# Simpson's Paradox: Filling in the numbers

• Phox
In summary, the conversation discusses the task of coming up with numbers for various patient and cure totals in two hospitals, A and B, with two separate wards each (LR for low-risk patients and HR for high-risk patients). The given information includes the total number of patients and cured patients in each hospital, as well as the fact that Hospital A has lower cure rates in both LR and HR wards compared to Hospital B. To solve the task, one can create a table and choose extreme cases where the numbers of patients and cured patients are greatly imbalanced between the wards, making the task easier to solve.
Phox

## Homework Statement

We are given that there are two hospitals A & B.
Each hospital has two separate wards: one for low-risk patients (LR) and one for high-risk patients (HR.)

Hospital A had 120 patients total and cured 60 total. (.5 cure rate)
Hospital B had 700 patients total and cured 280 total. (.4 cure rate)

Hospital A's LR ward had a lower cure rate than Hospital B's LR ward.
Hospital A's HR ward had a lower cure rate than hospital B's HR ward.

Come up with numbers for the following to make this true:
• Hospital A LR Total Patients
• Hospital A LR Cured Patients
• Hospital A HR Total Patients
• Hospital A HR Cured Patients
• Hospital B LR Total Patients
• Hospital B LR Cured Patients
• Hospital B HR Total Patients
• Hospital B HR Cured Patients

## The Attempt at a Solution

I've created a table. I don't know how you'd go about finding numbers that would satisfy the problem.

Appreciate the help.

okay so where's the table,? We can't just give you the answer. We can only give hints.

Phox said:

## Homework Statement

We are given that there are two hospitals A & B.
Each hospital has two separate wards: one for low-risk patients (LR) and one for high-risk patients (HR.)

Hospital A had 120 patients total and cured 60 total. (.5 cure rate)
Hospital B had 700 patients total and cured 280 total. (.4 cure rate)

Hospital A's LR ward had a lower cure rate than Hospital B's LR ward.
Hospital A's HR ward had a lower cure rate than hospital B's HR ward.

Come up with numbers for the following to make this true:
• Hospital A LR Total Patients
• Hospital A LR Cured Patients
• Hospital A HR Total Patients
• Hospital A HR Cured Patients
• Hospital B LR Total Patients
• Hospital B LR Cured Patients
• Hospital B HR Total Patients
• Hospital B HR Cured Patients

## The Attempt at a Solution

I've created a table. I don't know how you'd go about finding numbers that would satisfy the problem.

Appreciate the help.

By thinking about it mostly. You aren't given the number of patients in the HR or LR wards. So you get to make them up. Suppose Hospital A's LR ward contains one patient who dies. Suppose Hospital B's HR ward contains one patient who lives. You make up the rest of the numbers.

Dick said:
By thinking about it mostly. You aren't given the number of patients in the HR or LR wards. So you get to make them up. Suppose Hospital A's LR ward contains one patient who dies. Suppose Hospital B's HR ward contains one patient who lives. You make up the rest of the numbers.

Excellent, got it.

Thank you.

Phox said:
Excellent, got it.

Thank you.

You're welcome. The trick is to pick an extreme case where the numbers of patients in the wards are as lopsided as possible. Then it looks easy.

## 1. What is Simpson's Paradox?

Simpson's Paradox is a statistical phenomenon in which a trend or relationship appears when data is analyzed separately, but reverses or disappears when the data is combined.

## 2. How is Simpson's Paradox caused?

Simpson's Paradox is caused by lurking variables, also known as confounding variables, that are not accounted for in the data analysis. These variables can influence the relationship between the variables being studied and lead to misleading conclusions.

## 3. Can Simpson's Paradox be avoided?

While Simpson's Paradox cannot be entirely avoided, it can be minimized by carefully selecting and controlling for variables in the data analysis. It is important to consider all relevant variables and their potential influence on the relationship being studied.

## 4. What are some real-life examples of Simpson's Paradox?

Simpson's Paradox has been observed in various fields, including medicine, economics, and education. For example, a study may show that a certain treatment is effective for a specific group, but when the groups are combined, the treatment appears to be ineffective. This can also occur in sports, where a player's performance may appear to improve when looking at individual game statistics, but when looking at the overall season, their performance may have actually declined.

## 5. How can Simpson's Paradox impact decision-making?

If not recognized and properly accounted for, Simpson's Paradox can lead to incorrect conclusions and decisions. It is important for researchers and decision-makers to thoroughly analyze the data and consider all potential variables to avoid making decisions based on misleading results.

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