A.3.3.2 Associations in Categorical Data

What might it mean for two variables to be associated? For example: 1. The color of a car’s seats and whether the owner returns to the dealership for maintenance or not. 2. The color of a car’s seats and whether the owner is ever burned from the seats being hot.

The two-way table displays data about 55 different locations. Scientists have a list of possible chemicals that may influence the health of the coral. They first look at how nitrate concentration might be related to coral health. The table displays the health of the coral (healthy or unhealthy) and nitrate concentration (low or high). Complete the two-way relative frequency table for the data in the two-way table in which the relative frequencies are based on the total for each column.

When there is a low nitrate concentration, which had a higher relative frequency, healthy or unhealthy coral?

When there is a high nitrate concentration, is there a higher relative frequency of healthy or unhealthy coral?

Based on this data, is there a possible association between coral health and the level of nitrate concentration? Explain your reasoning.

The scientists next look at how silicon dioxide concentration might be related to coral health. The relative frequencies based on the total for each column are shown in the table. Based on this data, is there a possible association between coral health and the level of silicon dioxide concentration? Explain your reasoning.

Jada surveyed 300 people from various age groups about their shoe preference. The two-way table summarizes the results of the survey.  This table shows row relative frequencies: This table shows column relative frequencies: Jada concludes that there is a possible association between age and shoe preference. Is Jada’s conclusion reasonable? Explain your reasoning.

The two-way table summarizes data on writing utensil preference and the dominant hand for a sample of 100 people.                 Is there a possible association between dominant hand and writing utensil preference? Explain your reasoning.

What does it mean for two categorical variables to have an association?

For the data in Jada’s survey, the same number of people preferred sneakers without laces in the two youngest age groups. Why doesn’t this matter when deciding if there is an association between age group and shoe preference?