Question

Select whether a chi-square test for association is the most appropriate for the following scenarios: Most appropriate or Not appropriate

a) Emma wishes to know whether gender has any relation with whether one prefers wine, beer, or liqueur. She surveys a group of men and women and records the number of participants who prefer wine, the number who prefer beer and the number who prefer liqueur. (yes or no)

b) Danielle surveys a group of people on how often they eat dinner at restaurants and diners. The age and annual income of each participant are recorded. Danielle is interested in knowing whether these two factors are important in determining how often one goes out for dinner. (yes or no)

c) A study intends to determine whether the average annual interest rate has any relation with the number of households who go overseas on a holiday at least once a year. Heidi collects data on the average annual interest rate and the number of households that travelled overseas at least once in that year over 6 years. (yes or no)

d) It has been proposed that one's education level has a strong relation with one's income level. Barbara collects data from a large group of 38 year-old adults about their education level (primary and lower, secondary, tertiary and higher) and their income level (to the nearest $100). Barbara plans to test this data to see whether the mean income in each education level is the same across all three levels. (yes or no)

Answer 1

The Chi-square test of association is used to discover if there is a relationship between two categorical variables. The two assumptions for applying the Chi-square test of association are as follows:

1. The two variables should be measured at an ordinal or nominal level (that is categorical data).

2. The two variables should consist of two or more categorical, independent groups. For example, gender (2 groups: males and Females), ethnicity (example 3 groups: Hispanic, Indian, African).

(a)

Emma wishes to know whether gender has any relation with whether one prefers wine, beer, or liqueur. Therefore, the objective of Chi-square test of association is met. Here, the two variables are "Gender" and "Type of alcohol". Therefore, first assumption of Chi-square test of association is satisfied. The variable "Gender" has two categories, namely "Male" and "Female". The variable "Type of alcohol" has three categories, namely "Wine", "Beer", and "Liqueur". Therefore, second assumption is satisfied. Hence, the Chi-square test of association is "appropriate" in this case.

(b)

Danielle surveys a group of people on how often they eat dinner at restaurants and diners. The age and annual income of each participant are recorded. Here, the variables are "Age", "Annual income", and "Number of times an individual eat at restaurants and diners". All the three variables are quantitative variables as there are no categories associated with any variable. Therefore, the assumptions of Chi-square test of association are not satisfied. Danielle is interested in knowing whether the two factors, Age and Annual income, are important in determining how often one goes out for diner. The objective is also not matching with that of the Chi-square test of association. Hence, the Chi-square test of association is "not appropriate" in this case. The more appropriate procedure would be the Linear regression.

(c)

A study intends to determine whether the average annual interest rate has any relation with the number of households who go overseas on a holiday at least once a year. The objective of Chi-square test of association is met. Heidi collects data on the average annual interest and the number of households that travelled overseas at least once a year over 6 years. Here, the variables are "Average annual interest" and "Number of households that travelled overseas". Both the variables are quantitative variables. Therefore, both the assumptions of Chi-square test of association are not satisfied. Hence, the Chi-square test of association is "not appropriate" in this case.

(d)

It has been proposed that one's education level has a strong relation with one's income level. Barbara collects data from a large group of 38 -year-old adults about their education level (primary and lower, secondary, tertiary and higher) and their income level (to the nearest \(\$ 100\) ). The variables are "Educational level" and "Income level". The variable "Educational level" is a categorical variable with categories "primary and lower", "secondary", and "tertiary and higher", but the variable "Income level" is not a categorical variable as it does not have any category. Therefore, both the assumptions of Chi-square test of association are not satisfied. Hence, the Chi-square test of association is "not appropriate" in this case.