1. The t-Test for Differences Between Groups

2. The t-Test
Tests whether the means of two groups are statistically different from each other

3. Statistical Analysis

4. Statistical Analysis
Control
group
mean

5. Statistical Analysis
Control
group
mean
Treatment
group
mean

6. Statistical Analysis Is there a difference? Control group mean
Treatment
group
mean
Is there a difference?

7. What Does Difference Mean?

8. What Does Difference Mean?
Medium
variability

9. What Does Difference Mean?
Medium
variability
High
variability

10. What Does Difference Mean?
Medium
variability
High
variability
Low
variability

11. What Does Difference Mean?
The mean difference
is the same for all
three cases.
Medium
variability
High
variability
Low
variability

12. What Does Difference Mean?
Medium
variability
High
variability
Which one shows
the greatest
difference?
Low
variability

13. What Does Difference Mean?
A statistical difference is a function of the difference between means relative to the variability.
A small difference between means with large variability could be due to chance.
Like a signal-to-noise ratio.
Which one shows
the greatest
difference?
Low
variability

14. What Do We Estimate?
Low
variability

15. What Do We Estimate?
Signal
Noise
Low
variability

16. Difference between group means
What Do We Estimate?
Signal
Difference between group means =
Noise
Low
variability

17. Difference between group means
What Do We Estimate?
Signal
Difference between group means =
Noise
Variability of groups
Low
variability

18. Difference between group means
What Do We Estimate?
Signal
Difference between group means =
Noise
Variability of groups _ _
XT - XC = _ _
SE(XT - XC)
Low
variability

19. Difference between group means
What Do We Estimate?
Signal
Difference between group means =
Noise
Variability of groups _ _
XT - XC = _ _
SE(XT - XC) =
t-value
Low
variability

20. What Do We Estimate?
The t-test, one-way Analysis of Variance (ANOVA) and a form of regression all test the same thing and can be considered equivalent alternative analyses.
The regression model is emphasized here because it is the most general.
Low
variability