One sample problems Statistics 2126 introduction Yeah z

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 H 0

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)