t-tests for two samples and for gains
Content for Thursday, February 18, 2027
Goals
By the end of this topic, you should be able to:
- Run a t-test for two independent samples, with a pooled variance
- Run a t-test on gains, and say why pairing helps
- Say what a gain alone can’t tell you, and why control groups exist
Reading
- Before session 1: Chapter 10. Skip Hartley’s F-max test (in 10-3) and r² (in 10-4).
- Before session 2: Chapter 11. Skip r² (in 11-4).
NoteThe book and our slides
- The book: writes the pooled variance as s²_p. Our slides: write σ̂²_p.
- The book: analyzes before-and-after gains in one group as evidence that a treatment worked. Our slides: without a control group, a gain also includes growth that would have happened anyway. Session 2 shows how much that matters for Mindspark.