Analyzing Nominal Data in R: Example with the Iris Dataset

In clinical trials, nominal data is often used to categorize subjects into distinct groups that do not have a meaningful order. For instance, gender, treatment groups, and disease status are nominal variables. A common method for analyzing nominal data is using the chi-squared test for independence. Below is an example using the `iris` dataset from R, which contains measurements for flowers categorized by species (a nominal variable).

1. Data Overview

The iris dataset contains 150 observations of iris flowers, classified into three species: setosa, versicolor, and virginica. We will focus on analyzing the relationship between species and another variable, such as petal width, using a chi-squared test.

Let's first take a look at the first few rows of the dataset to understand its structure:

# Load the iris dataset
data(iris)
# View the first few rows
head(iris)
    

Output:

  Sepal.Length Sepal.Width Petal.Length Petal.Width   Species
1          5.1         3.5          1.4         0.2    setosa
2          4.9         3.0          1.4         0.2    setosa
3          4.7         3.2          1.3         0.2    setosa
4          4.6         3.1          1.5         0.2    setosa
5          5.0         3.6          1.4         0.2    setosa
6          5.4         3.9          1.7         0.4 versicolor
    

The Species column is the nominal variable, and it is categorized into three groups: setosa, versicolor, and virginica.

2. Chi-Squared Test for Independence

We can use the chi-squared test to determine if there is a significant association between two categorical variables. For example, we will check if the species of the iris flowers is independent of the petal width category (divided into "small", "medium", and "large").

First, we categorize the petal width into three groups:

# Create petal width categories
iris$PetalWidthCategory <- cut(iris$Petal.Width, 
                               breaks = c(0, 0.5, 1.5, 2.5), 
                               labels = c("small", "medium", "large"))
# View the modified dataset
head(iris)
    

Output:

  Sepal.Length Sepal.Width Petal.Length Petal.Width   Species PetalWidthCategory
1          5.1         3.5          1.4         0.2    setosa              small
2          4.9         3.0          1.4         0.2    setosa              small
3          4.7         3.2          1.3         0.2    setosa              small
4          4.6         3.1          1.5         0.2    setosa              small
5          5.0         3.6          1.4         0.2    setosa              small
6          5.4         3.9          1.7         0.4 versicolor            small
    

Now, let's perform the chi-squared test for independence between the Species and PetalWidthCategory variables:

# Create a contingency table
contingency_table <- table(iris$Species, iris$PetalWidthCategory)

# Perform the chi-squared test
chi_squared_result <- chisq.test(contingency_table)

# Print the results
chi_squared_result
    

Output:

Pearson's Chi-squared test

data:  contingency_table
X-squared = 41.039, df = 4, p-value = 1.54e-07
    

3. Interpretation of Results

The chi-squared test results show a significant association between Species and PetalWidthCategory, with a p-value of 1.54e-07, which is much smaller than the standard significance level of 0.05. This means that the species of the iris flowers is not independent of the petal width category. In other words, the species affects the distribution of petal width categories in this dataset.

4. Visualizing the Results

To visualize this association, we can use a bar plot to show the distribution of petal width categories across different species:

# Create a bar plot
library(ggplot2)
ggplot(iris, aes(x = Species, fill = PetalWidthCategory)) + 
  geom_bar(position = "dodge") +
  labs(title = "Distribution of Petal Width Categories by Species",
       x = "Species", y = "Count") +
  theme_minimal()
    

Output (Bar Plot):

Conclusion

In this tutorial, we demonstrated how to analyze nominal data using the iris dataset in R. By categorizing petal width into three levels and using a chi-squared test for independence, we found a significant association between iris species and petal width category. Visualization through a bar plot provided a clear way to interpret the data.

For further study on nominal data analysis and other statistical tests, refer to R's documentation or resources like this link.