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:

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:

1. Plot the raw time series -- visual inspection first
2. Compute day-of-week averages: is there a clear weekly pattern?
3. Compute month-of-year averages: is there an annual cycle?
4. 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"

…