Exploratory Data Analysis
Beginner 12 min read Exploratory Data Analysis

Bivariate Analysis

The first 'does one thing move with another?'

Two variables, one question: does X move with Y? Cross-tabs for categories, scatter/grouped-box for numerics, correlation and segment-mixed means point to the hypotheses worth testing.

cross-tabscattercorrelationgrouped boxconfoundsegment
Prerequisites: Univariate Analysis
Before we start

What you will learn

  • Build cross-tabs for category pairs
  • Read scatter, grouped box and correlation together
  • Spot segment-mixed relationships and confounding cues
Introduction

What is this?

Bivariate analysis pairs variables: crosstab for two categoricals, grouped box/bar for a numeric-by-category, scatter for two numerics, and Pearson correlation as a scalar summary. The recurring trap is the confound — a third variable that actually drives both, which bivariate pairs can only hint at.

Motivation

Why do you need it?

  • The sharpest analysis questions are relational: does plan change spend?
  • A confound seen early ('older users churn more' hides 'legacy plan') redirects the analysis.
  • Crosstabs and grouped summaries are the raw material of every dashboard segment.
  • Correlation, honestly read, is the pre-causation checkpoint.
Think about it

Mental model

Imagine

Marriage records vs states studied together

Think of

Bivariate analysis

Looking at marriage rate by state and temperature by the same states suggests two maps that 'appear' related — until you notice population density moves both. Bivariate charts show the apparent link; the confound lurks one dimension deeper.

Mechanics

How it works

  • pd.crosstab(df.a, df.b) tabulates category co-occurrences.
  • df.groupby(cat)[num].agg(['mean','median']) summarizes a numeric per segment.
  • Scatter (df.plot.scatter x, y) shows direction, shape and outliers together.
  • Grouped box plots compare segment distributions tail-to-tail.
  • df[num_cols].corr() gives the numeric correlation matrix in one call.
  • Stratify: re-slice by a likely confounder and watch the relationship change.

Question → view → readout.

Q
Types
View
Confound
Finding
Hands-on

Examples

Numeric-by-category, then stratify

Numeric-by-category, then stratify
import numpy as np, pandas as pd
df = pd.DataFrame({
    "plan": ["basic", "pro"] * 50,
    "tenure": np.random.default_rng(6).integers(1, 60, 100),
})
df["spend"] = df["plan"].map({"basic": 20, "pro": 60}) + df["tenure"] * 0.5 + np.random.default_rng(6).normal(0, 5, 100)
print(df.groupby("plan")["spend"].agg(["mean", "median"]).round(1))
print(df[["tenure", "spend"]].corr().round(3))

Grouped summaries show plan differences; the correlation with tenure hints a confound worth stratifying.

Real world

In production

  • A support team crosstabs ticket priority by region and finds the SLA rule drives both.
  • A marketing BI slice shows spend-by-channel, then by user's plan to expose channel-plan confounds.
  • A retention analysis scatters days-since-last-login vs churn probability segmented by plan tier.
Guidelines

Best practices

  • Always pair the crosstab with row/column percentages (normalize=True) — counts alone deceive on unbalanced groups.
  • Add the confounder stratify step before claiming any relationship.
  • Correlation is a readout, not a conclusion — anchor it to the scatter.
  • Keep segment sample sizes visible; tiny cells look like big effects.
Watch out

Common mistakes

  • Confusing correlation with causation straight out of the scatter.
  • Crosstabs with raw counts hiding wildly different group sizes.
  • Ignoring the confound that reverses the relationship when stratified.
  • Reporting high correlation from a handful of outliers.
When things break

Debugging tips

  • A correlation flips sign when segmented → it was confounded; report both layers.
  • Scatter with a tight vertical line → a factor or rounding dominates; fix scale first.
  • Grouped means close but spreads huge → report medians and IQRs too.
  • When a cross-tab cell is disproportionate, break it by the third variable.
Interviews

Interview checkpoint

Practice

Hands-on lab

Profile Plan vs Spend with Stratification
30 min · beginner
In progress
Objectives
  • Build grouped means and a crosstab
  • Read correlation with scatter intuition
  • Stratify by a confounder and compare

Profile Plan vs Spend with Stratification

30 min · beginner

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sandbox · Linux sandbox
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Test yourself

Quick quiz

0/2
1

A high correlation between X and Y most often means:

2

Stratifying by a third variable can change the direction of an apparent relationship.

Go deeper

Official documentation

pandas: crosstab
docs