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.
THIS IS THE TABLE:
__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
For the first question, the accurate description of Simpson's paradox is:
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.
For the second question, the statements that are true are:
A. I only
For the first question, the accurate description of Simpson's paradox is:
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.
To understand Simpson's paradox, one must compare the associations observed within separate groups with the association observed when the groups are combined. In some cases, when separate groups are aggregated, the overall association can appear to reverse direction compared to the direction observed within individual groups. This can occur when a lurking variable (a variable that is not initially considered but affects the results) is present in the data.
For the second question, the following statements are true:
I. The sum of the values of all the conditional distributions must be 1.
This statement is true because the sum of probabilities in any distribution must always be equal to 1.
II. Temperature and crime rate appear to be related (the warmer the temperature, the higher the crime rate).
This statement is true because within each conditional distribution, the crime rate tends to be higher as temperature increases.
III. The conditional distribution for Normal Crime Rate is roughly similar to the marginal distribution Temperature.
This statement is false because the conditional distribution for Normal Crime Rate is not symmetrical or similar to the marginal distribution of Temperature. The values within each row (conditional distribution) do not align with the values in the corresponding column (marginal distribution).
Therefore, the correct answer is:
B. II only.