1. T test

2. Rationale
What do we do when we want to compare two groups and the standard deviation of the population is not know?

3. Rationale
Since the standard deviation of the population is unknown, we will use an estimate instead.
One group

4. Rationale
Since the standard deviation of the population is unknown, we will use an estimate instead.
Two independent groups

5. Rationale
Since the standard deviation of the population is unknown, we will use an estimate instead.
Note: If n1 = n2, then the equation can be simplified

6. Rationale
Since the standard deviation of the population is unknown, we will use an estimate instead.
Two independent groups

7. Student T distribution

8. Student T distribution

9. Example (independent groups)

10. Example (independent groups)
General Linear Model (correlation)
Group 1
Group 2
The idea is to construct an independent variable that is going to identify to which group a given participant belongs to.
Ex1: 1 = first group and 0 = second group
Ex2: 1 = first group and -1 = second group

11. Example (independent groups)
1 = first group and -1 = second group

12. Example (independent groups)
General Linear Model (correlation)
Therefore, the t test is a special case of correlation (regression)

13. Power