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AP Stats Chapter 11
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Terms in this set (18)
chi-square statistic
a measure of how far the observed counts are from the expected counts. this allows us to determine whether a hypothesized distribution seems valid.
chi-square formula
x^2=sum((observed-expected)^2/expected)
what does the sampling distribution of the chi square statistic look like?
not normal- right-skewed with only positive values
can chi square statistics be negative?
no- the "square" part does not allow negativity
what is a chi square goodness of fit test?
a significance test that is applied when you have one categorical variable from a single population. It is used to determine whether sample data are consistent with a hypothesized distribution.
what is df for a chi square goodness of fit test
df=number of categories - 1
what are the conditions for a chi square gof test?
RANDOM: data must come from a random sample or randomized experiment
LARGE SAMPLE SIZE: all expected counts are at least 5
INDEPENDENT: individual observations are independent - when sampling without replacement, check that the population is at least 10x bigger than the sample
what do hypotheses look like for a chi square gof test?
Ho: The specified distribution of the categorical variable is correct
Ha: the specified distribution of the categorical variable is not correct
EX:
Ho: the company's stated color distribution for M&Ms candies is correct
Ha: the company's stated color distribution for M&Ms candies is not correct
does the chi square test statistic compare counts or proportions?
counts
chi square test for homogeneity
used when we want to test whether the distribution is the same for some variable in 2 or more populations
hypotheses for a chi square test for homogeneity
Ho: there is no difference in the distribution of a categorical variable for several populations or treatments
Ha: there is a difference in the distribution of a categorical variable for several populations or treatments
degrees freedom for a chi square test for homogeneity
df=(# of rows -1)(# of columns -1)
how do you find the expected counts for a two way table
expected count=(row total x column total)/table total
what are the conditions that must be met to perform a chi square test for homogeneity?
same as for a gof test: RANDOM, LARGE SAMPLE SIZE, INDEPENDENT
when is a chi square test for association/independence applied?
when we want to test 2 categorical variables from one population
hypotheses for chi square test for association/independence
Ho: there is no association between 2 categorical variables in the population of interest
Ha: there is an association between 2 categorical variables in the population of intrest
what kind of table do the test for homogeneity and association/independence come from?
a two way table
what is the difference between a chi square test for homogeneity and for association/independence
homogeneity comes from several populations and association/independence comes from one population
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