# Answer to Question #15221 in Statistics and Probability for heather

Question #15221

What does it mean for two categorical variables to be “independent?” Then, create a contingency table to show us an example of two categorical variables that are not independent and explain why.

Expert's answer

In statistics, a categorical variable is a variable that can take on one of a limited, and usually fixed, number of possible values. Categorical variables are often used to represent categorical data. In computer science and some branches of mathematics, categorical variables are referred to as enumerations or enumerated types.

Examples of values that might be represented in a categorical variable:

The blood type of a person: A, B, AB or O.

Two categorical variables are independent if the conditional distribution of the response variable does not change, as we switch from one value to another of the explanatory variable.

When two variables are independent, knowledge of the values of one variable does not help us predict the outcome of the other variable.

Two categorical variables are associated if the conditional distribution of the response variable does change, as we switch from one value to another of the explanatory variable

Association on Two Categorical Variables

• association : when two variables are related in some way.

• response variable : is the outcome variable on which comparisons are made.

• explanatory variable : defines the groups to be compared with respect to values on

the response variable

• grade school goals : students were surveyed (1992) in Michigan for a study. students

indicated which of grades, popularity and sports was most important, students were

in grades 4 - 6.

Grades Popular Sports Total

Boy 117 50 60 227

Girl 130 91 30 251

Total 247 141 90 478

given gender, how likely is each of the goal categories? in this case, goal is the response

variable and gender the explanatory variable.

Grades Popular Sports

Boy 0.515 0.22 0.264

Girl 0.518 0.362 0.119

given the goal category, how likely is each gender? in this case, gender is the response

variable and goal is the explanatory variable.

Examples of values that might be represented in a categorical variable:

The blood type of a person: A, B, AB or O.

Two categorical variables are independent if the conditional distribution of the response variable does not change, as we switch from one value to another of the explanatory variable.

When two variables are independent, knowledge of the values of one variable does not help us predict the outcome of the other variable.

Two categorical variables are associated if the conditional distribution of the response variable does change, as we switch from one value to another of the explanatory variable

Association on Two Categorical Variables

• association : when two variables are related in some way.

• response variable : is the outcome variable on which comparisons are made.

• explanatory variable : defines the groups to be compared with respect to values on

the response variable

• grade school goals : students were surveyed (1992) in Michigan for a study. students

indicated which of grades, popularity and sports was most important, students were

in grades 4 - 6.

Grades Popular Sports Total

Boy 117 50 60 227

Girl 130 91 30 251

Total 247 141 90 478

given gender, how likely is each of the goal categories? in this case, goal is the response

variable and gender the explanatory variable.

Grades Popular Sports

Boy 0.515 0.22 0.264

Girl 0.518 0.362 0.119

given the goal category, how likely is each gender? in this case, gender is the response

variable and goal is the explanatory variable.

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