Odds ratio

The success probability of therapy A is $0.83 .$ Therapy B has a success probability of $0.51 .$

Question

What is the odds ratio relative to therapy A?

This is an odds ratio.
Convert $π$ to the respective odds, $odds = \frac{π}{1 - π} .$
Convert $π$ to the respective odds, $odds = \frac{π}{1 - π} .$
Divide $odds_b$ by $odds_a$ to determine the OR.

This is an odds ratio.
Convert $π$ to the respective odds, $odds = \frac{π}{1 - π} .$
Convert $π$ to the respective odds, $odds = \frac{π}{1 - π} .$
Divide $odds_b$ by $odds_a$ to determine the OR.

Feedback

Waiting for response...

Solution(s)

The system accepts the following correct response(s)

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = {odds}_{B} / {odds}_{A}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Correctly determined the odds from $π_{B} .$
Sucessfully calculated ${odds}_{B} / {odds}_{A} .$

Incorrect responses

The system detects the following incorrect responses

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = {odds}_{B} / {odds}_{A}$

Correctly identified the problem and the main steps of the calculation.
Please remember to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Please remember to convert $π_{B}$ to ${odds}_{B} = \frac{π_{B}}{1 - π_{B}} .$
Sucessfully calculated ${odds}_{B} / {odds}_{A} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = {odds}_{B} / {odds}_{A}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Please remember to convert $π_{B}$ to ${odds}_{B} = \frac{π_{B}}{1 - π_{B}} .$
Sucessfully calculated ${odds}_{B} / {odds}_{A} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = \underset{instead of {odds}_{B} / {odds}_{A}}{\underset{⏟}{{odds}_{A} / {odds}_{B}}}$

Correctly identified the problem and the main steps of the calculation.
Please remember to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Please remember to convert $π_{B}$ to ${odds}_{B} = \frac{π_{B}}{1 - π_{B}} .$
The result matches the inverse, with ${odds}_{A}$ being divided by ${odds}_{B}$ instead of ${odds}_{B} / {odds}_{A} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = \underset{instead of {odds}_{B} / {odds}_{A}}{\underset{⏟}{{odds}_{A} / {odds}_{B}}}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Please remember to convert $π_{B}$ to ${odds}_{B} = \frac{π_{B}}{1 - π_{B}} .$
The result matches the inverse, with ${odds}_{A}$ being divided by ${odds}_{B}$ instead of ${odds}_{B} / {odds}_{A} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = \underset{instead of {odds}_{B} / {odds}_{A}}{\underset{⏟}{{odds}_{A} / {odds}_{B}}}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Correctly determined the odds from $π_{B} .$
The result matches the inverse, with ${odds}_{A}$ being divided by ${odds}_{B}$ instead of ${odds}_{B} / {odds}_{A} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = \underset{instead of {odds}_{B} / {odds}_{A}}{\underset{⏟}{{odds}_{A} {odds}_{B}}}$

Correctly identified the problem and the main steps of the calculation.
Please remember to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Please remember to convert $π_{B}$ to ${odds}_{B} = \frac{π_{B}}{1 - π_{B}} .$
The result matches the product of the two odds instead of the ratio, ${odds}_{B} / {odds}_{A} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = \underset{instead of {odds}_{B} / {odds}_{A}}{\underset{⏟}{{odds}_{A} {odds}_{B}}}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Please remember to convert $π_{B}$ to ${odds}_{B} = \frac{π_{B}}{1 - π_{B}} .$
The result matches the product of the two odds instead of the ratio, ${odds}_{B} / {odds}_{A} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \frac{π_{B}}{1 - π_{B}}$
$OR = \underset{instead of {odds}_{B} / {odds}_{A}}{\underset{⏟}{{odds}_{A} {odds}_{B}}}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Correctly determined the odds from $π_{B} .$
The result matches the product of the two odds instead of the ratio, ${odds}_{B} / {odds}_{A} .$

Traps

Avoid these traps

Make sure to calculate the ratio (not the product).
Make sure to put the correct odds into the denominator.
Do not forget to convert $π$ to the respective odds.