Chi-Squared Video Guide

Why do you use the Chi-Square Test?

To determine if there is a statistically significant relationship between two categorical variables by comparing observed data to expected data

Define the Null Hypothesis.

States that there is no significant effect or relationship between variables, and any observed differences are due to random chance

What is the whole point of the Chi-Square Test?

To determine if there is a significant association between two categorical variables or if an observed distribution matches an expected distribution

How do you calculate the “Degrees of Freedom”?

One-sample test

Formula: df = n - 1

Explanation: Subtract 1 from the sample size (n). B/c one degree of freedom is used to estimate the sample mean

Two-sample t-test

Formula: df = n1 + n2 - 2

Explanation: Add the sample sizes of the two groups (n1 and n2) and subtract because a degree of freedom is used for each sample’s mean.

Chi-square test of independence

Formula: df = (r - 1) x (c - 1) • Explanation: Subtract 1 from the number of rows (r) and the number of columns (c), and then multiply the

results.

Example: For a table with 3 rows and 4 columns, the degrees of freedom would be (3 - 1) x (4 - 1) =6

What is the limit of the critical value?

• No single limit for a critical value

• Value is determined by the chosen significance (a) and type of test (one-tailed or two-tailed)

• One-tailed test: Critical value is a single point that defines one rejection region (either the left or right tail)

• Two-tailed test: Rejection region is split into two equal parts, one in each tail, so there are two critical values

How much data do you need to get to apply the Chi-Square test?

Need a large enough sample size so that the expected frequency in each cell is at least 5

Do expected values need to be whole numbers?

No; often decimals because they represent averages