Chi Squared Test for Independence

1
Chi Squared Test for Independence Using a
Graphics Calculator And Contingency Tables Using
Matrices
2
Recall yesterdays problem regarding eye and hair
color. This can be done using matrices and the X2
- Test on your TI-83 or TI-84 calculator.
1 Set up the contingency table for observed
values using matrices. Press MATRIX and move the
cursor to EDIT. 2 Specify the number of rows
and columns, in this case 2 x 2 and enter the
values in the matrix cells.
3
3 Press STAT. Move the cursor to TESTS.
Press ENTER and use the down arrow keys to
select option C X2 Test
4
4 The expected values are automatically
calculated and placed in Matrix B. All that
remains is to select Calculate. Move the cursor
over Calculate and press ENTER. 5 Read from
the screen, the calculated value X2 U and make
your conclusion.
5
Notice that the calculator does not give a
critical value only a p-value. This p-value
gives the probability of calculating a value of
U as or more extreme than the one obtained if H0
were assumed to be true.
If no critical values are available use the
p-value.
6
The corresponding p-values for set levels of
significance, a, are as follows
If p lt 0.01, then reject H0 at the 1 level of
significance. If p lt 0.05, then reject H0 at
the 5 level of significance. If p lt 0.10, then
reject H0 at the 10 level of significance.
7
Use your calculator to check homework problem 1.
Add the p-value to your homework so that you
have a problem worked using both a critical value
and the p-value.
8
A randomly selected individuals grouped by age
were polled as to their stand on capital
punishment. Their responses are summarised in the
table below. Is there evidence to support that
capital punishment opinion and age grouping is
dependent?
Age Group
Capital punishment
9
(No Transcript)
10
Compare your answer to one obtained manually.
X2calc 0.2160 note this includes rounding and
is different that the value obtained without
rounding. Also since the degrees of freedom is 2
we need a more complete table of critical values.
The critical value at d.f. of and 5 level of
significance is 5.99. We would accept the null
hypothesis since .2160lt5.99 at the 5 level of
significance. Opinion on capital punishment is
independent of age group.