What is a Chi-Squared Test?
A Chi-Squared (χ²) Test is a non-parametric statistical hypothesis test used to examine the relationship between categorical variables. It helps determine if there's a statistically significant difference between the observed frequencies and the expected frequencies in one or more categories, or if two categorical variables are independent of each other.
Key Principles and Types
The Chi-Squared test primarily operates on two main types: the Chi-Squared Goodness-of-Fit Test and the Chi-Squared Test for Independence. The Goodness-of-Fit test evaluates if an observed sample distribution matches an expected distribution. The Test for Independence assesses whether there is a significant association between two categorical variables, meaning whether they are dependent or independent.
A Practical Example
Imagine a scientist wants to know if there's a preference for certain colors among a group of people. They survey 100 individuals, asking their favorite color from a choice of red, blue, or green. The Chi-Squared test could then be used to determine if the observed distribution of color preferences significantly deviates from an equal distribution (expected frequencies), or if the preferences are randomly distributed.
Importance and Applications
The Chi-Squared test is crucial in various fields, including biology, social sciences, marketing, and medicine. It allows researchers to draw conclusions about population characteristics from sample data, such as determining if a new marketing campaign changed customer preferences, or if the incidence of a disease is independent of a particular risk factor. Its simplicity and applicability to categorical data make it a widely used tool for data analysis.