You submit a paper to a prestigious journal about the effects of coffee consumption on mesothelioma risk. The first reviewer lauds your clinical and scientific acumen, but expresses concern that your study does not have adequate statistical power. Statistical power refers to which of the following?
Q62
An investigator is conducting a study to identify potential risk factors for post-transplant hypertension. The investigator selects post-transplant patients with hypertension and gathers detailed information regarding their age, gender, preoperative blood pressure readings, and current medications. The results of the study reveal that some of the patients had been treated with cyclosporine. This study is best described as which of the following?
Q63
In 2013 the national mean score on the USMLE Step 1 exam was 227 with a standard deviation of 22. Assuming that the scores for 15,000 people follow a normal distribution, approximately how many students scored above the mean but below 250?
Q64
A vaccination campaign designed to increase the uptake of HPV vaccine was instituted in chosen counties of a certain state in order to educate parents not only about the disease itself, but also about why children should be vaccinated against this viral sexually transmitted disease. At the end of the campaign, children living in counties in which it was conducted were 3 times more likely to receive the HPV vaccine compared with children living in counties where no campaign was instituted. As well, after evaluating only the counties that were part of the vaccination campaign, the researchers found that families with higher incomes were 2 times more likely to vaccinate their children against HPV compared with families with lower incomes. What conclusion can be drawn from these results?
Q65
A group of investigators are studying the effects of transcranial direct current stimulation (tDCS) on cognitive performance in patients with Alzheimer disease. A cohort of 50 patients with mild Alzheimer disease were randomized 1:1 to either tDCS or sham tDCS over the temporoparietal cortex. Both procedures were conducted so that patients experienced the same sensations while receiving treatment. After 1 week of observation during which no treatments were delivered, the two groups were switched. Neuropsychiatric testing was subsequently conducted to assess differences in recognition memory between the two groups. Which of the following best describes the study design?
Q66
Many large clinics have noticed that the prevalence of primary biliary cholangitis (PBC) has increased significantly over the past 20 years. An epidemiologist is working to identify possible reasons for this. After analyzing a series of nationwide health surveillance databases, the epidemiologist finds that the incidence of PBC has remained stable over the past 20 years. Which of the following is the most plausible explanation for the increased prevalence of PBC?
Q67
A 68-year-old man presents to the office for his annual physical examination. He has no current complaints. Past medical history is unremarkable. He reports a 30-pack-year smoking history but no alcohol or drug use. Review of systems is only remarkable for thicker mucous production that is worse in the morning when he coughs. A non-contrast CT scan of his chest is performed, and the doctor informs him that a 2 cm nodule has been identified in his upper lobe of the left lung near the left main bronchus and that further testing is required to rule out malignancy. The patient is surprised by this news since he has never experienced any alarming symptoms. The doctor informs him that lung cancers don’t usually present with symptoms until late in the course of the disease. The doctor says that sometimes it may take several years before it becomes severe enough to cause symptoms, which is why patients with risk factors for developing lung cancer are screened at an earlier age than the general public. Which of the following concepts is being described by the doctor to this patient?
Q68
A 64-year-old male retired farmer presents to the orthopaedic surgery clinic with chronic left knee pain. Radiographic imaging demonstrates severe tricompartmental osteoarthritis. The patient has a history of diabetes mellitus, chronic kidney disease, hypertension, hyperlipidemia, and congestive heart failure. He undergoes a left knee replacement without complications. A Foley catheter was placed in the operating room and removed in the post-anesthesia care unit. He receives subcutaneous heparin and has sequential compression devices in place to prevent deep venous thromboses. On post-operative day 1, he develops suprapubic pain and dysuria and is subsequently found to have a urinary tract infection. He is discharged on post-operative day 2 with an appropriate antibiotic regimen. However, he presents to the emergency room on post-operative day 6 with severe left leg pain. Venous dopplers demonstrate an occlusive thrombus in the popliteal vein. He is readmitted for anticoagulation and monitoring. A quality improvement team in the hospital estimates that the probability of getting both a urinary tract infection and a deep venous thrombosis is 0.00008 in patients undergoing routine total knee replacement. Furthermore, they estimate that the probability of getting a urinary tract infection in a similar patient population is 0.04. Assuming that the development of urinary tract infections and deep venous thromboses are independent, what is the risk of developing a deep venous thrombosis following total knee replacement?
Q69
A study is conducted in a hospital to estimate the prevalence of handwashing among healthcare workers. All of the hospital staff members are informed that the study is being conducted for 1 month, and the study method will be a passive observation of their daily routine at the hospital. A total of 89 medical staff members give their consent for the study, and they are followed for a month. This study could most likely suffer from which of the following biases?
Q70
A pilot study is conducted to determine the therapeutic response of a new antidepressant drug in patients with persistent depressive disorder. Twelve participants are randomized into a control and a treatment group (n=6 patients in each). They are asked to subjectively rate the severity of their depression from 1 (low) to 10 (high) before and after taking a pill (control group = placebo; treatment group = antidepressant). The data from this study are shown in the following table:
Subject Control group Treatment group
Depression ranking before intervention Depression ranking after intervention Depression ranking before intervention Depression ranking after intervention
1 7 5 6 4
2 8 6 8 4
3 7 6 9 2
4 5 5 7 5
5 6 6 10 3
6 9 7 6 4
Which of the following is the difference between the median of the depression scores before intervention in the treatment group and the control group?
Study Design US Medical PG Practice Questions and MCQs
Question 61: You submit a paper to a prestigious journal about the effects of coffee consumption on mesothelioma risk. The first reviewer lauds your clinical and scientific acumen, but expresses concern that your study does not have adequate statistical power. Statistical power refers to which of the following?
A. The probability of detecting an association when no association exists.
B. The probability of not detecting an association when an association does exist.
C. The probability of detecting an association when an association does exist. (Correct Answer)
D. The first derivative of work.
E. The square root of the variance.
Explanation: ***The probability of detecting an association when an association does exist.***
- **Statistical power** is defined as the probability that a study will correctly reject a false null hypothesis, meaning it will detect a true effect or association if one exists.
- A study with **adequate statistical power** is less likely to miss a real effect.
*The probability of detecting an association when no association exists.*
- This describes a **Type I error** or **false positive**, often represented by **alpha (α)**.
- It is the probability of incorrectly concluding an effect or association exists when, in reality, there is none.
*The probability of not detecting an association when an association does exist.*
- This refers to a **Type II error** or **false negative**, represented by **beta (β)**.
- **Statistical power** is calculated as **1 - β**, so this option describes the complement of power.
*The first derivative of work.*
- The first derivative of work with respect to time represents **power** in physics, which is the rate at which work is done.
- This option is a **distractor** from physics and is unrelated to statistical power in research.
*The square root of the variance.*
- The **square root of the variance** is the **standard deviation**, a measure of the dispersion or spread of data.
- This is a statistical concept but is not the definition of statistical power.
Question 62: An investigator is conducting a study to identify potential risk factors for post-transplant hypertension. The investigator selects post-transplant patients with hypertension and gathers detailed information regarding their age, gender, preoperative blood pressure readings, and current medications. The results of the study reveal that some of the patients had been treated with cyclosporine. This study is best described as which of the following?
A. Cross-sectional study
B. Retrospective cohort study
C. Prospective cohort study
D. Case series
E. Case-control study (Correct Answer)
Explanation: ***Case-control study***
- A **case-control study** compares individuals with a disease (cases) to individuals without the disease (controls) to identify risk factors retrospectively.
- In this study, the investigator selects post-transplant patients **with hypertension** (the cases) and looks backward at their exposures, including cyclosporine use, to identify potential risk factors.
- The analytical goal of "identifying risk factors" and the observation that **some patients had been treated with cyclosporine** (implying comparison with those who were not) indicates a case-control design.
- Even if controls are not explicitly mentioned, the study design involves analyzing exposure patterns among cases to identify associations with risk factors.
*Case series*
- A **case series** is purely descriptive and involves collecting detailed information on a group of patients with a common condition without any comparison or analytical hypothesis testing.
- While this study does describe patients with post-transplant hypertension, the key difference is the **analytical intent** to identify risk factors, which goes beyond simple description.
- A true case series would simply report clinical characteristics without attempting to establish associations between exposures and outcomes.
*Cross-sectional study*
- A **cross-sectional study** assesses both exposure and outcome simultaneously at a single point in time to determine prevalence.
- This approach would involve surveying a population of post-transplant patients to determine the prevalence of hypertension and associated factors at that moment.
- The study described has already selected patients with the outcome (hypertension), making it retrospective rather than cross-sectional.
*Retrospective cohort study*
- A **retrospective cohort study** examines past data by first classifying patients based on **exposure status** (e.g., cyclosporine use vs. no cyclosporine), then following them forward in time to see who developed the outcome.
- The key difference is that cohort studies **start with exposure** and move to outcome, whereas this study **starts with outcome** (hypertension) and looks back at exposures.
- If the investigator had selected all transplant patients, divided them by cyclosporine exposure, and then determined hypertension rates in each group, it would be a retrospective cohort study.
*Prospective cohort study*
- A **prospective cohort study** identifies a cohort at baseline (before the outcome) and follows them forward in time to observe who develops the outcome.
- This study has already selected patients **with the outcome present**, making it retrospective rather than prospective.
- A prospective design would require identifying transplant patients at the time of transplant and following them over time to see who develops hypertension.
Question 63: In 2013 the national mean score on the USMLE Step 1 exam was 227 with a standard deviation of 22. Assuming that the scores for 15,000 people follow a normal distribution, approximately how many students scored above the mean but below 250?
A. 5,100 (Correct Answer)
B. 4,500
C. 6,000
D. 3,750
E. 6,750
Explanation: ***5,100***
- To solve this, first calculate the **z-score** for 250: (250 - 227) / 22 = 1.045.
- Using a **z-table**, the area under the curve from the mean (z=0) to z=1.045 is approximately 0.353. Multiplying this by 15,000 students gives approximately **5,295 students**, which is closest to 5,100.
*4,500*
- This answer would imply a smaller proportion of students between the mean and 250 (around 30%), which is lower than the calculated z-score of 1.045 suggests.
- It does not accurately reflect the area under the **normal distribution curve** for the given range.
*6,000*
- This option would mean that approximately 40% of students scored in this range, which would correspond to a z-score much higher than 1.045 or a different standard deviation.
- This calculation overestimates the number of students within the specified range.
*3,750*
- This value represents 25% of the total students (15,000 * 0.25), indicating that only a quarter of the distribution lies in this range.
- This significantly underestimates the proportion of students scoring between the mean and 250 for the given standard deviation.
*6,750*
- This option reflects approximately 45% of the total student population (15,000 * 0.45), which would correspond to a much larger z-score or a different distribution.
- This value is an overestimation and does not align with the standard normal distribution probabilities for the given parameters.
Question 64: A vaccination campaign designed to increase the uptake of HPV vaccine was instituted in chosen counties of a certain state in order to educate parents not only about the disease itself, but also about why children should be vaccinated against this viral sexually transmitted disease. At the end of the campaign, children living in counties in which it was conducted were 3 times more likely to receive the HPV vaccine compared with children living in counties where no campaign was instituted. As well, after evaluating only the counties that were part of the vaccination campaign, the researchers found that families with higher incomes were 2 times more likely to vaccinate their children against HPV compared with families with lower incomes. What conclusion can be drawn from these results?
A. Family income appears to be an effect modifier. (Correct Answer)
B. The vaccination campaign appears to have been ineffective.
C. The vaccination campaign is the study outcome.
D. The vaccine uptake is the study exposure.
E. Family income appears to be a confounder.
Explanation: ***Family income appears to be an effect modifier.***
- An **effect modifier** occurs when the relationship between an exposure (vaccination campaign) and an outcome (vaccine uptake) differs across categories of a third variable (family income).
- Here, the campaign's effect on vaccine uptake is *different* depending on family income (higher-income families were still more likely to vaccinate even within campaign counties), indicating **effect modification**.
*The vaccination campaign appears to have been ineffective.*
- The campaign actually led to a **3-fold increase** in HPV vaccine uptake in campaign counties compared to non-campaign counties, demonstrating its effectiveness in increasing overall uptake.
- While income still played a role, the campaign itself achieved its primary goal of increasing vaccination rates where implemented.
*The vaccination campaign is the study outcome.*
- The **vaccination campaign** is the **exposure** or intervention being studied, as its impact on vaccination rates is being assessed.
- The **outcome** is the **HPV vaccine uptake** (i.e., whether children received the vaccine or not).
*The vaccine uptake is the study exposure.*
- **Vaccine uptake** is the **outcome** or the dependent variable that is being measured, to see if it changes in response to the campaign.
- The **exposure** is the **vaccination campaign** itself, or living in a county with a campaign.
*Family income appears to be a confounder.*
- A **confounder** is a variable that is associated with both the exposure and the outcome, and *distorts* the observed association between them.
- While family income is associated with vaccine uptake, its main role here is to show *how* the campaign's effect varied by income, not necessarily to create a spurious association between the campaign and uptake where none existed. If it were a confounder, it would need to be associated with both the campaign (which it isn't, as campaigns were in specific counties regardless of income distribution) and the outcome, and not be on the causal pathway.
Question 65: A group of investigators are studying the effects of transcranial direct current stimulation (tDCS) on cognitive performance in patients with Alzheimer disease. A cohort of 50 patients with mild Alzheimer disease were randomized 1:1 to either tDCS or sham tDCS over the temporoparietal cortex. Both procedures were conducted so that patients experienced the same sensations while receiving treatment. After 1 week of observation during which no treatments were delivered, the two groups were switched. Neuropsychiatric testing was subsequently conducted to assess differences in recognition memory between the two groups. Which of the following best describes the study design?
A. Parallel group
B. Factorial
C. Meta-analysis
D. Crossover (Correct Answer)
E. Pretest-posttest
Explanation: ***Crossover***
- In a **crossover design**, each participant receives both the **experimental treatment (tDCS)** and the **control treatment (sham tDCS)** at different times.
- The study explicitly states that "the two groups were switched" after an initial observation period, which is characteristic of a crossover design.
*Parallel group*
- A **parallel group design** involves different groups of participants receiving only **one type of intervention** (e.g., one group gets tDCS, another gets sham tDCS throughout the study).
- This design does not involve switching treatments between groups, unlike what is described.
*Factorial*
- A **factorial design** investigates the effects of **two or more independent variables** (factors) on an outcome.
- This study primarily focuses on one intervention (tDCS vs. sham) and does not describe multiple independent variables being tested simultaneously.
*Meta-analysis*
- A **meta-analysis** is a statistical method that combines the results of **multiple independent studies** to derive an overall conclusion.
- This description is of a single, new study being conducted, not an analysis of existing research.
*Pretest-posttest*
- A **pretest-posttest design** involves measuring an outcome **before and after** an intervention in a single group, without necessarily comparing it to another intervention or control in a crossover manner.
- While pretest-posttest measurements might be part of this study, it doesn't describe the overarching design where groups switch interventions.
Question 66: Many large clinics have noticed that the prevalence of primary biliary cholangitis (PBC) has increased significantly over the past 20 years. An epidemiologist is working to identify possible reasons for this. After analyzing a series of nationwide health surveillance databases, the epidemiologist finds that the incidence of PBC has remained stable over the past 20 years. Which of the following is the most plausible explanation for the increased prevalence of PBC?
A. Improved quality of care for PBC (Correct Answer)
B. Increased availability of diagnostic testing for PBC
C. Increased exposure to environmental risk factors for PBC
D. Increased awareness of PBC among clinicians
E. Increased average age of the population at risk for PBC
Explanation: ***Improved quality of care for PBC***
- This leads to a **longer survival time** for patients with PBC. When incidence remains stable but patients live longer, the cumulative number of living cases (prevalence) naturally increases.
- An increase in prevalence with stable incidence is a classic indicator of **improved patient survival** due to better management or treatment.
*Increased availability of diagnostic testing for PBC*
- This would primarily impact the **incidence** of PBC by detecting more cases that were previously undiagnosed. The question states that the incidence has remained stable.
- While improved diagnostics might initially increase *reported* incidence, if the true incidence is stable, it wouldn't explain a sustained rise in prevalence without a corresponding change in incidence or survival.
*Increased exposure to environmental risk factors for PBC*
- This would directly lead to an **increase in the incidence** of PBC, as more people would be developing the disease.
- Since the incidence is stable, an increase in environmental risk factors is not the most plausible explanation for increased prevalence.
*Increased awareness of PBC among clinicians*
- Similar to increased diagnostic testing, increased awareness would likely lead to the diagnosis of more new cases, thus **increasing the incidence** of PBC.
- A stable incidence despite increased awareness means that the actual rate of new cases developing the disease has not changed, ruling this out as the primary cause of increased prevalence.
*Increased average age of the population at risk for PBC*
- An aging population could potentially increase the incidence of age-related diseases. However, if the **incidence has remained stable**, it implies that even with an older population, the rate of new diagnoses has not increased.
- While age is a risk factor for PBC, an increase in prevalence without a change in incidence suggests a factor influencing the duration of the disease rather than its onset.
Question 67: A 68-year-old man presents to the office for his annual physical examination. He has no current complaints. Past medical history is unremarkable. He reports a 30-pack-year smoking history but no alcohol or drug use. Review of systems is only remarkable for thicker mucous production that is worse in the morning when he coughs. A non-contrast CT scan of his chest is performed, and the doctor informs him that a 2 cm nodule has been identified in his upper lobe of the left lung near the left main bronchus and that further testing is required to rule out malignancy. The patient is surprised by this news since he has never experienced any alarming symptoms. The doctor informs him that lung cancers don’t usually present with symptoms until late in the course of the disease. The doctor says that sometimes it may take several years before it becomes severe enough to cause symptoms, which is why patients with risk factors for developing lung cancer are screened at an earlier age than the general public. Which of the following concepts is being described by the doctor to this patient?
A. Confounding bias
B. Latent period (Correct Answer)
C. Induction period
D. Lead time bias
E. Surveillance bias
Explanation: ***Latent period***
- This refers to the interval between the **disease onset** (biological initiation) and the appearance of **detectable symptoms**.
- In lung cancer, this period can be long, explaining why a large nodule is found in an asymptomatic patient.
*Confounding bias*
- This occurs when an **unaccounted-for variable** (the confounder) influences both the exposure and the outcome, distorting their true relationship.
- It relates to study design and interpretation, not the natural history of a disease.
*Induction period*
- This is the time from **causal exposure** (e.g., smoking) to the initiation of the disease, which is the **biological onset**.
- While smoking is a cause of lung cancer, the doctor is describing the time from the disease's silent progression to symptom manifestation.
*Lead time bias*
- This bias occurs in screening programs when **early detection** (by screening) makes it seem like patients live longer, even if their actual survival time from disease onset hasn't changed.
- The doctor is explaining why the patient is asymptomatic despite a large nodule, not a bias related to screening effectiveness.
*Surveillance bias*
- Occurs when a **higher rate of diagnosis** is observed in one group due to more frequent or intense monitoring, leading to an apparent increase in disease incidence.
- This is a form of information bias in epidemiological studies, not a description of disease progression.
Question 68: A 64-year-old male retired farmer presents to the orthopaedic surgery clinic with chronic left knee pain. Radiographic imaging demonstrates severe tricompartmental osteoarthritis. The patient has a history of diabetes mellitus, chronic kidney disease, hypertension, hyperlipidemia, and congestive heart failure. He undergoes a left knee replacement without complications. A Foley catheter was placed in the operating room and removed in the post-anesthesia care unit. He receives subcutaneous heparin and has sequential compression devices in place to prevent deep venous thromboses. On post-operative day 1, he develops suprapubic pain and dysuria and is subsequently found to have a urinary tract infection. He is discharged on post-operative day 2 with an appropriate antibiotic regimen. However, he presents to the emergency room on post-operative day 6 with severe left leg pain. Venous dopplers demonstrate an occlusive thrombus in the popliteal vein. He is readmitted for anticoagulation and monitoring. A quality improvement team in the hospital estimates that the probability of getting both a urinary tract infection and a deep venous thrombosis is 0.00008 in patients undergoing routine total knee replacement. Furthermore, they estimate that the probability of getting a urinary tract infection in a similar patient population is 0.04. Assuming that the development of urinary tract infections and deep venous thromboses are independent, what is the risk of developing a deep venous thrombosis following total knee replacement?
A. 0.02
B. Cannot be determined
C. 0.002 (Correct Answer)
D. 0.00002
E. 0.0002
Explanation: ***0.002***
- For **independent events**, the probability of both occurring is: **P(A and B) = P(A) × P(B)**
- Rearranging: **P(DVT) = P(UTI and DVT) / P(UTI)**
- Calculation: P(DVT) = 0.00008 / 0.04 = **0.002** (or 0.2%)
- This represents the baseline risk of DVT despite prophylactic measures (subcutaneous heparin and sequential compression devices)
*0.02*
- This represents an error in decimal placement during division
- This would suggest a 2% DVT risk, which is **10 times higher** than the correct value
- Does not result from correct application of the multiplication rule for independent probabilities
*Cannot be determined*
- This is incorrect because **sufficient information is provided** to calculate P(DVT)
- When two events are independent and we know P(A and B) and P(A), we can always determine P(B)
- The independence assumption is explicitly stated in the question stem
*0.00002*
- This value results from calculation error, possibly **inverting the division** (0.04 / 0.00008 instead of 0.00008 / 0.04) and then applying additional incorrect operations
- This would suggest a DVT risk of 0.002%, which is **100 times lower** than the correct value
- Does not reflect proper application of probability rules for independent events
*0.0002*
- This represents a **decimal point error** during calculation (0.00008 / 0.04)
- This would suggest a 0.02% DVT risk, which is **10 times lower** than the correct value
- Results from miscalculation rather than correct mathematical reasoning
Question 69: A study is conducted in a hospital to estimate the prevalence of handwashing among healthcare workers. All of the hospital staff members are informed that the study is being conducted for 1 month, and the study method will be a passive observation of their daily routine at the hospital. A total of 89 medical staff members give their consent for the study, and they are followed for a month. This study could most likely suffer from which of the following biases?
A. Attrition bias
B. Hawthorne effect (Correct Answer)
C. Confounding bias
D. Berksonian bias
E. Observer-expectancy bias
Explanation: ***Hawthorne effect***
- This bias occurs when individuals modify their behavior in response to being **observed** or knowing they are part of a study. In this scenario, healthcare workers, knowing they are being observed for handwashing, are likely to wash their hands more frequently than usual.
- The intent of the study is to estimate the **prevalence** of handwashing; however, the observed rates will be artificially inflated due to the subjects' awareness of being studied, leading to an inaccurate estimate.
*Attrition bias*
- **Attrition bias** arises when there is **differential loss to follow-up** between study groups, which can lead to biased results.
- This study design involves observing a defined group for a month, but there's no indication of loss of participants or differential dropout from specific intervention or control groups.
*Confounding bias*
- **Confounding bias** occurs when an unmeasured or uncontrolled factor (a **confounder**) is associated with both the exposure and the outcome, distorting the true association.
- While confounding is a common bias in observational studies, the primary issue described here is the direct impact of observation on behavior, not an unmeasured external variable influencing both the behavior and its measurement.
*Berksonian bias*
- **Berksonian bias** (or admission rate bias) is a type of selection bias that occurs in case-control studies when hospital-based controls or cases are used, and the probability of being admitted to the hospital is influenced by both the exposure and the disease itself.
- This study is a **prevalence study** involving direct observation of healthcare workers, not a case-control study, making Berksonian bias irrelevant.
*Observer-expectancy bias*
- **Observer-expectancy bias** occurs when the **researcher's expectations** or beliefs influence their observations or interpretation of data.
- The scenario describes the participants (healthcare workers) changing their behavior due to being observed, not the observer's expectations influencing the recorded data, which would be the **Hawthorne effect**.
Question 70: A pilot study is conducted to determine the therapeutic response of a new antidepressant drug in patients with persistent depressive disorder. Twelve participants are randomized into a control and a treatment group (n=6 patients in each). They are asked to subjectively rate the severity of their depression from 1 (low) to 10 (high) before and after taking a pill (control group = placebo; treatment group = antidepressant). The data from this study are shown in the following table:
Subject Control group Treatment group
Depression ranking before intervention Depression ranking after intervention Depression ranking before intervention Depression ranking after intervention
1 7 5 6 4
2 8 6 8 4
3 7 6 9 2
4 5 5 7 5
5 6 6 10 3
6 9 7 6 4
Which of the following is the difference between the median of the depression scores before intervention in the treatment group and the control group?
A. 2.1
B. 0.7
C. 1
D. 0.5 (Correct Answer)
E. 2
Explanation: ***0.5***
- To find the **median of the control group's depression scores before intervention**, order the scores: 5, 6, 7, 7, 8, 9. The median is the average of the two middle numbers (7 + 7) / 2 = **7**.
- To find the **median of the treatment group's depression scores before intervention**, order the scores: 6, 6, 7, 8, 9, 10. The median is the average of the two middle numbers (7 + 8) / 2 = **7.5**. The difference is 7.5 - 7 = **0.5**.
*2.1*
- This value is not derived from the correct calculation of medians for either group before intervention. It may arise from an incorrect computation or comparison of other data points.
- This answer suggests an error in identifying the **median** or in the subtraction step.
*0.7*
- This value is not derived from the correct calculation of medians for either group before intervention. It may result from a miscalculation or if the wrong data points were selected for analysis.
- This answer indicates a misunderstanding of how to correctly determine the median of an **even set of numbers**.
*1*
- This value would result if one of the medians was calculated incorrectly, e.g., if the treatment group median was 8 or the control group median was 6. However, both were correctly calculated as 7 and 7.5 respectively.
- This answer implies a miscalculation of one or both medians, leading to an incorrect difference.
*2*
- This value would arise if there was a larger difference between the calculated medians, such as 9 - 7 or 8 - 6. Both of these are not the correct medians.
- This answer suggests a significant error in determining the appropriate **median values** from the given datasets.
