MATH / STATISTICAL INFERENCE

Difference Between Means Confidence Interval Calculator

Estimate an independent two-mean difference using an unpooled standard error and supplied critical value. Inspect the equation, substituted values, result, assumptions, and interpretation in one guided workspace.

01 Calculated in this tab
02 Values stay in this browser tab
03 Use boundary

Conversion input

Known value

Filter by unit name, symbol, or code. Your current selections remain available.

Equation inputs

First sample meanEnter the first sample mean for the same dataset or geometry.Second sample meanEnter the second sample mean for the same dataset or geometry.First sample standard deviationEnter the first sample standard deviation for the same dataset or geometry.Second sample standard deviationEnter the second sample standard deviation for the same dataset or geometry.First sample sizeEnter the first sample size for the same dataset or geometry.Second sample sizeEnter the second sample size for the same dataset or geometry.Critical valueEnter the critical value for the same dataset or geometry.

Preparing the calculator...

Use boundary

Calculation path

Estimate an independent two-mean difference using an unpooled standard error and supplied critical value. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.

Calculation path

(x1-x2) +/- c sqrt(s1^2/n1+s2^2/n2)

What you provide

First sample mean, using the same scenario as the other inputs
Second sample mean, using the same scenario as the other inputs
First sample standard deviation, using the same scenario as the other inputs
Second sample standard deviation, using the same scenario as the other inputs
First sample size, using the same scenario as the other inputs
Second sample size, using the same scenario as the other inputs
Critical value, using the same scenario as the other inputs

What you receive

Lower confidence bound from the stated equation
A symbolic formula plus substituted working with your values
Visible assumptions, field guidance, and an authoritative learning reference

Use boundary

Choose the maximum decimal places shown. This does not increase source accuracy.

Samples are independent and the selected critical value matches the intended sampling model and confidence level.

Use internally consistent units and retain extra precision when carrying the result into another calculation.

Reviewed reference factors

OpenStax Introductory Statistics 2e

Difference Between Means Confidence Interval Calculator

Calculation path

What you provide

What you receive

Choose the maximum decimal places shown. This does not increase source accuracy.

Reviewed reference factors

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