19 - Goodness of Fit Flashcards
(18 cards)
What is Goodness of Fit concerned with?
Measuring how well an observed frequency distribution fits a known distribution.
Name the distributions that the Goodness of Fit method can test.
Discrete Binomial, Poisson, Specified Discrete Distribution, Continuous Exponential and Normal.
What distribution is used in the Goodness of Fit method?
Chi-Squared distribution (πΒ²) with π degrees of freedom.
State the null and alternative hypotheses for Goodness of Fit.
H0: Suitable model
H1: Not a suitable model
What is the formula for calculating the Chi-Squared test statistic?
πΒ² = β (πβπΈ) Β² / πΈ where O is observed frequency and E is expected frequency.
What should you do if an expected frequency is less than 5?
Combine it with the group it shares the most features with.
List the conditions for a Binomial Distribution.
Fixed number of trials
Independent outcomes
Two outcomes per trial
Constant probability of success
How do you calculate the expected frequency (Ex) for a Binomial Distribution?
πΈπ₯ = π Γ π (π = π₯) where N is the total of the observed frequencies.
How do you estimate βpβ (probability of success) in a Binomial Goodness of Fit test?
π = (π‘ππ‘ππ ππ’ππππ ππ π π’ππππ π ππ ) / (ππ’ππππ ππ π‘πππππ Γ π)
Degrees of freedom (π) for Binomial if βpβ is given vs. estimated?
βpβ given: π = (number of cells after combining) - 1
βpβ estimated: π = (number of cells after combining) - 2
List the conditions for a Poisson Distribution.
Events occur independently
Events occur singly and randomly
Events occur at a constant rate
Mean and variance are equal
How do you estimate lambda (Ξ») for a Poisson Goodness of Fit test?
π = β (π Γ ππ) / π where βrβ is the number of occurrences and βfrβ is the frequency of that occurrence.
Degrees of freedom (π) for Poisson if Ξ» is given vs. estimated?
Ξ» given: π = (number of cells after combining) - 1
Ξ» estimated: π = (number of cells after combining) - 2
Degrees of freedom (π) for a Specified Discrete Distribution?
π = (number of categories) - 1
What are some indicators that a Normal Distribution might be expected?
Distribution is bell-shaped and symmetrical
Approximately two-thirds of values fall within one standard deviation of the mean
What are the unbiased estimates for ΞΌ and ΟΒ² in a Normal Goodness of Fit test?
xΜ (sample mean) and sΒ² (sample variance)
Degrees of freedom (π) for Normal Goodness of Fit with no parameters estimated, one parameter estimated, and two parameters estimated?
No parameters estimated: π = (number of cells) - 1
One parameter estimated: π = (number of cells) - 2
Two parameters estimated: π = (number of cells) - 3
Degrees of freedom (π) for Exponential Goodness of Fit?
π = (number of cells) - 2
