There are three different tests in this chapter, but only two distinct methods.
The first method is what you used in class to determine whether your sample was reasonably consistent with the hypothesized proportions by color of Goldfish, Froot Loops, or Smarties. You determine the expected counts by multiplying the hypothesized proportion by the total of objects. The number of degrees of freedom is the number of categories minus one. This was a Chi-square goodness of fit test.
The next method you will use is the Chi-square test of homogeneity. This is used when you have two populations that you are comparing to see if they have a common distribution by the categorical variable. You base this decision on your sample comparison. Using the same methods, you can perform a Chi-square test of independence. This is used to determine whether a sample described in a two-way table by two different characteristics demonstrates independence between the two variables or if there appears to be a connection. In these cases, you have to multiply the row total by the column total and divide by the table total to get the expected count for each cell. You will use (r-1)*(c-1) for the number of degrees of freedom. This is the number of cells you would have to fill in (if you knew all of the totals) before the rest of the cells' values are determined.
You have now seen every topic on the Barron's guide and on the AP exam syllabus. We're almost there!
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2 comments:
Question 1: yes, you wind up with two multi-colored bars so you can compare the widths of the sections of the bars
Question 2: What are you using for the expected value? Not the probabilities (.1), I hope!
Segmented bar graphs? There are some nicve websites on this. They work like a pie graph except they are a vertical smear of color instead of a circle. They are effective in comparing two distributions because you can see that the graph on the left has a whole lot more of the oh--let's say green --segment than the one on the right does and a lot less gold. Or is it orange and blue?
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