Goodness of fit tests Flashcards

1
Q

what do goodness of fit tests compare

A

an observed frequency distribution with a theoretical expectation

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2
Q

what is a limit of binomial tests

A

limited to categorical variables with only TWO outcomes

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3
Q

what is the probability model

A

frequency of an event is proportional to the number of opportunities

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4
Q

what type of model is the proportional probability under

A

NULL model

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5
Q

what is the chai goodness of fit test

A

test that compares frequency data to a model stated by the null hypothesis UNDER THE PROPORTION PROBABILITY MODEL

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6
Q

observed vs expected frequency

A

observed - frequency based on actual data collected

expected - frequency based on null hypothesis generated by the proportion probability model

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7
Q

how to find the expected frequency in data

A

take the observed frequency and divide by total observations THEN multiply that proportion by the sample size (n)

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8
Q

how do calculate based on chai squared test

A
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9
Q

what is the test statistic for the chai squared test

A

measure of discrepancy between observed and expected frequencies

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10
Q

what is the formula for the test statistic for this test

A
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11
Q

does chai squared work on absolute or relative frequencies

A

absolute frequency (counted)

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12
Q

degrees of freedom specifies

A

which chai squared distribution to use as the null distribution

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13
Q

define degrees of freedom

A

the number of values in the calculations of a test statistic that may be varied independently

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14
Q

how to calculate degrees of freedom for Chai squared test

A
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15
Q

what is the P-value

A

the probability of getting a result as extreme or more extreme than the observed result under null hypothesis

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16
Q

what are two assumptions for the chai squared test

A
  1. individuals in the data set are random sample of population

2.no categories has EXPECTED frequency LESS than 1

  1. no more than 20% if the categories have EXPECETD frequency below 5
17
Q

what is to be done if the assumptions for this test is VIOLATED

A
  1. blend categories together (that are able to be)
  2. use an alterative test (like binomial test)
18
Q

what does the chai squared goodness of fit test assume

A
  1. random sample
  2. expected frequencies are sufficiently high
19
Q

what does the chai squared goodness of fit test compare

A

frequency data to a model stated by the null hypothesis (generally the proportion probability model)

20
Q

how to determine P value of the test `

A

compare with critical chai value in statistical table

21
Q

does a binomial test provide the exact P value

22
Q

when is a binomial test better than a chai squared test

A

when there are only two categories and assumptions of chai squared test are NOT met

23
Q

what other model besides the proportional probability model is used to model the null hypothesis in goodness of fit test s

A

binomial distribution

24
Q

what does it mean if a data set is NOT binomially distributed

A

the assumptions of the binomial distribution must be violated

25
what is the poisson distribution
describes the number of success in blocks of time or space
26
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
27
does the poisson distribution have a set sample size
NO
28
what are three subcategories for data in a poisson distribution
1. clumped 2. random 3. dispersed
29
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
30
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
31
how does variance associate with mean in poisson distribution
it EQULAS the mean
32
what distribution results from the variance being GREATER than the mean (poisson distribution)
clumped distribution
33
what distribution results from the variance being LESS than the mean (poisson distribution)
dispersed distribution