Conduct and Interpret the Chi-Square Test of Independence

What is the Chi-Square Test of Independence?

The Chi-Square Test of Independence is also known as Pearson’s Chi-Square and has two major applications: 1) Goodness of fit test and 2) Test of independence.

First, the Chi-Square Test can test whether the frequencies of a categorical variable are equal across categories.

Second, the Chi-Square Test can be used to test of independence between two categorical variables.  Specifically, it tests whether the frequencies of one categorical variable differ across levels of another categorical variable.  In other words, it tests whether or not a statistically significant relationship exists between the two variables.


Exploring Relationships in Various Fields with Simple Examples

In Healthcare:

  • Question: Do patients with access to online health resources have fewer in-person doctor visits?
  • What We’re Looking At: This question examines if there’s a link between the availability of online health resources and the frequency of in-person visits to a doctor. It’s about understanding how digital access to health information might impact traditional healthcare practices.

In Behavioral Science:

  • Question: Are people who see positive content on social media more likely to engage in healthy behaviors?
  • What We’re Looking At: Here, we’re exploring the potential influence of social media content on individuals’ health choices. It’s an investigation into how the things we see online can affect our real-world actions, particularly regarding health and wellness.

In Social Science:

  • Question: Are white-collar workers more likely to quit their jobs than blue-collar workers?
  • What We’re Looking At: This question delves into job satisfaction and career mobility across different types of employment. By comparing white-collar (typically office-based) and blue-collar (often manual labor) roles, we aim to uncover patterns in job turnover and what these might say about work in different sectors.

Simplifying the Approach

Each of these questions seeks to uncover relationships between two factors, whether it’s the impact of online resources on doctor visits, the effect of social media on health behaviors, or job satisfaction across different types of work. By asking such questions, researchers in healthcare, behavioral science, and social science can better understand complex interactions in our world, guiding improvements in various fields.

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Pearson’s Chi Square Test of Independence is an approximate test.  This means that the distribution of test statistics produced by this analysis only approximate the Chi-Square distribution.  This approximation improves with large sample sizes.  However, it poses a problem with small sample sizes, such as when expected cell sizes are below five.

Taking this into consideration, Fisher developed an exact test for contingency tables with small samples.  Exact tests do not need to approximate a theoretical distribution, such as the Chi-Square distribution.  In Fisher’s exact test, the exact distribution of possible outcomes is known, so the p-value produced by the test represents the exact probability of obtaining an outcome as extreme as the observed result under the null hypothesis that the two nominal variables are independent.

A rule of thumb is to use exact tests with sample sizes less than ten. Both Fisher’s exact test and Pearson’s Chi-Square Test of Independence can be easily calculated with statistical software such as Intellectus Statistics.