Chi-Squared Tests: Goodness of Fit & Association in Nominal Data

What is the purpose of the Chi-squared test?

To determine whether there is a significant association between nominal categories.

How is the Chi-squared test represented mathematically?

It is written as X².

What does the Chi-squared test compare?

It compares observed data (counts and frequencies) to expected frequencies under a specific hypothesis.

What are the two types of Chi-squared tests?

1. Chi-square Test - Goodness of fit (one variable); 2. Chi-squared Test - Test of association (two variables).

What type of data is the Chi-squared test used with?

Nominal data, which is categorical and has no natural order or ranking.

What is the alternative hypothesis in a Chi-squared test?

It is always non-directional, indicating deviation without specifying direction.

What is the assumption regarding the type of data for the Chi-squared test?

Data must always be nominal or ordinal, never continuous.

What does mutual exclusivity mean in the context of the Chi-squared test?

Variables and categories should always be mutually exclusive.

What is the minimum expected frequency per cell for the Chi-squared test?

The expected frequency should be 5 or more per cell.

What should be done if the expected frequency is less than 5?

A larger sample is needed, or Fisher's Exact Test may be more appropriate.

What does independence of observations mean?

One observation should not affect the value of any other observation.

Why is random sampling important in the Chi-squared test?

It ensures representativeness and avoids bias.

What does the Chi-squared test of association tell you?

It indicates whether there is a significant association between two categorical variables overall.

How are expected frequencies calculated in a Chi-squared test?

Using the formula: (Row total x Column total) / Grand total.

What is the significance of the test statistic in a Chi-squared test?

It can be compared against a critical value to determine the outcome.

What is the formula used to report the results of a Chi-squared test?

X² (df, N = XX) = XX.XX, p = .XX.

What does 'df' stand for in the Chi-squared test results?

Degrees of freedom.

What does a larger Chi-squared value indicate?

More deviation from the expected frequencies.

What is the critical value used for in the Chi-squared test?

It is used to determine whether to reject or fail to reject the null hypothesis.

What does it mean if X² > critical value?

Reject the null hypothesis; there is a significant difference.

What does it mean if X² < critical value?

Fail to reject the null hypothesis; there is no significant difference.

What is the role of the analysis table in reporting Chi-squared test results?

It is used to compare results using the p-value to critical values.

What should be referenced to determine where differences lie in Chi-squared test results?

The descriptive statistics.