Simpson's Paradox: Filling in the numbers

[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

Homework Equations

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.

 

[jedishrfu]

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

 

[Dick]

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

Homework Equations

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.

 

[Phox]

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.

 

[Dick]

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.