Chi Squared Goodness of Fit Flashcards
What is the purpose of the Chi-Squared Goodness of Fit Test?
To test if a sample comes from a specified distribution.
What is the null hypothesis (H₀) for a Goodness of Fit Test?
The sample comes from the specified distribution.
What is the alternative hypothesis (H₁) for a Goodness of Fit Test?
The sample does not come from the specified distribution.
How do you calculate the expected counts E_i?
E_i = n × p_i, where p_i is the probability under H₀.
What is the formula for the Chi-Squared test statistic W?
W = Σ (O_i - E_i)² / E_i over all categories i.
What distribution does W approximately follow under H₀?
Chi-squared distribution with k-1 degrees of freedom.
Why do we use k-1 degrees of freedom instead of k?
Because the observed counts sum to n, making one category dependent.
What rule of thumb determines if sample size is large enough?
Each expected count E_i should be at least 5.
When do we reject H₀ in a Chi-Squared Goodness of Fit Test?
If W > Chi-squared critical value at significance level α with k-1 degrees of freedom.
How do you handle continuous data for a Goodness of Fit Test?
Bin the continuous data into intervals and apply the Chi-Squared test.
What is the risk when binning continuous data for the test?
Test results can vary depending on bin width and bin boundaries.
How are expected counts found for a binomial distribution?
Multiply sample size by binomial probability for each outcome.
What function in R gives the upper tail Chi-Square critical value?
Use qchisq(1 - α, df) where df = k-1.
What does failing to reject H₀ imply?
There is not strong evidence against H₀, but it does not prove H₀ is true.
What are the steps to perform a Chi-Squared Goodness of Fit Test?
State H₀ and H₁, compute observed and expected counts, calculate W, find critical value, apply decision rule.
