Transcript Section 14.2: Inference with Two Way Tables

Section 14.2: Inference with Two Way Tables
We will have to start by creating a two way table and then
the c2 test for Homogeneity (do different categories yield
the same results?) OR Association (is there a relationship
between the two variables?)
The dimensions of a two way table are given by the
number of rows and columns (without the totals). This is
referred to as a r x c table.
Example: Is there is a difference in their responses?
In these cases, the H0 is the distribution of the
response variable is the same for all populations
OR p1 = p2 = p3= … and Ha is the distribution is not
all the same OR p1 ≠ p2 ≠ p3 ≠ …
Expected count = row total x column total
n
We will, however do this with the calculator!!
• Enter the observed data as a MATRIX
• Do the test (Yes this is totally backwards)
• It will enter the expected counts into matrix B for
you to view
Conditions: Check these AFTER the test
• All individual expected counts are at least 1
• No more than 20% of expected counts are ≤ 5
Test Statistic and Conclusion
c2  
(O  E ) 2
E
(r – 1) (c – 1) degrees of freedom.
Use the table to find the P-value
Be sure that your conclusion is in context and
make note of any largest component, if
applicable.
c2 test for Association
H0: there is no association between the two categorical
variables (IN CONTEXT)
Ha: there is some association between the categorical
variables (IN CONTEXT)
The rest of the procedure is IDENTICAL
(expected counts, c2 statistic, p-value) to the
homogeneity test EXCEPT the conclusion would
indicate
There was sufficient/ insufficient evidence of an
association between _________ and ________.
Keep in mind that this test only determines IF there is a
relationship between the variables in the table, not what
is effecting the relationship.
Example: Is student smoking effected by parents
smoking?
Example: Market researchers know that background music
influences mood and purchasing behaviors of customers. A
supermarket in Northern Ireland conducted a study comparing
three treatments: no music, French accordion music, and
Italian string music. The number of bottles of each type of
wine sold was recorded (French, Italian, other).
Will different music yield a different distribution of wine sales?