Which of the following is an accurate description of Simpson's paradox?
When groups of data are aggregated, an association can get stronger because of a confounding variable. That confounding variable is usually the number of observations in different groups of data.
When groups of data are combined, an association can get stronger because of a lurking variable. That lurking variable is usually the number of observations in the different groups of data.
When groups of data are separated, an association can get stronger because of a lurking variable. That lurking variable is usually the number of observations in the different groups of data.
When separate groups of data are combined, an association can reverse direction because of a lurking variable that was lost when the different groups of data were lumped together.
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For the table below which of the following are true?
I. The sum of the values of all the conditional distributions must be 1.
II. Temperature and crime rate appear to be related (the warmer the temperature, the higher the crime rate).
III. The conditional distribution for Normal Crime Rate is roughly similar to the marginal distribution Temperature.
Crime Rate
________Below___ Normal____ Above
Temp. __Below 12 , 8 , 5
___ ___ Normal 35 , 41 , 24
______ Above 4 , 7 , 14
A. I only
B. II only
C. II and III only
D. III only
E. I and III only
http://www.google.com/search?client=safari&rls=en&q=Simpson's+paradox&ie=UTF-8&oe=UTF-8
What table?
The table is supposed to be that ugly fail that says "Crime Rate" at the top, "below," "normal," and average beneath it, etc.
Simpson's paradox is the phenomenon where an association that appears when analyzing the data as a whole disappears or reverses when the data is divided into subgroups. It often occurs when there is a lurking or confounding variable that affects the relationship between the variables being studied.
To determine which of the given options is an accurate description of Simpson's paradox, let's examine each option:
Option A: When groups of data are aggregated, an association can get stronger because of a confounding variable. That confounding variable is usually the number of observations in different groups of data.
This statement is not accurate. Simpson's paradox occurs when an association weakens or reverses when groups of data are combined, not when it gets stronger because of a confounding variable.
Option B: When groups of data are combined, an association can get stronger because of a lurking variable. That lurking variable is usually the number of observations in the different groups of data.
This statement is not accurate. Simpson's paradox occurs when an association weakens or reverses when groups of data are combined, not when it gets stronger because of a lurking variable.
Option C: When groups of data are separated, an association can get stronger because of a lurking variable. That lurking variable is usually the number of observations in the different groups of data.
This statement is not accurate. Simpson's paradox occurs when an association weakens or reverses when groups of data are combined, not when it gets stronger because of a lurking variable.
Option D: When separate groups of data are combined, an association can reverse direction because of a lurking variable that was lost when the different groups of data were lumped together.
This is an accurate description of Simpson's paradox. When separate groups of data are combined, the association between variables can reverse direction due to the presence of a lurking variable that becomes obscured when the groups are combined.
Therefore, the correct answer is D. III only.
As for the second question, let's evaluate each statement:
I. The sum of the values of all the conditional distributions must be 1.
This statement is true. The sum of the probabilities in a conditional distribution must always equal 1.
II. Temperature and crime rate appear to be related (the warmer the temperature, the higher the crime rate).
Based on the table provided, there is no clear pattern or relationship between temperature and crime rate. Therefore, this statement is not true.
III. The conditional distribution for Normal Crime Rate is roughly similar to the marginal distribution Temperature.
Based on the table, the conditional distribution for Normal Crime Rate is not similar to the marginal distribution for Temperature. Therefore, this statement is not true.
So, the correct answer is A. I only.