): Typically 0.05 (5% chance of false positive)
Compute test statistic and p-value
Interpret: If p < alpha, reject H0 (evidence of a real difference)

Common Tests

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

Practical Significance vs. Statistical Significance

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:

Effect size: How big is the difference? (e.g., "Variant B improved conversion by 0.3 percentage points")
Confidence interval: What's the range of plausible true effects?
Business impact: What does this translate to in revenue, users, or other business terms?

Sample Size Considerations

Small samples produce unreliable results, even with significant p-values
Rule of thumb for proportions: Need at least 30 events per group for basic reliability
For detecting small effects (e.g., 1% conversion rate change), you may need thousands of observations per group
If your sample is small, say so: "With only 200 observations per group, we have limited power to detect effects smaller than X%"

When to Be Cautious About Statistical Claims

Correlation Is Not Causation

When you find a correlation, explicitly consider:

Reverse causation: Maybe B causes A, not A causes B
Confounding variables: Maybe C causes both A and B
Coincidence: With enough variables, spurious correlations are inevitable

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"

Multiple Comparisons Problem

When you test many hypotheses, some will be "significant" by chance:

Testing 20 metrics at p=0.05 means ~1 will be falsely significant
If you looked at many segments before finding one that's different, note that
Adjust for multiple comparisons with Bonferroni correction (divide alpha by number of tests) or report how many tests were run

Simpson's Paradox

A trend in aggregated data can reverse when data is segmented:

Always check whether the conclusion holds across key segments
Example: Overall conversion goes up, but conversion goes down in every segment -- because the mix shifted toward a higher-converting segment

Survivorship Bias

You can only analyze entities that "survived" to be in your dataset:

Analyzing active users ignores those who churned
Analyzing successful companies ignores those that failed
Always ask: "Who is missing from this dataset, and would their inclusion change the conclusion?"

Ecological Fallacy

Aggregate trends may not apply to individuals:

"Countries with higher X have higher Y" does NOT mean "individuals with higher X have higher Y"
Be careful about applying group-level findings to individual cases

Anchoring on Specific Numbers

Be wary of false precision:

"Churn will be 4.73% next quarter" implies more certainty than is warranted
Prefer ranges: "We expect churn between 4-6% based on historical patterns"
Round appropriately: "About 5%" is often more honest than "4.73%"

Files

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Requirements and compatibility

Written for: Claude Code, Claude apps

Works with: Claude Code, Claude apps, OpenAI Codex, GitHub Copilot, Cursor, Gemini CLI, Kiro, OpenCode, Goose, Amp, Roo Code, JetBrains Junie, Factory Droid, Devin (ex-Windsurf), Mistral Vibe, OpenHands, Letta

“Works with” means the tool reads the open Agent Skills format; a skill written for one tool may use features others lack.

Needs: Claude Code frontmatter, Needs Python

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Attribution and licence

Published by

Anthropic

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Anthropic (Official)

Source

anthropics/knowledge-work-plugins · data/skills/statistical-analysis · commit e050c2e

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2026-11-09

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