Chi-Square Test Concepts

The video tutorial explains the Chi-Square test for independence, a non-parametric test used to evaluate the relationship between two categorical variables. An example involving elementary school students' favorite colors is used to illustrate the process. The tutorial covers setting up null and alternative hypotheses, calculating degrees of freedom, and determining the critical value. It then demonstrates how to calculate the Chi-Square statistic and interpret the results, concluding that there is a relationship between gender and favorite color.

What type of data is the Chi-Square Test for Independence used on?

• Ratio data

• Interval data

• Categorical data

• Continuous data

In the example scenario, what are the two variables being analyzed for a relationship?

• Weight and favorite color

• Height and favorite color

• Gender and favorite color

• Age and favorite color

What is the null hypothesis in the context of the Chi-Square Test for Independence?

• The variables are independent

• The variables are related

• The variables are not related

• The variables are identical

How are degrees of freedom calculated for the Chi-Square Test for Independence?

• Rows - Columns

• Rows * Columns

• Rows - 1 * Columns - 1

• Rows + Columns

What is the critical value used in the example for the Chi-Square Test?

• 7.81

• 9.49

• 5.99

• 3.84

How do you calculate the expected frequency for a cell in the Chi-Square Test?

• Multiply row total by column total and divide by total number of subjects

• Add row total and column total

• Subtract row total from column total

• Divide row total by column total

What is the calculated Chi-Square statistic in the example?

• 5.99

• 10.83

• 27.64

• 15.51

What conclusion is drawn if the calculated Chi-Square is greater than the critical value?

• Accept the null hypothesis

• Reject the null hypothesis

• Reject the alternative hypothesis

• Accept the alternative hypothesis

What does rejecting the null hypothesis imply about the relationship between the variables?

• There is no relationship

• There is a relationship

• The variables are identical

• The variables are independent

What is the significance level (alpha) used in the example?

• 0.05

• 0.15

• 0.01

• 0.10