Goodness of fit tests Flashcards
what do goodness of fit tests compare
an observed frequency distribution with a theoretical expectation
what is a limit of binomial tests
limited to categorical variables with only TWO outcomes
what is the probability model
frequency of an event is proportional to the number of opportunities
what type of model is the proportional probability under
NULL model
what is the chai goodness of fit test
test that compares frequency data to a model stated by the null hypothesis UNDER THE PROPORTION PROBABILITY MODEL
observed vs expected frequency
observed - frequency based on actual data collected
expected - frequency based on null hypothesis generated by the proportion probability model
how to find the expected frequency in data
take the observed frequency and divide by total observations THEN multiply that proportion by the sample size (n)
how do calculate based on chai squared test
what is the test statistic for the chai squared test
measure of discrepancy between observed and expected frequencies
what is the formula for the test statistic for this test
does chai squared work on absolute or relative frequencies
absolute frequency (counted)
degrees of freedom specifies
which chai squared distribution to use as the null distribution
define degrees of freedom
the number of values in the calculations of a test statistic that may be varied independently
how to calculate degrees of freedom for Chai squared test
what is the P-value
the probability of getting a result as extreme or more extreme than the observed result under null hypothesis
what are two assumptions for the chai squared test
- individuals in the data set are random sample of population
2.no categories has EXPECTED frequency LESS than 1
- no more than 20% if the categories have EXPECETD frequency below 5
what is to be done if the assumptions for this test is VIOLATED
- blend categories together (that are able to be)
- use an alterative test (like binomial test)
what does the chai squared goodness of fit test assume
- random sample
- expected frequencies are sufficiently high
what does the chai squared goodness of fit test compare
frequency data to a model stated by the null hypothesis (generally the proportion probability model)
how to determine P value of the test `
compare with critical chai value in statistical table
does a binomial test provide the exact P value
YES
when is a binomial test better than a chai squared test
when there are only two categories and assumptions of chai squared test are NOT met
what other model besides the proportional probability model is used to model the null hypothesis in goodness of fit test s
binomial distribution
what does it mean if a data set is NOT binomially distributed
the assumptions of the binomial distribution must be violated
what is the poisson distribution
describes the number of success in blocks of time or space
contrast the poisson distribution from the binomial distribution
binomial
- describes the number of successes in N trials
poisson
- describes the number of successes in blocks or time or space
does the poisson distribution have a set sample size
NO
what are three subcategories for data in a poisson distribution
- clumped
- random
- dispersed
dispersed vs clumped displays of poisson distribution
dispersed
- very little clumping of data
- could be territorial organisms or competition
clumped
- highly grouped data in an area
- could be offspring don’t migrate from parents or animals live in herds
how to find mean number of each outcome in data for the poisson distribution
sum the products of each row and divide by the n
how does variance associate with mean in poisson distribution
it EQULAS the mean
what distribution results from the variance being GREATER than the mean (poisson distribution)
clumped distribution
what distribution results from the variance being LESS than the mean (poisson distribution)
dispersed distribution
