8. Combine the data for small and large stones into a single 2-by-2 table. Now a
ID: 3257734 • Letter: 8
Question
8.
Combine the data for small and large stones into a single 2-by-2 table.
Now answer the following questions using the pooled data.
Step 1:
Which procedure had the highest overall success rate?
Step 2:
Is the difference significant?
Give the chi-square statistic, the degrees of freedom and the P-value for a chi-square test.
Step 3:
The following conclusion can be made:
True or False:
There is no statistical evidence of a difference in success rates between open surgery and PCNL, when both types of stones are combined.
Step 4:
The success rates of PCNL for both small and large kidney stones were lower than the success rates of the open surgery.
Yet, for the combined data it is the opposite.
What is the reason for this strange situation?
Explanation / Answer
Answer:
Open
PCNL
Total
Success
Observed
273
289
562
% of column
78.0%
82.6%
80.3%
Failure
Observed
77
61
138
% of column
22.0%
17.4%
19.7%
Total
Observed
350
350
700
% of column
100.0%
100.0%
100.0%
2.31
chi-square
1
df
.1285
p-value
Step 1:
Which procedure had the highest overall success rate?
The two procedures have the same overall success rate.
The open surgery procedure.
Answer: The PCNL procedure.
Step 2:
Is the difference significant?
Give the chi-square statistic, the degrees of freedom and the P-value for a chi-square test.
2 = 0.128, df = 1, P = 0.721
Answer: 2 = 2.311, df = 1, P = 0.128
2 = 2.311, df = 1, P = 0.256
2 = 0.128, df = 1, P = 0.361
Step 3:
The following conclusion can be made:
True or False:
There is no statistical evidence of a difference in success rates between open surgery and PCNL, when both types of stones are combined.
Answer: True
False
Step 4:
The success rates of PCNL for both small and large kidney stones were lower than the success rates of the open surgery.
Yet, for the combined data it is the opposite.
What is the reason for this strange situation?
This is a retrospective observational study, not an experiment, therefore the results are inaccurate.
Result: The reason is that PCNL was chosen more often when the stones were small, and small stones appear easier to treat.
The reason is that the treatment was not chosen at random, but according to the physician's decision.
These results are contradictory and can be explain only by some kind of an error.
Open
PCNL
Total
Success
Observed
273
289
562
% of column
78.0%
82.6%
80.3%
Failure
Observed
77
61
138
% of column
22.0%
17.4%
19.7%
Total
Observed
350
350
700
% of column
100.0%
100.0%
100.0%
2.31
chi-square
1
df
.1285
p-value
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