One sample problems Statistics 2126

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…

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

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

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

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

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?

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

Confidence intervals? Why not…

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)