← All worksheets
WEEK 7 · INDEPENDENT PRACTICE

Two groups: paired and independent t-tests

Concepts, calculations, scientific claims and a formative self-check.

4 × 5 = 20 marks30–45 minutesNo R required

Scenario: Suppose three people have pre/post scores of 60/63, 70/76 and 80/82. These are not independent groups.

Use the fictional dataset if the question refers to it. Always show your reasoning; an exact number without context is not enough. The four written tasks are teacher-assessed. The self-check below is formative and does not affect the 20-mark assignment.

Written problem set

TASK 1 · 5 MARKS

Define and frame

Calculate the three within-person post-minus-pre differences and their mean.

TASK 2 · 5 MARKS

Calculate or apply

Explain why a paired t-test is appropriate and how it differs from a two-independent-group comparison.

TASK 3 · 5 MARKS

Evaluate the design

Explain why Welch's test is useful when comparing independent A and B groups with potentially unequal variances.

TASK 4 · 5 MARKS

Interpret and communicate

Give two reasons a pre/post increase does not prove the method caused improvement.

Standard scoring guide

Each written task is worth 5 points: correct key idea (2), justified application or computation (2), and a clear statement with limits (1). This original rubric is not official UCL assessment.

Formative self-check · 4 questions

Choose one answer for each item, then check the feedback. Answers and explanations are available on this public study page; the separate written-task instructor key is private.

1. Test for before/after observations from the same person?
2. Mean of differences 3,6,2?
3. A benefit of Welch's t-test?
4. Why is pre/post improvement alone not causal?