30 Questions
What does the two-way chi-square test examine?
The association between two categorical variables
What is the purpose of calculating the expected frequencies in a two-way chi-square test?
To test the null hypothesis of independence
What is the basis for calculating the degrees of freedom in a two-way chi-square test?
The number of categories in both variables
Why is it sometimes better to calculate the two-way chi-square test by hand?
Because you only have the cell means, not the raw data
What is another name for the two-way chi-square test?
Test of Independence
What is the null hypothesis in a two-way chi-square test, also known as a chi-square test of independence?
The two variables are distributed independently.
What does a two-way chi-square test examine?
The independence of two categorical variables.
In a contingency table, what do the cells contain?
The frequencies of individuals in that particular sample and category.
What is meant by the term 'independence' in the context of a two-way chi-square test?
The frequency distribution of one variable has the same shape for all levels of the second variable.
What is the main difference between a one-way chi-square test and a two-way chi-square test?
The question being tested, with one-way testing goodness-of-fit and two-way testing independence.
What is the main objective of the two-way chi-square test in this example?
To determine if the variables are distributed independently or not
What is the null hypothesis (H0) in this example?
The variables are distributed independently
What do the marginal totals represent in the table?
The probability of each variable separately
What is the purpose of obtaining the expected frequencies in the chi-square test?
To compare the observed frequencies with the expected frequencies
What is the assumption of the chi-square test in this example?
The variables are categorical and independent
What is the reason for calculating the expected frequencies in the two-way chi-square test?
To compare with the observed frequencies
How do you calculate the degree of freedom in a two-way chi-square test?
Number of cells minus one multiplied by the number of columns minus one
What is the purpose of the chi-square table in the two-way chi-square test?
To find the critical value
What is the characteristic of the chi-square value in a two-way chi-square test?
It is always a positive value
What is the purpose of the contingency table in the two-way chi-square test?
To display the observed and expected frequencies
What is the formula for calculating the chi-square value in a two-way chi-square test?
($observed - expected$)^2 / expected
What is the interpretation of a significant chi-square value in a two-way chi-square test?
There is a significant difference between the observed and expected frequencies
What is the advantage of using the two-way chi-square test over the one-way chi-square test?
It can examine the relationship between two variables
What is the assumption of the chi-square test in this example?
The data is categorical
What is the result of rejecting the null hypothesis in a two-way chi-square test?
The variables are dependent
What is the primary difference between a one-way chi square and a two-way chi square?
The number of variables tested
A researcher wants to examine the relationship between exercise frequency and weight loss. What type of chi square test would be most appropriate?
Two-way chi square
In a two-way chi square test, what is the purpose of calculating the expected frequencies?
To compare with the observed frequencies
What is the goal of a two-way chi square test?
To examine the relationship between two variables
A two-way chi square test is often referred to as which type of test?
Test of Independence
Study Notes
Two-Way Chi-Square
- Also known as Chi-Square Test of Independence
- Tests the relationship between two variables
- Null hypothesis: the two variables are distributed independently
- Referred to as Chi-Square contingency
Contingency Tables
- A table that contains the frequencies of individuals in a particular sample and category
- Example: M&Ms colors by gender
Independence
- Two variables are considered independent when the frequency distribution for one variable has the same shape for all levels of the second variable
- Example: salary is independent of gender if the frequency distribution of salary levels is the same for both males and females
Types of Chi-Square Tests
- One-way chi-square (goodness-of-fit): tests whether the observed data fit a model
- Two-way chi-square (test of independence): tests whether two variables are independent
Example of Two-Way Chi-Square
- Research question: Is there a relationship between class attendance and passing/failing an exam?
- Example table: attendance and pass/fail status
- Expected frequencies are calculated using the marginal totals and the grand total
Expected Frequencies
- Calculated using the marginal totals and the grand total
- Example: expected frequencies for attendance and pass/fail status
- We are interested in the marginal totals, not the frequencies within the body of the table
Logic of the Test of Independence
- If the null hypothesis is true, the marginals are all we need to understand the variables as they would be distributed independently
- We obtain the necessary expected frequencies using the marginal totals and the grand total
Conclusion
- If we reject the null hypothesis of independence, we conclude that the two variables are associated
- We need to supply the meaning to the statistical output
- Crosstabs can be used to calculate the chi-square test in SPSS
Summary
- The two-way chi-square test is used to test the association between two categorical variables
- It is also referred to as the Test of Independence
- Expected frequencies are calculated using the marginal totals and the grand total
- The obtained chi-square is tested against the chi-square distribution
- The calculation of degrees of freedom involves the number of categories of both variables, not the sample size
Two-Way Chi Square Test
- The two-way Chi Square test is used to determine the relationship between two variables, and it is also known as the test of independence.
- The test is used to determine if the two variables are distributed independently, and the null hypothesis states that the two variables are independent.
Contingency Table
- The two-way Chi Square test is presented as a contingency table, which shows the frequencies of the individuals in each category.
- The contingency table has cells that contain the frequencies of the individuals in each category.
How the Two-Way Chi Square Test Works
- Conceptually, the two-way Chi Square test looks at the shape of the frequency distribution of two variables to determine if they are independent.
- The test is used to determine if the frequency distribution of one variable has the same shape at all levels of the second variable.
Example of Independence
- If the shape of the frequency distribution is the same for men and women, then the variables are independent.
- For example, if the salary distribution is the same for men and women, then salary is independent of gender.
Example of Dependence
- If the shape of the frequency distribution is different for men and women, then the variables are dependent.
- For example, if the salary distribution is different for men and women, then salary is dependent on gender.
Calculating Expected Frequencies
- The expected frequencies are calculated using the marginal totals and the grand total.
- The formula for calculating expected frequencies is: (Row Total * Column Total) / Grand Total.
Calculating Chi Square Value
- The Chi Square value is calculated using the observed frequencies and the expected frequencies.
- The formula for calculating Chi Square is: Σ [(Observed Frequency - Expected Frequency)^2 / Expected Frequency].
Degrees of Freedom
- The degrees of freedom for the two-way Chi Square test are calculated as: (Number of Rows - 1) * (Number of Columns - 1).
- In the example given, the degrees of freedom would be 1.
Interpreting the Results
- The Chi Square value is compared to the critical value from the Chi Square table to determine if the null hypothesis is rejected.
- If the Chi Square value is greater than the critical value, then the null hypothesis is rejected, and it is concluded that the variables are dependent.
Chi Square Analysis
- There are two types of chi square analyses: one-way chi square and two-way chi square.
One-Way Chi Square
- Involves a single variable, such as course performance (pass/fail) or car color preference (green/blue/red).
- Also referred to as the Goodness of Fit chi square.
Two-Way Chi Square
- Involves two variables, such as lecture attendance status and course performance (pass/fail).
- Also referred to as the Test of Independence or Contingency Chi Square.
- Used to analyze the relationship between two variables.
This quiz covers the concept of survey design and analysis in psychology, specifically focusing on the Chi-Square test of independence. It tests the relationship between two variables and determines if they are distributed independently.
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