Chapter 10 - Hypothesis Testing (Categorical Data)

Question 1

Categorical data

Answer 1

• discrete data require inference too
• we will strictly focus on categorical data that can be assumed to have an underlying binomial distribution
• our goal is to infer about parameter p

Question 2

Contingency table method

Answer 2

• a 2 x 2 contingency table is a table composed of two rows cross-classified by two columns
• displays data that can be classified by two different variables, each of which has only two possible outcomes

Question 3

Contingency table - types of tests

Answer 3

• test for homogeneity of binomial proportions

- test of independence or a test of association

Question 4

Test for homogeneity of binomial proportions

Answer 4

• tests whether the proportions are the same in two independent samples

Question 5

Test of independence or a test of association

Answer 5

• tests whether there is some association between two reported measures of a characteristic

Question 6

Contingency tables - the cells

Answer 6

• (1,1)
• (1, 2) = first row, second column
• (2, 1) = second row, first column
• (2,2)

Question 7

Contingency tables - presentation of totals

Answer 7

• the number of units in each row are displayed in the right margins, which are called row marginal totals, or row margins
• the number of units in each column are displayed in the bottom margins, which are called column marginal totals, or column margins
• the total number of units in the four cells, which is displayed in the lower-right hand corner of the table, is called the grand total

Question 8

Chi-square test statistics

Answer 8

• if there are large difference between observed and expected values then that provides evidence against H0
• this is referred to as the Pearson chi-square test statistic as it has a chi-square distribution with 1 df