Stats exam 2 Chi squared test

Count (attribute or nominal) data

tests based on sample information summarized as the number of sample items in each of several categories

Count =

#of items in a category

Frequency

#of sample items in a category

Goodness of fit test

used to “judge” whether or not a particular probability distribution could reasonably model our sample data

Contingency test

used to “judge” whether two categorical variables are independent or associated to one another

x =

primary variable of interest which can be continuous

In goodness of fit H0:

The distribution of X is a particular probability distribution

In goodness of fit HA:

The distribution of X is NOT a particular probability distribution

Contingency test H0:

Variable A is independent of variable B

Contingency test HA:

Variable A is NOT independent of variable B

Observed count =

# of items in the sample with a given
characteristic or set of characteristics
Also called the observed frequency

Expected Count =

# of items in the sample that should have a
given characteristic or set of characteristics (i.e., should be in a
certain category) if the statement in H0 is true

Large differences in the observed and expected counts:

• Indicate incompatibility between what is occurring and what should occur under H0:

• Cause X squared to be large

• Large values of x squared select the null hypothesis

Required data conditions for Goodness of fit

• SRS

• Data summarized as counts per category

• N >=30 and all expected counts >=5

Required data conditions for Contingency

• SRS

• Data summarized as counts per category

• All expected counts >=5

M =

#of parameters estimated

DF=

Goodness of fit: K - m - 1

Contingency: (r-1)(c-1)