---
title: "Lift measure with example"
subject: "Data Mining"
chapter: 4
key: "semester_7/data_mining:lift-measure"
source: https://www.bctengineer.com/q/semester_7/data_mining/lift-measure
site: BCT Engineering
---

# Lift measure with example

Data Mining · Chapter 4: Association Analysis

- Asked in: year not given
- Video: [Machine Learning | LIFT Measure](https://www.youtube.com/watch?v=FGGlscdeMOQ) — RANJI RAJ
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/data_mining/lift-measure
- Whole chapter: https://www.bctengineer.com/md/semester_7/data_mining/chapter-4

## Question

Define the measure "Lift" with suitable example. What does it signify?

## Short answer

Lift = P(A∪B)/(P(A)P(B)) = confidence/support(B). Measures correlation: >1 positive, =1 independent, <1 negative. Example: 6 transactions, 4 Chips, 3 Coke, 3 both. Support=0.5, P(Chips)=0.667, P(Coke)=0.5, Lift=1.5. Indicates Coke makes Chips 1.5x more likely.

## Answer

**Lift** is a correlation measure of an association rule that tells whether the occurrence of A and B together is more (or less) than expected if they were independent. Support and confidence alone can be misleading, since a rule can have high confidence only because B is itself very common.

#### Definition
For the rule A → B:

Lift(A, B) = P(A ∪ B) / (P(A)·P(B)) = confidence(A → B) / support(B)

#### What it signifies
| Lift value | Meaning |
| --- | --- |
| > 1 | A and B are **positively correlated**: A makes B more likely |
| = 1 | A and B are **independent**; the rule is not useful |
| < 1 | A and B are **negatively correlated**: A makes B less likely |

The larger the lift, the stronger the association; lift is symmetric: lift(A, B) = lift(B, A).

#### Example
Among 6 transactions of a shop: 4 contain Chips, 3 contain Coke, and 3 contain both.
- Support(Chips ∪ Coke) = 3/6 = 0.5
- P(Chips) = 4/6 = 0.667; P(Coke) = 3/6 = 0.5
- Lift = 0.5/(0.667 × 0.5) = **1.5**

Lift 1.5 > 1: buying Coke makes Chips 1.5 times more likely than average, so they are positively correlated.

*Misleading-rule example*: of 10000 customers, 6000 buy computer games, 7500 buy videos, 4000 buy both. Rule games → videos has confidence 4000/6000 = 66.7% and looks strong, but lift = 0.4/(0.6 × 0.75) = 0.89 < 1: games and videos are actually negatively correlated.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which expresses lift of A -> B?
   A. confidence(A -> B) / support(B)
   B. support(A) / support(B)
   C. confidence(A -> B) x support(B)
   D. support(A union B) / support(A)
   Answer: A. Lift = P(A union B)/(P(A)P(B)) = confidence/support(B). (Key point: Lift formula)

2. What does lift = 1 signify?
   A. A and B are strongly positively correlated
   B. A and B are independent; the rule is not useful
   C. A and B are negatively correlated
   D. The rule has 100% confidence
   Answer: B. Lift 1 means joint occurrence is just as expected under independence. (Key point: Meaning of value 1)

3. Chips 4/6, Coke 3/6, both 3/6. What is lift?
   A. 0.75
   B. 1.0
   C. 1.5
   D. 0.89
   Answer: C. 0.5/(0.667 x 0.5) = 1.5 > 1, so positively correlated. (Key point: Example)

4. Games -> videos has 66.7% confidence but lift 0.89. What does this show?
   A. The rule is strong and reliable
   B. The items are independent
   C. The rule has high support but low confidence
   D. The items are negatively correlated, so high confidence was misleading
   Answer: D. Videos are common (75%), so confidence 66.7% is below the expected rate; lift < 1. (Key point: Misleading rule)