EVEN IF YOUR QUIZ SCORES ARE GOOD

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EVEN IF YOUR QUIZ SCORES ARE GOOD

• PRINT THE TEST TOPICS
• START STUDYING FOR THE TEST NOW
• BEWARE THAT YOU MAY HAVE FORGOTTEN THE OLD TOPICS
• CONSIDER DOING EXTRA CREDIT FOR THE REVIEW DAY

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ANNOUNCEMENTS
Computer printouts are required for Lessons 18,
20. Last day to drop with a W is coming soon.
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5. DEPENDENCE OF VARIABLES
BY HAND 5.1 Dependence When a Two-Way Table Is
Given BY MINITAB 5.2 Dependence When a Two-Way
Table Is Given. 5.3 Dependence When Only a Data
Set Is Given.
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5. DEPENDENCE OF VARIABLES
Statistical practice uses many indicators of an
association between two variables sample
information about the level of one variable is a
clue to the level of the other variable. The
simplest indicator of association is dependence
Two 1.7. We would often like to know whether
two variables are dependent in the population,
but all we have is sample data. We must imagine
what the population must be like. BY HAND
5.1 Dependence When a Two-Way Table Is Given We
start with a two-way table showing how the levels
of two nominal variables combine.
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EXAMPLE G Consider the variables (furnace)Type
and CHLiner(type) in the DATA\furnace data set.
Is there evidence at the 1 level that the type
of chimney liner depends on the type of furnace?
The hypotheses are   H1 CHLiner depends on
(furnace)Type H0 CHLiner is independent of
(furnace)Type
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EXAMPLE G Consider the variables (furnace)Type
and CHLiner(type) in the DATA\furnace data set.
Is there evidence at the 1 level that the type
of chimney liner depends on the type of furnace?
The hypotheses are   H1 CHLiner depends on
(furnace)Type H0 CHLiner is independent of
(furnace)Type
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EXAMPLE G Consider the variables (furnace)Type
and CHLiner(type) in the DATA\furnace data set.
Is there evidence at the 1 level that the type
of chimney liner depends on the type of furnace?
The hypotheses are   H1 CHLiner depends on
(furnace)Type H0 CHLiner is independent of
(furnace)Type
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EXAMPLE G Consider the variables (furnace)Type
and CHLiner(type) in the DATA\furnace data set.
Is there evidence at the 1 level that the type
of chimney liner depends on the type of furnace?
The hypotheses are   H1 CHLiner depends on
(furnace)Type H0 CHLiner is independent of
(furnace)Type
There are 4 degrees of freedom.
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EXAMPLE G Consider the variables (furnace)Type
and CHLiner(type) in the DATA\furnace data set.
Is there evidence at the 1 level that the type
of chimney liner depends on the type of furnace?
The hypotheses are   H1 CHLiner depends on
(furnace)Type H0 CHLiner is independent of
(furnace)Type
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There are 4 degrees of freedom. CONCLUSION At
the .003 level, there is evidence that the sample
comes from a population of installations in which
chimney liner depends on furnace type. There is
also evidence at the 1 level.   But there are
values in model cells as low as zero, which leads
to an erroneously small observed level under the
chi-square approximation. (Any expected cell
count below 5 may cause error.)
M155 L19 Dependence -- Slide 6
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BY MINITAB 5.2 Dependence When a Two-Way Table
Is Given. When you have a contingency table,
you can enter the numbers inside the table in a
few rows and columns of MINITAB. (Do not enter
the row and column sums.) Then Click on Stat gt
Tables gt Chi-Square Test , double click on the
columns, and click on OK.
M155 L19 Dependence -- Slide 7
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Let us analyze the MINITAB output.  Chi-Sq
0.304 0.001 0.329 8.959
1.464 1.966 1.618 1.967
0.279 16.887 DF 4, P-Value 0.002 6 cells
with expected counts less than 5.0   Compare this
MINITAB output with the earlier discussion of the
same data.   CONCLUSION At the .002 level, there
is evidence that the sample comes from a
population of installations in which chimney
liner depends on furnace type. There is also
evidence at the 1 level.
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CAUTION The previous use of MINITAB was for a
contingency table previously entered in the
worksheet. If you use the same method on
variables in columns, it will not work! The
following shows what happens.
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The solution to this error is to Cross-Tabulate
first and do the chi-square analysis under
Cross-Tabulation.
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5.3 Dependence When Only a Data Set Is
Given.
If only a data set is given, use MINITAB to form
the table as well as the chi-square analysis.
  EXAMPLE H Choose Stat gt Tables gt
Cross-Tabulation . Double-click on Type and
CHLiner. Choose Chi-square analysis, Above and
expected count .   The format of the printout is
nearly the same as in 5.1, and you didn't need
a separate step to do the cross-tabulation.
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Chi-Square 16.887, DF 4, P-Value 0.002 6
cells with expected counts less than 5.0 Cell
Contents Count
Exp Freq If you also choose Row percents
when doing the cross-tabulation, the row percents
appear above the counts in the various cells.
M155 L19 Dependence -- Slide 11
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Rows Type Columns CH.Liner 0
1 2 All 1 23.68 44.74
31.58 100.00 18 34 24
76 20.49 34.16 21.35 76.00
2 85.71 14.29 -- 100.00
6 1 0 7 1.89
3.15 1.97 7.00 3 -- 83.33
16.67 100.00 0 5 1
6 1.62 2.70 1.69 6.00
All 26.97 44.94 28.09 100.00
24 40 25 89 24.00
40.00 25.00 89.00
M155 L19 Dependence -- Slide 12
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Chi-Square 16.887, DF 4, P-Value 0.002 6
cells with expected counts less than 5.0 Cell
Contents -- of Row
Count Exp Freq
M155 L19 Dependence -- Slide 13