Understanding Relationships with Chi-Square Test

In this analysis, we will explore the relationship between two categorical variables using the Chi-Square Test of Independence. This statistical test helps us determine whether there is a significant association between the variables, providing valuable insights into the data.

Generating Random Data

To illustrate the Chi-Square Test, let’s generate a random dataset with two categorical variables, Variable1 and Variable2. We’ll create 100 observations for each variable.

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##    Variable1 Variable2
## 1 Category_A   Group_X
## 2 Category_A   Group_Z
## 3 Category_A   Group_Y
## 4 Category_A   Group_X
## 5 Category_B   Group_X
## 6 Category_B   Group_Y

The generated dataset looks like this:

   Variable1 Variable2
1 Category_C   Group_X
2 Category_B   Group_X
3 Category_B   Group_X
4 Category_A   Group_Z
5 Category_A   Group_Z
6 Category_A   Group_Y

Chi-Square Test of Independence

Now, let’s run the Chi-Square Test to examine the independence between Variable1 and Variable2.

## 
##  Pearson's Chi-squared test
## 
## data:  your_data$Variable1 and your_data$Variable2
## X-squared = 2.2715, df = 4, p-value = 0.686

The Chi-Square Test results show the Chi-Square value, degrees of freedom, and the p-value. These metrics will guide us in interpreting the relationship between the variables.

Interpretation

## The Chi-Square Test is not statistically significant, suggesting no significant relationship between Variable1 and Variable2.

The interpretation of the test is crucial. If the p-value is less than 0.05, we conclude that there is a statistically significant relationship between the variables. Additional post hoc paired comparisons or analyses may be performed to explore this relationship further.

Visualizing the Data

Bar Chart

Let’s visualize the data with a bar chart to gain a clearer understanding of the distribution of categories within each variable.

The bar chart visually represents the distribution of categories in Variable1 and Variable2, providing additional insights.

Mosaic Plot

Let’s create a mosaic plot to visualize the relationship between the two categorical variables.

The mosaic plot displays the proportions of each category within Variable1 and Variable2 and helps visualize their relationship.

Heatmap

Finally, let’s create a heatmap to show the frequency of each combination of categories.

## `summarise()` has grouped output by 'Variable1'. You can override using the
## `.groups` argument.

The heatmap provides a visual representation of the frequency of each combination of categories, further aiding our understanding.