Chi-square Test Flashcards
What are parametric tests?
Tests that make assumptions about population parameters, such as z test, t test, ANOVA, or Pearson’s r.
What assumptions are made when using parametric tests?
Data are normally distributed, equal variances among samples, linear relationship between variables, known underlying distribution.
What type of data can parametric tests be performed on?
Numerical data that are continuous or of ratio type.
What types of data cannot be analyzed using parametric tests?
Nominal and ordinal data.
What is the role of hypothesis testing in parametric tests?
To compare means.
What are nonparametric tests?
Tests that make no assumptions about the population parameters.
What is the chi-square (x2) test used for?
To analyze strictly nominal data.
How can nominal variables be described?
In terms of their frequency.
What is a frequency table?
A table that displays the count of categories in nominal data.
What is the expected frequency in a chi-square test?
The frequency that would be expected if the null hypothesis is true.
What are the steps for calculating a chi-square statistic?
- Calculate the difference (O - E) 2. Square the difference (O - E)² 3. Divide by expected frequency (O−E)²/E 4. Sum all categories Σ(O−E)²/E.
What does the chi-square statistic indicate?
The statistical significance of the difference between observed and expected frequencies.
What are the assumptions of the chi-square test?
- Data are reported as frequencies or counts * Each participant can only be in one category * Membership in each category is independent * Expected frequency must be at least five.
What are the two types of chi-square tests?
- Goodness of Fit test * Test for Independence.
What are the four steps of hypothesis testing?
- State the Hypotheses * Establish the Decision Criteria * Collect Data and Compute Sample Statistics * Make a Decision.
Fill in the blank: The chi-square distribution is positively ______.
skewed.
True or False: The degrees of freedom for a chi-square test is determined by the sample size.
False.
What is the equation for degrees of freedom in a chi-square test?
df = k - 1, where k is the number of categories.
What is the significance of the critical region in a chi-square distribution?
It provides evidence for rejecting the null hypothesis.
What happens to the chi-square distribution as degrees of freedom increase?
The distribution shifts to the right.
