Statistical Principles: Measures of Effect Page 1/3
The table below shows the number of patients who developed an infection while in hospital as well as those who remained infection free. The results from two different hospitals over the same time period are displayed.
|
Infection |
No Infection |
Total |
|
|
Hospital A |
16 |
237 |
253 |
|
Hospital B |
27 |
594 |
621 |
A study was conducted to look at the number of early neonatal deaths in a county of the United Kingdom to see if there was a relationship with gender. 104 early neonatal deaths occurred in 34,261 Male babies and 75 early neonatal deaths occurred in 32,494 Female babies.
The table below shows the number of children who received an MMR vaccination as well as those who didn’t get vaccinated in three different schools.
|
Vaccinated |
Not Vaccinated |
Total |
|
|
School A |
1003 |
230 |
1233 |
|
School B |
714 |
127 |
841 |
|
School C |
581 |
64 |
645 |
Welcome to the "Measures of Effect" quiz. There are 17 questions to answer.
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Q1. What is the proportion of patients who developed an infection in Hospital A (to 3 decimal places)?
The answer is 0.063. The Proportion of infections in Hospital A is calculated by dividing the number with an infection in the hospital by the total number of cases in the hospital. In this case it is 16/253=0.063
Q2. What are the Odds for an infection in Hospital B (to 3 decimal places)?
The answer is 0.045. The Odds of infection in Hospital B is calculated by dividing the number with an infection in the hospital by the number without an infection in the hospital. In this case it is 27/594=0.045.
Q3. What is the percentage of patients who developed an infection in Hospital A (to 1 decimal place)?
The answer is 6.3%. The Percentage of infections in Hospital A is calculated by dividing the number with an infection in the hospital by the total number of cases in the hospital and then multiplying by 100. In this case it is (16/253)x100=6.3%.
Q4. What is the difference in the proportion of infections between Hospital A and Hospital B (Hospital A – Hospital B, to 3 decimal places)?
The answer is 0.020. The difference in proportions is the proportion in one Hospital minus the proportion in the other. We are asked to calculate Hospital A – Hospital B. The proportion in Hospital A is 16/253=0.063… and the proportion in Hospital B is 27/621=0.043… The difference in proportions is therefore 0.063…-0.043…=0.020 to 3 decimal places. Try to keep all of the precision in your working until you get to the final answer.
Q5. What is the relative risk for infection in Hospital A compared to Hospital B (i.e. using Hospital B as the reference group)? Compute the final answer to 2 decimal places.
The answer is 1.45. The Relative Risk is the proportion in one Hospital divided by the proportion in the other. We are asked to use Hospital B as the reference group, which means we need to divide by Hospital B. The proportion in Hospital A is 16/253=0.063… and the proportion in Hospital B is 27/621=0.043… The Relative Risk is therefore 0.063…/0.043…=1.45 to 2 decimal places. Try to keep all of the precision in your working until you get to the final answer.
Q6. What is the odds ratio for Infection in Hospital A compared to Hospital B (i.e. using Hospital B as the reference group)? Compute the final answer to 2 decimal places.
The answer is 1.49. The Odds ratio is the Odds in one Hospital divided by the Odds in the other. We are asked to use Hospital B as the reference group, which means we need to divide by Hospital B. The Odds in Hospital A are 16/237=0.0675… and the Odds in Hospital B are 27/594=0.045… The Odds ratio is therefore 0.0675…/0.045…=1.49 to 2 decimal places. Try to keep all of the precision in your working until you get to the final answer.
Q7. What is the proportion of Male babies who died in the early neonatal period? (to 4 decimal places)
The answer is 0.0030. The Proportion of early neonatal deaths in Male babies is calculated by dividing the number of male babies who died in the early neonatal period by the total number of male babies. In this case it is 104/34261=0.0030.
Q8. What are the Odds for an early neonatal death in Female babies? (to 4 decimal places)
The answer is 0.0023. The Odds of early neonatal deaths in Female babies are calculated by dividing the number of female babies who died in the early neonatal period by the number of female babies who survived past the early neonatal period. In this case it is 75/(32494-75)=75/32419=0.0023.
Q9. What is the difference in proportion of early Neonatal deaths between Male and Female babies (Male – Female, to 5 decimal places)?
The answer is 0.00073. The difference in proportions is the proportion of early neonatal deaths in one gender minus the proportion in the other. We are asked to calculate Male– Female. The proportion in Male babies is 104/34261=0.0030… and the proportion in Female babies is 75/32494=0.0023… The difference in proportions is therefore 0.0030-0.0023…=0.00073 to 5 decimal places. Try to keep all of the precision in your working until you get to the final answer.
Q10. What is the relative risk for an early neonatal death in Male compared to Female babies? (i.e. using Female babies as the reference group) Compute the final answer to 2 decimal places.
The answer is 1.32. The relative risk for an early neonatal death is the proportion of early neonatal deaths in one gender divided by the proportion in the other. We are asked to use Females as the reference group and so we need to divide by the Female result. The proportion in Male babies is 104/34261=0.0030… and the proportion in Female babies is 75/32494=0.0023… The relative risk is therefore 0.0030…/0.0023…=1.315 to 3 decimal places. Try to keep all of the precision in your working until you get to the final answer.
Q11. What is the odds ratio for an early neonatal death in Male compared to Female babies? (i.e. using Female babies as the reference group)? Compute the final answer to 2 decimal places.
The answer is 1.32. The Odds ratio for an early neonatal death is the Odds of early neonatal deaths in one gender divided by the Odds in the other. We are asked to use Females as the reference group and so we need to divide by the Female result. The Odds in Male babies are 104/(34261-104)=104/34157=0.0030… and the Odds in Female babies are 75/(32494-75)=75/32419=0.0023… The relative risk is therefore 0.0030…/0.0023…=1.32 to 2 decimal places. Try to keep all of the precision in your working until you get to the final answer.
Q12. What is the proportion of children who were vaccinated in School C (to 3 decimal places)?
The answer is 0.901. The Proportion of infections in School C is calculated by dividing the number vaccinated in the school by the total number of children in the school. In this case it is 581/645=0.901
Q13. What are the Odds for being vaccinated in School C? (to 2 decimal points).
The answer is 9.08. The Odds of vaccination in School C are calculated by dividing the number vaccinated in the school by the number not vaccinated in the school. In this case it is 581/64=9.08.
Q14. What are the Odds for NOT being vaccinated in School B (to 3 decimal places)?
The answer is 0.178. The Odds of not being vaccinated in School C are calculated by dividing the number not vaccinated in the school by the number vaccinated in the school. In this case it is 127/714=0.178.
Q15. What is the difference in the proportion of vaccinated pupils between School A and School C (School A – School C, to 3 decimal places)?
The answer is -0.081. The difference in proportions is the proportion in one School minus the proportion in the other. We are asked to calculate School A – School C. The proportion in School A is 1003/1233=0.813… and the proportion in School C is 581/645=0.901… The difference in proportions is therefore 0.813…-0.901…=-0.081 to 3 decimal places. Try to keep all of the precision in your working until you get to the final answer.
Q16. What is the relative risk for NOT BEING Vaccinated in School A compared to School B? (i.e. using School B as the reference group) Compute the final answer to 2 decimal places.
The answer is 1.25. The Relative Risk for not being vaccinated is the proportion in one School divided by the proportion in the other. We are asked to use School B as the reference group, which means we need to divide by School B. The proportion not vaccinated in School A is 230/1233=0.186… and the proportion not vaccinated in School B is 127/841=0.151… The Relative Risk is therefore 0.186…/0.151…=1.24 to 2 decimal places. Try to keep all of the precision in your working until you get to the final answer.
Q17. What is the odds ratio for being vaccinated in School A compared to School C? (i.e. using School C as the reference group)? Compute the final answer to 3 decimal places.
The answer is 0.480. The Odds ratio is the Odds in one School divided by the Odds in the other. We are asked to use School C as the reference group, which means we need to divide by School C. The Odds in School A are 1003/230=4.360… and the Odds in School C are 581/64=9.078… The Odds ratio is therefore 4.360…/9.078…=0.480 to 3 decimal places. Try to keep all of the precision in your working until you get to the final answer.
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