Chapter 12 Inference on Categorical Data

Question 1

Marginal Distribution of a Variable

Answer 1

A frequency or relative frequency distribution of either the row or column variable in the contingency table.

A marginal distribution removes the effect of either the row variable or the column variable in the contingency table.

Question 2

Conditional Distribution

Answer 2

A list of the relative frequency of each category of the response variable, given a specific value of the explanatory variable in a contingency table.

Question 3

Contingency Table

Answer 3

A table that relates two categories of data. Also called a two-way table.

Question 4

Lurking given by E=μ=np.

Answer 4

An explanatory variable that was not considered in the observational study, but that affects the value of the response variable. In addition, lurking variables are typically related to explanatory variables considered in the study.

Question 5

Simpson’s Paradox

Answer 5

Describes a situation in which an association between two variables inverts or goes away when a third variable is introduced to the analysis.

Question 6

Multiplication Rule for Independent Events

Answer 6

If two events E and F are independent, then:

P(EandF) = P(E) ⋅ P(F)

Question 7

The expected value of a binomial random variable for n independent trials of a binomial experiment with probability of success p

Answer 7

It is given by E = μ = np.

Question 8

Chi-Square Test for Independence

Answer 8

Used to determine whether there is an association between a row variable and a column variable in a contingency table constructed from sample data.

The null hypothesis is that the variables are not associated, or independent.
The alternative hypothesis is that the variables are associated, or dependent.

Question 9

Finding the Expected Frequencies in a Chi-Square Test for Independence

Answer 9

Multiply the cell’s row total by its column total and divide this result by the table total. That is,

Question 10

Chi-Square Test for Independence Using the TI-84 Calculator

Answer 10

1. Access the MATRIX menu. Highlight the EDIT menu, and select 1: [A].
2. Enter the number of rows and columns of the contingency table (matrix).
3. Enter the cell entries for the observed matrix, and press 2nd QUIT.
4. Press STAT, highlight TESTS, and select C: $\chi ^2$-Test.
5. With the cursor after Observed:, enter matrix [A] by accessing the MATRIX menu, highlighting NAMES, and selecting 1:[A].
6. With the cursor after Expected:, enter matrix [B] by accessing the MATRIX menu, highlighting NAMES, and selecting 2:[B].
7. Highlight Calculate or Draw, and press ENTER.
   Results will be the test statistic and P-value.

Question 11

Chi-Square Test for Independence or Homogeneity of Proportions

Answer 11

1. Enter the given contingency table into a worksheet, including column and row labels.
2. Select XLSTAT > Correlation/Association tests > Tests on contingency tables (Chi-square…)
3. General Tab: Fill in the box as follows:
   Contingency table: Highlight the contingency table cell range (such as A1:D4)
   Data format: Select the contingency table option.
   Range/Sheet/Workbook: Select the Sheet option.
   Labels included: Check this box.
4. Options Tab: Check the box for Chi-square test
5. Outputs tab: Check the boxes for Theoretical frequencies, Proportions/Row, and Proportions/Column. Also select Proportions. Click OK.

Question 12

Chi-Square Test for Homogeneity of Proportions

Answer 12

A test of whether different populations have the same proportion of individuals with some characteristic.

Question 13

Chi-Square Test for Homogeneity of Proportions Using TI-84 Calculator

Answer 13

1. Access the MATRIX menu. Highlight the EDIT menu, and select 1: [A].
2. Enter the number of rows and columns of the contingency table (matrix).
3. Enter the cell entries for the observed matrix, and press 2nd QUIT.
4. Press STAT, highlight TESTS, and select C: χ2-Test.
5. With the cursor after Observed:, enter matrix [A] by accessing the MATRIX menu, highlighting NAMES, and selecting 1:[A].
6. With the cursor after Expected:, enter matrix [B] by accessing the MATRIX menu, highlighting NAMES, and selecting 2:[B].
7. Highlight Calculate or Draw, and press ENTER.

Question 14

What if the requirements for performing a chi-square test are not satisfied?

Answer 14

The researcher has one of two options:

(1) combine two or more columns (or rows) to increase the expected frequencies or
(2) increase the sample size.