Week 3 Flashcards
What is the purpose of the Chi-Square Goodness of Fit test?
To compare observed frequencies in categorical data to expected frequencies specified by a null hypothesis.
What type of data is required for the Chi-Square Goodness of Fit test?
Nominal (categorical) data, with frequency counts in each category
What are the main steps in calculating the Chi-Square (χ²) statistic
Subtract the expected count from the observed count, square the result, divide by the expected count, then sum these values for all categories.
What assumptions must be met for the Chi-Square test?
Observations must be independent, and expected frequencies should be greater than 5 in each category.
What is the null hypothesis (H₀) in a Chi-Square Goodness of Fit test?
That there is no difference between the observed and expected proportions.
What determines if the Chi-Square test result is significant?
The χ² value must exceed the critical value for the given degrees of freedom and α level (usually 0.05).
In a Chi-Square test with 1 degree of freedom, what is the critical value at α = 0.05?
3.84
What is the purpose of the Multinomial Test?
To test if the observed frequencies match a specified expected distribution across multiple categories.
How is the Multinomial Test performed in JASP software?
Import data, set factors and counts, and choose equal or specific proportions for comparison.
If χ² = 2.00 and p = 0.16 in a Multinomial Test, what does this indicate?
The result is not significant, so the null hypothesis cannot be rejected.
How does sample size affect the Chi-Square test’s ability to detect differences?
Larger sample sizes improve the test’s power, making it easier to detect small differences
What is indicated if the observed proportions significantly differ from the expected proportions in a Goodness of Fit test?
The null hypothesis is rejected, indicating a difference between observed and expected proportions.
In Chi-Square tests, why should expected frequencies ideally be no less than 5?
To reduce the risk of Type I errors and maintain the validity of the test.
When there are more than two categories in a Chi-Square test, what does a significant result tell you?
It indicates that the observed frequencies differ from expected, but it doesn’t specify which category differs.
