Chi Squared Distribution Flashcards
What is a Contingency Table?
A table displaying sample values for two different factors; it helps determine conditional probabilities.
What are common applications of the chi-square distribution?
- Testing if data fits a distribution, 2. Comparing distributions of two populations, 3. Testing independence of events, 4. Testing variability.
What is the random variable in a chi-square distribution?
The sum of squares of df independent standard normal variables.
How does the shape of the chi-square distribution depend on degrees of freedom (df)?
It is right-skewed and becomes approximately normal when df > 90.
What is the range of chi-square test statistics?
Always greater than or equal to zero.
Are chi-square tests usually one-tailed or two-tailed?
They are almost always right-tailed.
What does the goodness-of-fit test assess?
Whether a data set fits a specific distribution.
What is the null hypothesis in a goodness-of-fit test?
The data come from the assumed distribution.
What are the conditions for the goodness-of-fit test?
Expected value in each category must be at least five.
What does the test of independence assess?
Whether two factors are independent.
What is the null hypothesis in the test of independence?
The two factors are independent.
What are the conditions for the test of independence?
Expected value in each cell must be at least five.
What does the test for homogeneity assess?
Whether two data sets come from the same distribution.
What is the null hypothesis in the test for homogeneity?
The populations come from the same distribution.
What are the conditions for the test for homogeneity?
Expected value in each category must be at least five.
When is the goodness-of-fit test used?
To determine if data fits a particular distribution.
When is the test of independence used?
To determine the independence of two factors using a contingency table.
When is the test for homogeneity used?
To determine whether two populations come from the same distribution.
What does the test of a single variance assess?
Whether the variability in a population matches a hypothesized value.
How are the hypotheses expressed in a single variance test?
In terms of variance or standard deviation.
What tails can a test of single variance be?
Left-tailed, right-tailed, or two-tailed.
