Hypothesis Testing and Chi Square Flashcards
What is the purpose of hypothesis testing?
To determine whether a relationship exists between two variables or groups beyond random chance.
What are the two main goals of hypothesis testing?
Determine if parameters in a model take specified values.
Detect statistically significant differences.
What are the five steps in hypothesis testing?
State Assumptions & Meet Test Requirements
State the Null Hypothesis (H₀) & Alternative Hypothesis (H₁)
Select the Sampling Distribution & Establish the Critical Region
Compute the Test Statistic
Make a Decision & Interpret the Results
What is the critical region in hypothesis testing?
The area under the sampling distribution that includes “unlikely” sample outcomes, based on the alpha (α) level.
What happens when a test statistic falls in the critical region?
The null hypothesis is rejected because the result is unlikely to occur by chance.
What is a p-value?
The exact probability of obtaining a test result at least as extreme as the observed value, assuming H₀ is true.
What is a Type I error?
Rejecting a true null hypothesis (false positive).
What is a Type II error?
Failing to reject a false null hypothesis (false negative).
How are Type I and Type II errors related?
Reducing the chance of one increases the likelihood of the other.
What type of variables is the chi-square (χ²) test used for?
Nominal and ordinal variables (tabular data).
What does the chi-square test measure?
Whether two categorical variables are independent or related.
What is the null hypothesis (H₀) in a chi-square test?
The two variables are independent.
What is the alternative hypothesis (H₁) in a chi-square test?
The two variables are dependent (related).
How are independent and dependent variables arranged in a cross-tabulation?
Independent Variable (IV) → Columns
Dependent Variable (DV) → Rows
What are “marginals” in a cross-tabulation?
The row and column totals for each category.
What are the steps to calculate the chi-square test statistic?
Compute expected frequencies for each cell.
Subtract expected from observed frequency for each cell (O - E).
Square the difference ((O - E)²).
Divide by expected frequency ((O - E)² / E).
Sum all values to get χ²(obtained).
Compare χ²(obtained) to χ²(critical) from Appendix C.
What are the key assumptions for using chi-square?
Random sample.
Observations are independent.
Both variables are nominal/ordinal.
At least 80% of expected cell counts must be greater than 5.
What does a significant chi-square test tell us?
That the two variables are dependent (not independent).
What does chi-square NOT tell us?
The strength or direction of the relationship.
How do we determine the pattern of the relationship?
By calculating column percentages in the cross-tabulation.
What are three limitations of the chi-square test?
Difficult to interpret when variables have many categories.
Not reliable for small samples (when expected frequencies ≤ 5).
Sensitive to large samples (small differences may appear significant).
