Chapter 11 Tests for significance

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The applet on this webpage should be enlightening regarding Type I and Type II error. Scroll down the linked page a bunch until you find the yellow box entitled Statistical Errors Applet. Read the information in the little yellow box and click on the link where it says Applet 1. Statistical Errors near the little graph to display the applet. Move the box in the scroll bar at the top to change the value of alpha (the probability of a Type I error). In real life you can change this value, but pick your alpha before you collect your data! Otherwise, you might be accused of manipulating the data and giving statisticiansa bad name.
Now, move the middle of a NEW and IMPROVED distribution by sliding the box in the scroll bar at the bottom of the window. See what the yellow region looks like when you overlap the distributions. The yellow area represents the probability of a Type II error.
So, what effect does changing alpha have on the probabilty of a Type II error? When is beta maximized? When is it minimized?

TYPE I and TYPE II errors
PLEASE read the section in the book regarding these topics.

You will only be able to calculate a POWER or a BETA (the probability of a Type II error) when some NEW mean is introduced. The power of the test is the probability that the test will be able to distinguish between your original hypothesized mu and the newly proposed mu. The probability of an error is BETA.

To calculate BETA:
Find the boundaries of the FTR region for your original hypothesis. Find the probability that x-bar would fall between that lower bound and upper bound GIVEN the NEW mu and standard error of the mean. In calculator language [that you would NEVER write on a test] it would be normcdf(LB, UB, NEWmu, sigma of x-bar).


HW due Wednesday: 11.36-11.40. Your test is Thursday.


You should have worked problems 11.5, .6, .27, .28, .29, .30, .49, .50, & .51 by Tuesday. Your test is Thursday.

The excerpt in class today was from The Lady Tasting Tea by David Salsburg.

HW due Thursday: 11.3, 11.4, 11.6

Please note that (1) null hypotheses ALWAYS have an "equals" concept
(2) null and alternative hypotheses do NOT include statistics.

In inference testing, the results of our sample may make us reject the null hypothesis if they are so unlikely that they would be unbelievably unlikely due to randomness.

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