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Mathematics for Framing Questions  ›  Lesson

Absolute and Relative Change

Mathematics 12 minA change in a rate can be reported as an absolute difference in percentage points or as a relative change divided by the old value, and a clear report states both.

Absolute and Relative Change

Quick Checkout's early numbers are in: conversion went from 10% to 11%. One slide says "conversion up 1%". Another says "conversion up 10%". Both writers looked at the same two numbers, and a reader cannot tell which one means what, which is how a small win gets oversold or a big one gets ignored.

The rule

Points subtract; percents divide. Always say which one you mean.

When the thing you are measuring is already a percentage, there are two ways to describe a change.

  • Absolute change is the plain difference, measured in percentage points: 11% − 10% = 1 point.
  • Relative change divides that difference by the starting value:
relative change=new−oldold=11−1010=10%\text{relative change} = \frac{\text{new} - \text{old}}{\text{old}} = \frac{11 - 10}{10} = 10\%

In A/B testing the word lift usually means the relative change, so "a 10% lift" and "a 1-point rise" can describe the very same result. Neither is wrong. Leaving the reader to guess is wrong.

Relative change becomes dramatic on a small base. If complaints about damaged eggs go from 2 to 4 in a month, they "doubled", a 100% rise, but that is two extra complaints. Report the counts alongside.

Percent changes also do not cancel out. If weekly orders rise 50% and then fall 50%, you end at 1.5 × 0.5 = 0.75 of where you started, not back at the start.

The shortcut

Subtract for points, divide by the old value for percent, then write both, points first: "up 1 point (a 10% lift)". Dividing by the old value, never the new one, is the whole trick.

Refund rate falls from 4% to 3%Step 1 of 4

  1. Subtract

    3 − 4 = −1. Refunds fell by 1 percentage point.

Finally, turn points into things people can count. If 200,000 users reach checkout each month, a 1-point rise in conversion is 200,000 × 0.01 = 2,000 extra orders a month.

Drills

Answer fast — trust the rule.

Conversion rose from 10% to 11%. What is the relative change, in percent?
(11−10)÷10×100= ?(11 - 10) \div 10 \times 100 = \,?
quick drill

A rate moves from 20% to 25%. Which description is correct?

The share of orders flagged as fraud falls from 0.8% to 0.6%. What is the relative change, in percent?
(0.6−0.8)÷0.8×100= ?(0.6 - 0.8) \div 0.8 \times 100 = \,?
200,000 users reach checkout each month. How many extra orders a month does a 1-point rise in conversion add?
200000×1100= ?200000 \times \tfrac{1}{100} = \,?
quick drill

Weekly orders rise 50% one month and fall 50% the next. Compared with the start, orders are now:

Remember

  • Points subtract; percents divide by the old value.
  • Write both, points first: "up 1 point (a 10% lift)".
  • Trap: big percentages on tiny bases. Put the raw counts next to them.

Practice — level up

0/1 solved

Write your answer, then compare it with a rubric and a model answer.

ExplainFix the slide

A slide says: 'Quick Checkout improved conversion by 1%.' Conversion actually went from 10% to 11%. Explain what is ambiguous about the sentence, rewrite it so nobody can misread it, and say how many extra orders a month it means if 200,000 users reach checkout each month.