1. One sample problems
Statistics 2126

2. introduction Yeah z tests are great You can do statistical tests!
You simply need  and 
Ok the mean is easy, the standard deviation, not so much
What to do, what to do…

3. A thought… Well let’s look at the z formula
What if we could substitute something for ?

4. Introducing….
The t statistic!
You do just that, put s in for 

5. Powerful technique Think about this
You now don’t really need to know anything
A theoretical value for the population mean
And a calculated sample standard deviation

6. The critical value of t Unlike z, t changes depending on sample size
It has a certain number of ‘degrees of freedom’
In our case, n-1 so if we have 22 subjects we have 21 df
We look up the critical value with 21 df

7. An example
Four black capped chickadees in a memory experiment with two alternatives.
Their average percentage correct was 82.33
Standard deviation was 12.5
Are they better than chance?

9. Now look up the critical value
We have 3 degrees of freedom
Let’s use an alpha of .05 (as usual)
Just use the table
Critical value is 2.35
Our obtained value is 5.17
Reject H0

10. Confidence intervals? Why not…

11. Again, just think about this
That is incredible, we can estimate, we know that accuracy of the estimate and we do not need to know ANYTHING about the population beyond some theoretical population mean
(which is usually pretty easy to figure out)