1. Comparing Two Groups
Statistics 2126

2. So far..
We have been able to compare a sample mean to a population mean
z test
t test
Often times though we have two groups to compare
Is Group 1 different from Group 2

3. Matched pairs or correlated t test
AKA dependent sample t test
When subjects are matched on a variable or are used as their own controls, a sort of before and after thing if you will
Be very careful with this
But it is way powerful and easy to do

4. Back to our mythical IQ course..
Before
After
Difference
103 98 -5
100
107 7
111
119 8 97 3
133
134 1
106 5 87 85 -2

5. A couple of summary statistics

6. Now it is a simple t test

7. And now for the decision
tobt = 2.95
Reject H0
Our IQ course works!!

8. Two sample problems
While is is useful to know how to compare a sample mean to a population mean and check for significance it is not all that common
We rarely know μ
Sometimes we do IQ
Differences
Theoretical values

9. The much more common question is…
Does one group differ from another?
Let’s say we had two classes with different teaching methods
Is there an effect of teaching method?

10. Some (made up) data Statistic Class 1 Class 2 Mean 77 71
Standard deviation
6.2
6.7
Number of students 49 52

11. Our hypotheses Are the two classes different? H0 μ1 = μ2 HA μ1 ≠ μ2
Or we could restate them like this:
H0 μ1 - μ2 = 0
HA μ1 ≠ μ2 ≠ 0

12. Let’s go back to the original t formula
Statistic ↓ H0 ↓
← Error

13. Figure it out

14. Now about that error…
We cannot just add the values of s for each group
They must be weighted

15. So the formula is

16. Degrees of freedom
With a one sample t test we lose one degree of freedom
Because we calculated one standard deviation
Here was have calculated 2
So we lose 2 df
In our case we have 99 df

17. Sub in the values

18. conclusions All t tests are based on the same formula
Keep the assumptions in mind
SRS
Homogeneity of variance
Independence of observations