McClass

Question

What is the odds ratio relative to therapy A if the success probability for therapy B is $0.77$ ?

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 $π_{B} .$
Correctly determined the odds ratio ${odds}_{B} / {odds}_{A} .$

Incorrect responses

The system detects the following incorrect responses

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Question

What is the success probability of therapy B if the odds ratio relative to therapy A is $4.66$ ?

This is an odds ratio.
Convert the success probability of therapy A, $π_{A},$ to the respective odds, ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Multiply ${odds}_{A}$ by the odds ratio to obtain ${odds}_{B} .$
Back-transform ${odds}_{B}$ to the respective success probability, $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

Feedback

Waiting for response...

Solution(s)

The system accepts the following correct response(s)

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

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

Incorrect responses

The system detects the following incorrect responses

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

Correctly identified the problem and the main steps of the calculation.
Forgot to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Forgot to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

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

Correctly identified the problem and the main steps of the calculation.
Forgot to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Correctly determined ${odds}_{B} .$
Forgot to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

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

Correctly identified the problem and the main steps of the calculation.
The odds ratio $OR$ was mistakenly used to calculate ${odds}_{A} .$
Correctly determined ${odds}_{B} .$
Forgot to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

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

Correctly identified the problem and the main steps of the calculation.
The odds ratio $OR$ was mistakenly used to calculate ${odds}_{A} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Correctly determined the success probability from ${odds}_{B} .$

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

Correctly identified the problem and the main steps of the calculation.
The odds ratio $OR$ was mistakenly used to calculate ${odds}_{A} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Forgot to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

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

Correctly identified the problem and the main steps of the calculation.
Forgot to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Correctly determined the success probability from ${odds}_{B} .$

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

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Correctly determined the success probability from ${odds}_{B} .$

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

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Forgot to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

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

Correctly identified the problem and the main steps of the calculation.
Forgot to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Correctly determined ${odds}_{B} .$
Correctly determined the success probability from ${odds}_{B} .$

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

Correctly identified the problem and the main steps of the calculation.
The odds ratio $OR$ was mistakenly used to calculate ${odds}_{A} .$
Correctly determined ${odds}_{B} .$
Correctly determined the success probability from ${odds}_{B} .$

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

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Correctly determined ${odds}_{B} .$
Forgot to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

Traps

Avoid these traps

Make sure to multiply by $OR$ instead of dividing by it.
Do not forget to convert $π_{A}$ to the respective odds.
Do not forget to back-transform ${odds}_{B}$ to the respective probability.
Do not use the odds ratio $OR$ to calculate ${odds}_{A} .$ Use the the success probability $π_{A}$ instead.

Odds ratio

Question

Result 1

Result 2

1.23...1.37

0.55

0.94

1.07

0.21...0.23

0.21...0.23

0.30...0.31

0.30...0.31

0.73...0.81

1.88...1.97

1.88...1.97

2.28...2.41

2.28...2.41

3.19...3.35

3.19...3.35

4.40...4.66

4.40...4.66

7.75...8.61

Question

0.88...0.97

0.15

3.35

-5.95...-5.92

-0.39...-0.37

-0.27...-0.27

0.13...0.14

0.33...0.37

0.53...0.55

0.77...0.77

1.19...1.21

11.40...11.98