# Class 34: Review of Key Concepts

This outline is also available in PDF.

Held: Wednesday, 23 April 2008

Notes:

• I got enough questions on Topic 25 that I will not hold a quiz today.
• If you plan to take the makeup exam tomorrow, please let me know when asap. Makeups will be in 3813.
• I will be around that room to answer questions on the project all morning, too.
• Projects remain due Friday. I will look at them over the weekend and, if I have suggested changes, may email those suggestions to you.
• A peer-review form is now available, and gives hints as to the kinds of things I will expect.
• On Friday, we return to the book, and will work on topic 20.

Overview:

• Notes on chi-square tests.
• Questions and answers on the exam.
• More fun with the project.

## Chi-Square Tests, Revisited

• We have seen two kinds of chi-square tests.
• One is used with a single categorical variable (goodness of fit)
• One is used with a pair of categorical variables (more general)
• They have two different kinds of hypothesis:
• For goodness-of-fit, the hypothesis is "The distribution of the different responses is as follows."
• For two-variable, the hypothesis is "The two variables are independent."
• They have the same technique for finding the test statistic
• Compute an expected value for each entry.
• Compute the scaled squared difference between observed and expected.
• Sum those values.
• They use the same table for computing probabilities.
• Given the different hypotheses, they have different techniques for computing expected values:
• For goodness-of-fit, it's "expected proportion time sample size"
• For two-sample, it's "sum of row * sum of column / sample size"
• Why is the two-sample one given that way?
• Well, if the two variables are independent, the proportions in any row should should be the same as the proportions within the population.
• We compute the proportion in the population by suming the column and dividing by the sample size.
• This works the other way, two: The proportions in any column should be the same as the proportion in the population.
• We compute the proportion in the pupolatuion by suming the row and dividing by the sample size.

## Questions and Answers on Exam 2

• I'll spend as much or as little time as necessary going over any questions you may have on exam 2.
• Note that I grade without names, so I generally don't know what any particular person got wrong. (I do know scores, but that doesn't tell me much.)

## Some Project Notes

• The draft poster peer review form should give you a sense of things to work on.
• I have not found a good way to join rows or columns, other than by hand. However, there are still good reasons to merge.
• I'll do my best to answer any other questions you may have.

Disclaimer: I usually create these pages on the fly, which means that I rarely proofread them and they may contain bad grammar and incorrect details. It also means that I tend to update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.

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Samuel A. Rebelsky, rebelsky@grinnell.edu

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