Which test to use?
X2 Goodness of Fit
X2 Test for Homogeneity
X2 Test for Independence
A brokerage firm wants to see whether
the type of account a customer has
(Silver, Gold, Platinum) affects the type
of trades that a customer makes (in
person, by phone, or on the Internet).
It collects a random sample of trades
made for its customers over the past
year and performs a test.
Chi-squared independence
(one sample – 2 variables)
A brokerage firm wants to see whether the type of account
a customer has (Silver, Gold, Platinum) affects the type of
trades that a customer makes (in person, by phone, or on the
Internet). It collects a random sample of trades made for
its customers over the past year and performs a test.
That brokerage firm also wants to know if
the type of account affects the size of the
account (in dollars). It performs a test to
see if the mean size of the account is the
same for the three account types.
Chi-squared Goodness of Fit
The academic research office at a large
community college wants to see whether
the distribution of courses chosen
(Humanities, Social Science, or Science)
is different for its residential and
nonresidential students. It assembles
last semester’s data and performs a
test.
Chi squared – homogeneity
(one variable 2 groups)
Is the quality of a car affected by what
day it was built? A car manufacturer
examines a random sample of the
warranty claims filed over the past two
years to test whether defects are
randomly distributed across days of the
work week.
Chi squared GOF (existing model)
A medical researcher wants to know if
blood cholesterol level is related to
heart disease. She examines a database
of 10,000 patients, testing whether the
cholesterol level (in milligrams) is
related to whether a person has heart
disease or not.
Chi-squared independence
(one sample – 2 variables)
A student wants to find out whether
political leaning (liberal, moderate, or
conservative) is related to choice of
major. He surveys 500 randomly chosen
students and performs a test.
Chi-squared independence
(one sample – 2 variables)
Among randomly selected pets, 27% of
the 188 dogs and 18%of the 167 cats
had fleas. Does this indicate a
significant difference in rates of flea
problems for these two pets?
Difference of proportions
(two samples)
A supermarket chain wants to know
which of two merchandise display
methods is more effective. They
randomly assign 15 stores to use display
type A and 15 others to use display type
B, then collect data about the number of
items sold at each store.
Difference of means
(two independent samples)
Are there more broken bones in summer
or winter? We get records about the
number of fractures treated in January
and July at a random sample of 25
emergency rooms.
Mean of differences
(matched pairs)