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Inference for TwoWay Tables
Analysis of
TwoWay Tables
Section 9.1
© 2009 W.H. Freeman and Company
Twoway tables  review
!
An experiment has a
twoway
design if two
categorical
factors are
studied with several levels of each factor.
!
Twoway tables organize data about two categorical variables
obtained from a twoway, or block, design.
!
Example
: We call Education the
row variable
and Age group the
column variable
.
"
Each combination of values for these two variables is called a
cell
.
Marginal distributions (review)
We can look at each categorical variable separately in a twoway table
by studying the row totals and the column totals. They represent the
marginal distributions
,
expressed in counts or percentages (They are
written as if in a margin.)
2000 U.S. census
Conditional distributions (review)
#
In the table below, the 25 to 34 age group occupies the first column. To find
the complete distribution of education in this age group, look only at that
column. Compute each count as a percent of the column total.
#
These percents should add up to 100% because all persons in this age
group fall in one of the education categories. These four percents together
are the
conditional distribution
of education, given the 25 to 34 age group.
2000 U.S. census
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View Full Document The percents within the table represent the
conditional distributions
.
Comparing
the conditional distributions allows you to describe the “relationship” between both
categorical variables.
We can also compute each count as a percent of the column total. These percents
should add up to 100% and together are the
conditional distribution.
(Here the
percents are calculated by age range (columns)).
Conditional distributions (review)
29.30% =
11071
37785
=
cell total
.
column total
Hypothesis: no association
"
The question of interest is whether there is a relation between the row variable and the
column variable
"
We want to know if the differences in sample proportions are likely to have occurred just
by chance, because of the random sampling.
"
We use the
chisquare
(
!
2
)
test
to assess the null hypothesis of no relationship
between the two categorical variables of a twoway table.
Specific Hypotheses
"
The hypotheses for the
chisquare
(
!
2
)
test
are…
H
0
: There is no association between the row and column variables
H
a
: There is an association between the row and column variables
"
These hypotheses are neither on or two tailed
"
For an r x c two way table, in general
"
H
0
means that the c distributions of the row variable are identical
"
H
a
means that the distributions are not the same
"
The question being posed is “Are the observed cell counts different
from the expected counts?”
Expected counts in twoway tables
"
Twoway tables sort the data according to two categorical variables.
We want to test the hypothesis that there is no relationship between
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This note was uploaded on 12/11/2009 for the course STAT 212 taught by Professor Holt during the Spring '08 term at UVA.
 Spring '08
 HOLT

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