Goodness of fit tests Flashcards
What is the X2 goodness of fit test
The χ2 goodness-of-fit test compares the frequency distribution of a discrete or categorical variable with the frequencies expected from a probability model.
What assumptions must be met?
No expected frequencies are less than 1
Less than 20% of expected frequencies are less then 5
If these are not met:
- Clump the data
- Use the binomial test
The X2 statistic
This is worked out from the data.
The χ2 test statistic has a null distribution that is approximated by the theoretical χ2 distribution.
The probability of observing an X2 value is the area under the curve to the right of the value on the appropriate distribution (dependent on the degree of freedom).
Degrees of freedom for Chi squared test
(C-1)(r-1)
What is the Posson distirbution
The Poisson distribution describes the frequency distribution of successes in blocks of time or space when successes happen independently and with equal probability over time or space.
Its a proability model used to calculate the null hypothesis
Rejecting a null hypothesis of a Poisson distribution of successes implies that successes are not independent or that the probability of a success occurring is not constant over time or space.
Variance vs mean of poisson distirbution
Comparing the variance of the number of successes per block of time or space to the mean number of successes measures the direction of departure from randomness in time or space.
If the variance is greater than the mean, the successes are clumped; if the variance is less than the mean, successes are more evenly distributed than expected by the Poisson distribution.
Poisson distirbution and X2 test
The Poisson distribution is a way of getting the null hypothesis for the goodness of fit test.
Once this distribution (expected values) have been calculated the X2 method is the same.
Poisson distirbution equation
p(X number of success)= (e^-u x u)/ X!
u= the mean number of events per unit time
Total number of events/ number of time units
X= the number of successes for this particular calculation
