Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 2, Section 6



  1. How many variables go in to making a two-way table? What types of variables are they, generally (choose here between categorical or quantitative)? How many values are these variables allowed to take?

    A two-way table requires two (and only two) variables. Generally these variables are categorical. Nevertheless, there really is no limitation to the number of values these variables can take on, except that it must be a finite number.

  2. The ``Total" row and column (excluding the `grand total' where these two meet) are called marginal distributions. The fact that they are called `distributions' makes more sense when you look at the bar graph on p. 195 (Fig. 2.38), which is more in line with what we have called a distribution in the past. Make sure you see the relationship between Fig. 2.38 and the marginal distribution in the ``Total" column of Table 2.14 (p. 194).

  3. Starting with a 2-way table, how does one form a column percent in a cell? How about a row percent? Would it make sense to look at a bar graph of these column (or row) percents when the column (or row) is not a ``Total"?

    A cell's column percent is found by dividing the count in that cell by the total in that column. Similar, a cell's row percent is found by dividing its count by the total inits row. One can just as easily form bar graphs for inidividual columns or rows as one can for marginal distributions, and it is done frequently enough to have a name for these types of distributions: conditional distributions.

  4. What is the lesson from the example of Simpson's paradox (p. 199)?

    It is that seemingly apparent relationships between variables sometimes fall apart upon closer inspection. Lurking variables, such as patients' conditions from Example 2.32, once considered, may reveal a different relationship altogether. As the authors point out, the first table on p. 199 is an aggregation of the data in the other two (those other two taken together are considered to be one three-way table - can you explain why?), and obscures the role that patient condition plays.

    An important point here: the data in the first table of Example 2.32 as well as the enhanced data of the two tables below it, though fictitious, would be the result of an observational study. Can you describe how it is that experiments make small the possibility of some unconsidered lurking variable having an important effect on results?



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On 6 Apr 2001, 09:32.