Section 11.2

Inference about Two Means: Dependent Samples

Analyze matched-pairs data by working with the differences between paired observations.

1

Matched-Pairs Design

Dependent Samples

Observations in one sample are related to observations in the other:

Before / After

Same person, two measurements

Twins

Genetically linked pairs

Husband / Wife

Naturally paired observations

2

Working with Differences

Instead of comparing two means directly, compute the difference for each pair:

Mean of the differences

Standard deviation of the differences

3

t-Test Statistic

Requirements

Random matched-pairs sample
Differences are normally distributed OR
No outliers in differences

df = n - 1 (where n = number of pairs)

4

Confidence Interval for

This interval estimates the mean difference between matched pairs.

5

Matched Pairs Calculator

Matched Pairs (Dependent Samples) Calculator

t-test and CI for paired differences

Null:
Alternative:
df:
14
Test Statistic

t-Distribution (df = 14)

-2.1452.1450t₀ = 3.03

Classical Approach

Critical Region: t < -2.145 or t > 2.145
t₀ = 3.0258 is in rejection region

P-Value Approach

P-value = 0.0091
P-value < α = 0.05

Reject H₀

At the α = 0.05 level, there is sufficient evidence to conclude that the mean difference is different from 0.

!

Common Pitfalls

Using Two-Sample t-Test

Matched pairs require the one-sample t-test on differences, not the independent two-sample test.

Wrong n Value

n is the number of pairs, not the total number of observations.

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