Two means can be compared in two quite different situations, and using the wrong procedure is a serious error.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Paired data
Each observation in one group is matched to one in the other: before and after on the same subject, or matched twins.
Analyse the differences
For paired data, compute each difference and run a one-sample t procedure on those differences. There is one sample, not two.
Two-sample data
When the two groups contain unrelated individuals, a two-sample t procedure applies and the sample sizes may differ.
How to decide
Ask whether each value in one group has a natural partner in the other. If it does, the design is paired.
Why pairing helps
Pairing removes the variation between subjects, so a smaller real difference becomes detectable.
Paired or independent?
If each observation in one group is naturally matched with one in the other — before and after on the same subject — the data are paired and you analyse the differences. Treating paired data as independent discards the pairing and loses power.
A paired test is a one-sample test
Compute the difference for each pair and run a one-sample t procedure on those differences. Recognising this collapses an apparently new procedure into one already known.
Two-sample procedures
For genuinely independent groups, the two-sample t procedure applies, with conditions checked in each group. The degrees of freedom are awkward and are normally left to technology.
Identifying which applies
Ask whether the two samples have the same size by necessity and whether each observation has a natural partner. If yes to both, the design is paired. Getting this wrong invalidates the whole analysis.
Step 2: Try It Yourself
Tap and try it out.
- Minimum2
- Lower quartile3
- Median5
- Upper quartile7
- Maximum8
- Interquartile range4
Each of the four sections holds a quarter of the values, however wide it looks. A narrow box means the middle half of the data is packed close together.
Step 3: Watch an Example
One step at a time.
Watch Rosa Choose a Procedure
Rosa has the blood pressure of 20 patients before and after a treatment.
- Step 1
Each after reading belongs to the same patient as one before reading.
Step 4: Your Turn
Practice makes it stick.
The Design
Problem 1 of 2
Before and after readings on the same 20 patients. Paired or two-sample? 1 paired, 2 two-sample.
The Count
Problem 2 of 2
20 patients measured twice. How many differences are analysed?
Paired or Not
1 of 8
Two unrelated groups of 30 and 40 people. Paired or two-sample? 1 or 2?
2 of 8
Left and right hand strength on the same people. 1 paired, 2 two-sample.
3 of 8
Paired data with 15 subjects. Degrees of freedom for the t procedure?
4 of 8
Can two-sample groups have different sizes? 1 yes, 0 no.
5 of 8
Can paired groups have different sizes? 1 yes, 0 no.
6 of 8
Differences 2, 4, 6. What is their mean?
7 of 8
Sort each study by its design.
Tap something to move it.
- Empty
- Empty
8 of 8
Paired data with 25 subjects. Degrees of freedom?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Paired data with 12 subjects. What are the degrees of freedom?
Question 2 of 2
How do you decide whether a design is paired?
What You Learned
- Paired data has a natural partner for every observation.
- Analyse paired data as one sample of differences.
- Two independent groups need a two-sample procedure and may differ in size.