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# FM Categorical Data

## 2.2 Relationships between two Categorical Variables

### Discussing Associations between Categorical Datasets

• Remember to begin with context: what does the data represent?
• When analysing categorical datasets, try to find correlation, or lack of, between categories.
• You must also consider what this means in the context of the data. Does one cause the other? Do they tend to occur together? Is this the result of poor sampling practices?
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## 2.1 Response and Explanatory Variables

### Explanatory Variable

• The explanatory variable (EV) is the variable used to explain or predict another variable (the response variable).
• By convention, the explanatory variable is plotted along the x-axis of a graph, if it is numerical.

### Response Variable

• The response variable (RV) is the variable which is explained or predicted by the explanatory variable.
• By convention, the response variable is plotted along the y-axis of a graph, if it is numerical.

Note: both explanatory and response variables can be either categorical or numerical variables.

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## 1.3 Statistical Analysis of Categorical Distributions

Answering Statistical Questions on Categorical Distributions

### Mode

• The mode of categorical data refers to the category with the highest frequency.

Note: the mode of a categorical distribution is also known as the modal category, or dominant category

Example

Given the bar chart:

Red has the highest frequency and so it is the modal category.

### Guidelines to analysing categorical distributions

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## 1.2 Displaying Distributions of Categorical Data

Visualising Categorical Data

### Frequency

• The number of times a particular value or category occurs is known as the frequency. This is often used as the basis for displaying and analysing categorical data.

Example

In the following dataset of colours:

Red Red Blue Red

The frequency of each colour is:

Red: 3

Blue: 1

### Percentage

• The proportion of the total data points which belong to a particular group is known as the percentage.
• This can be calculated using the formula:
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## 1.1 Overview of Data Types

### Categorical Data

• Data which is sorted into groups is considered categorical data

Nominal Data

• Categorical data with no hierarchy (i.e. one category is not “greater than” another) is considered nominal data

Example

Eye colour can be considered a nominal data type as the data (each person’s eye colour) can be placed into groups and there is no hierarchy

Ordinal Data

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