Question

Suppose that you have bivariate data for an entire population.

a. How would you decide whether an association exists between the two variables under consideration?

b. Assuming that you make no calculation mistakes, could your conclusion be in error? Explain your answer.

Short answer

Part a. If all the conditional distributions are identical then no association exists between the two variables, otherwise, there is an association between the two variables.

Part b. No, because the data are for an entire population, no inference is being made from a sample to the population, the conclusion is a fact.

Step-by-step solution

Part (a) Step 1. Given Information

We are given a bivariate data for an entire population.

Part (a) Step 2. Explanation

To decide whether an association exists between the two variables under consideration first we obtain the conditional distribution of one of the variables for each possible value of the other variable.

If all the conditional distributions are identical then no association exists between the two variables, otherwise, there is an association between the two variables.

Part (b) Step 1. Explanation

If a calculation mistake is done then your conclusion could not be in error.

This is because the data are for an entire population, no inference is being made from a sample to the population, the conclusion is a fact.