Types of analysis: one, two or many variables

Most questions start with one variable, then ask how it relates to a second, and finally how several factors work together. Each step needs different summaries and different charts.

Three panels of synthetic data: a histogram of delivery days, a scatter plot of ad spend against revenue, and the same points coloured by sales channel.

Synthetic data for illustration.

Univariate analysis: one variable at a time

Question: What does this one variable look like?

You describe its centre (mean, median), spread (range, standard deviation) and shape (symmetric, skewed, any outliers).

Kind of variable Good summaries Good charts
Numbers (sales, days, age) Mean, median, minimum, maximum, spread Histogram, box plot
Categories (region, product type) Counts and percentages Bar chart sorted by size
Dates Counts per day, week or month Line chart over time

Business examples:

  • How long do deliveries usually take, and how long do the slowest ones take?
  • Which product category sells most often?
  • How many customer complaints arrive each week?

Watch for

A skewed shape. In the histogram above, most orders arrive within 1 to 5 days, but a long tail stretches past two weeks. The median (3 days) describes a typical order better than the mean (about 4 days), which the slow tail pulls upward.

Bivariate analysis: two variables together

Question: How does one variable change with another?

The two variables are… Good summaries Good charts
Number and number Correlation, trend line Scatter plot
Category and number Mean or median per group Bar chart, box plot per group
Category and category Counts in a cross-table Heat map, stacked or grouped bar
Date and number Change over time Line chart

Business examples:

  • Does higher advertising spend go with higher revenue?
  • Do some regions have longer delivery times than others?
  • Which customer segments buy which product categories?

Remember

A relationship between two variables is a correlation, not proof of cause. See How statistics can mislead.

Multivariate analysis: three or more variables

Question: Does the relationship change when we account for something else?

You add a third variable by using colour, size, small multiples (one small chart per group) or filters.

Business examples:

  • Does the link between ad spend and revenue differ by sales channel?
  • Do delivery times by region change once we separate standard and express shipping?
  • Is a profit drop explained by a change in the product mix?

The second and third panels show exactly the same points. Colouring by channel in the third panel shows that "Store" tends to sit above the others at the same spend, on average. That pattern is invisible in the two-variable chart.

Rule of thumb

Add one variable at a time. If a chart needs a long explanation, split it into small multiples instead.

Choosing a chart: quick guide

I want to show… Try
How values are distributed Histogram or box plot
A ranking Sorted bar chart
Change over time Line chart
Parts of a whole (few parts) Stacked bar; a pie only for two or three slices
Relationship between two numbers Scatter plot
Comparison across many groups Small multiples or a heat map
A single headline number Just the number, large and clearly labelled

Try it yourself

Exercise 1: classify the question

Is each question univariate, bivariate or multivariate?

  1. What is the typical order value?
  2. Do larger discounts go with lower profit?
  3. Does the discount–profit relationship differ between furniture and office supplies?
  4. How many orders were placed each month?

Exercise 2: pick the chart

For each question in Exercise 1, choose a chart type from the quick guide and say in one sentence why.

Exercise 3: your own data

Pick one variable from your own work. Write one univariate, one bivariate and one multivariate question you could ask about it.