Chi-square Test of Independence for Discrete Data

Question 1

It is one of the most popular methods for testing hypotheses on discrete data.

Answer 1

Chi-square

Question 2

It only requires simple summary statistics such as frequencies and percentages.

Answer 2

Chi-square

Question 3

What are used to get meaningful insight from discrete data?

Answer 3

Some chi-square statistics and contingency tables

Question 4

Examples where chi-square can be used

Answer 4

A researcher want to know if the performance of a firm (loss, breakeven, profit) is dependent on which country (low, middle, high income) it is located in.

Question 5

Three different types of chi-square analysis

Answer 5

Chi-square for:
- goodness of fit
- homogeneity
- independence

Question 6

It is used to test the hypothesis that two categorical variables are independent of each other.

Answer 6

Chi-square test of independence

Question 7

It is used to test if there is no association between the two categorical variables.

Answer 7

Chi-square test of independence

Question 8

What must be constructed and used to get meaningful insight from the data?

Answer 8

Contingency table

Question 9

What is the basis of the chi-square test of independence?

Answer 9

The difference between the observed frequency and the expected frequency of each cell of the contingency table.

Question 10

These are frequencies obtained from the performance of an ecperiment.

Answer 10

Observed frequencies

Question 11

It is denoted by O.

Answer 11

Observed frequencies

Question 12

It is denoted by E.

Answer 12

Expected frequencies

Question 13

These are frequencies that are expected to obtain if the null hypothesis is true.

Answer 13

Expected frequencies

Question 14

It is calculated by multiplying the total of the roq by the total of the column to which the cell belongs and then dividing by the total sample size.

Answer 14

Expected frequencies

Question 15

It presents the data in rxc tables.

Answer 15

Contingency Tables

Question 16

R is what?

Answer 16

number of rows

Question 17

C is what?

Answer 17

number of columns

Question 18

What is the table if the row varibale has three categories and the column variable has two categories?

Answer 18

3x2 table

Question 19

CSCCMC

Hypothesis Testing Using Chi-square

Answer 19

1. Construct the contingency table.
2. State the hypotheses and set the alpha level.
3. Calculate the degree of freedon and the criticial value.
4. Calculate the Chi-square value.
5. Make a statistical decision.
6. Conclude.

Question 20

Formula for df of a chi-square

Answer 20

df = (r-1)(c-1)

Question 21

Decision rule using the Fcritical value.

Answer 21

Chi-square value ≤ critical value : Fail to reject the null hypothesis

Chi-square value > critical value : Reject the null hypothesis

Question 22

Decision rule using the p-value.

Answer 22

p-value ≤ significance level : reject null hypothesis

p-value > significance level : fail to reject null hypothesis