9 Contingency Tables

Question 1

What is a contingency table used for?

Answer 1

To display frequencies for combinations of two variables categorised into groups

Question 2

Define the chi-squared distribution.

Answer 2

A special case of the gamma distribution used in inferential statistics

It tests for various associations, including independence and goodness of fit.

Question 3

What does degrees of freedom refer to?

Answer 3

The number of independent pieces of information used to calculate a statistic

It affects the shape of the chi-squared distribution.

Question 4

What is the formula for the degrees of freedom for a contingency table?

Answer 4

v=(rows-1)x(columns-1)

Question 5

What are expected frequencies?

Answer 5

Theoretical frequencies expected if two variables are independent

They are compared to observed frequencies in contingency tables.

Question 6

The formula for calculating expected frequency in a contingency table is based on what?

Answer 6

Question 7

What is the test statistic in the context of contingency tables?

Answer 7

Question 8

True or false: The null hypothesis in contingency tables assumes that the two variables are dependent.

Answer 8

FALSE

The null hypothesis assumes that the variables are independent.

Question 9

What should be done if the value of any expected frequency is less than 5?

Answer 9

Combine groups until all expected values are reasonably large

A group should be combine with the most similar other group(s) in the context of the question

Question 10

What does the contribution of each cell in a contingency table represent?

Answer 10

The value that it contributes to the total of the test statistic

Question 11

When are you expected to use the contributions for each cell?

Answer 11

When commenting on the nature of any association, the contirbutions must be referenced

The largest contributions need to be commented on

Question 12

What is the purpose of combining classes in contingency tables?

Answer 12

To increase expected values when they are too small

This allows for valid statistical analysis.

Question 13

What is the critical region in hypothesis testing?

Answer 13

The area in the tail(s) of the distribution where the null hypothesis can be rejected

It is determined by the significance level.

Question 14

What is the grand total in a contingency table?

Answer 14

The total number of observations across all categories

It is used to calculate expected frequencies.

Question 15

What type of variables are typically analysed using contingency tables?

Answer 15

Qualitative random variables

Catagorical Data

Question 16

In the context of an investigation, what does a χ2 test help to determine?

Answer 16

Independence of categorical variables

Specifically, it assesses whether the distribution of one categorical variable differs from another.

Question 17

What are the degrees of freedom on a 21x13 contingency table with no combining?

Answer 17

v=(21-1)x(13-1)=240

Question 18

What is the null hypothesis for ALL contingency table hypothesis tests?

Answer 18

H0: There is no association between…

Question 19

What is the alternative hypothesis for ALL contingency table hypothesis tests?

Answer 19

H1: There is an association between…

Question 20

When is it appropriate to perform a Chi-Squared contingency table test?

Answer 20

When testing catagorical data for an association

Question 21

What assumptions are made when carrying out the Chi-squared test?

Answer 21

• The sample used was selected randomly
• The onservations are independent