Biostatistics — MCQs

Biostatistics Indian Medical PG Practice Questions and MCQs

Question 811: In a clinical study, if the standard deviation of a measurement is 5 and the sample size is 25, what is the standard error of the mean?

A. 1.0 (Correct Answer)
B. 2.0
C. 0.2
D. 1.5

Explanation: **1.0** - The standard error of the mean (SEM) is calculated by dividing the **standard deviation (SD)** by the **square root of the sample size (n)**. - Given SD = 5 and n = 25, SEM = 5 / √25 = 5 / 5 = **1.0**. *2.0* - This value would result if the sample size was 6.25 (5 / √6.25 = 5 / 2.5 = 2.0), or if the formula was misapplied. - It does not correctly reflect the given **standard deviation** and **sample size**. *0.2* - This value would result if the standard deviation was 1 and the sample size was 25 (1 / √25 = 1 / 5 = 0.2), or if the standard deviation was divided by the sample size directly (5 / 25 = 0.2). - This calculation does not use the **square root of the sample size** in the denominator as required. *1.5* - This value does not correspond to the correct application of the **standard error of the mean formula** with the given parameters. - There is no direct calculation from SD=5 and n=25 that yields 1.5.

Question 812: In a randomized controlled trial, the relative risk reduction (RRR) for a new treatment compared to the standard treatment is calculated to be 25%. How should this result be interpreted?

A. 25% of patients in the treatment group did not experience the outcome.
B. The risk of the outcome is 25% of what it was in the standard treatment group.
C. The new treatment reduces the risk of the outcome by 25% compared to the standard treatment. (Correct Answer)
D. The new treatment is 25% less effective than the standard treatment.

Explanation: ***The new treatment reduces the risk of the outcome by 25% compared to the standard treatment.*** - **Relative risk reduction (RRR)** quantifies the proportion by which the intervention reduces the event rate in the treated group compared to the control group. - An RRR of 25% means that the **risk of the outcome** in the treated group is 25% lower than the risk in the control group. *25% of patients in the treatment group did not experience the outcome.* - This statement refers to the **absolute risk** or the **event rate** in the treatment group, not the relative reduction in risk compared to another group. - RRR does not directly indicate the proportion of patients *not* experiencing the outcome in the treatment arm alone. *The risk of the outcome is 25% of what it was in the standard treatment group.* - This statement indicates that the **relative risk (RR)** is 0.25 (25%), meaning the risk in the treatment group is 25% *of* the risk in the control group. - If RR is 0.25, then RRR = 1 - RR = 1 - 0.25 = 0.75 or 75%, which contradicts the given RRR of 25%. *The new treatment is 25% less effective than the standard treatment.* - An RRR of 25% means the new treatment is **more effective** in reducing the risk of the outcome, not less effective. - This interpretation would suggest the treatment has a detrimental effect or is inferior, which is incorrect.

Question 813: A study evaluates the impact of a new diabetes management program on patient outcomes. Which method is the best to analyze the effectiveness of the program?

A. Pre- and post-intervention comparison
B. Cross-sectional survey
C. Randomized controlled trial (Correct Answer)
D. Cohort study

Explanation: ***Randomized controlled trial*** - A **Randomized Controlled Trial (RCT)** is the **gold standard** for evaluating interventions because it minimizes bias by randomly assigning participants to either an intervention group or a control group. - This design allows for a direct comparison of outcomes, providing the strongest evidence of a program's **effectiveness** by controlling for confounding variables and ensuring that observed effects are likely due to the intervention. *Pre- and post-intervention comparison* - This method compares outcomes before and after an intervention in the same group of participants, but it lacks a **control group**. - Without a control group, it's difficult to attribute observed changes solely to the intervention, as other **confounding factors** or natural progression of the disease could also influence the results. *Cross-sectional survey* - A **cross-sectional survey** collects data at a single point in time, providing a snapshot of the prevalence of certain characteristics or outcomes. - This method is useful for describing populations but **cannot establish causality** or measure changes over time in response to an intervention. *Cohort study* - A **cohort study** follows a group of individuals over time to observe the development of outcomes, often comparing those exposed to a risk factor with those unexposed. - While useful for studying **risk factors** and disease incidence, it typically does not involve a controlled intervention and is more prone to **confounding biases** than an RCT when assessing program effectiveness.

Question 814: A researcher is calculating the standard error of the mean for a sample of 100 patients with a standard deviation of 10. What is the standard error of the mean?

A. 1.0 (Correct Answer)
B. 0.1
C. 10.0
D. 5.0

Explanation: ***Correct Answer: 1.0*** - The **standard error of the mean (SEM)** is calculated by dividing the **sample standard deviation** by the square root of the **sample size**. - Formula: SEM = SD / √n - In this case: SEM = 10 / √100 = 10 / 10 = **1.0** - SEM quantifies the **precision of the sample mean** as an estimate of the population mean. *Incorrect: 0.1* - This result would be obtained if the standard deviation was divided by 100 instead of the square root of 100 (i.e., 10/100 = 0.1). - Alternatively, this would be correct if SD = 1 and n = 100 (1/√100 = 0.1). - Represents a miscalculation where **√n was confused with n**. *Incorrect: 10.0* - This value is simply the **standard deviation** itself, not the standard error of the mean. - Common error: **forgetting to divide by √n** in the SEM formula. - Standard deviation measures the spread of individual data points, whereas SEM measures the **variability of sample means**. *Incorrect: 5.0* - This value would result if the standard deviation was divided by √4 instead of √100 (i.e., 10/2 = 5.0). - Represents a miscalculation with the **wrong sample size** used in the denominator. - Does not align with the given values (SD = 10, n = 100).

Question 815: A health researcher wants to compare the effectiveness of two different antihypertensive drugs. Which statistical test should be used to determine if there is a significant difference in blood pressure reduction between the two groups?

A. Chi-square test
B. t-test (Correct Answer)
C. ANOVA
D. Correlation analysis

Explanation: ***t-test*** - The **t-test** is appropriate for comparing the means of **two independent groups** to determine if a significant difference exists. In this scenario, we are comparing the mean blood pressure reduction between two drug groups. - Specifically, an **independent samples t-test** would be used as the two drug groups are distinct and unrelated. *Chi-square test* - The **chi-square test** is used to compare **categorical data** or frequencies, not continuous variables like blood pressure reduction. - It assesses whether there is a significant association between two categorical variables. *ANOVA* - **ANOVA (Analysis of Variance)** is used to compare the means of **three or more independent groups**. - While it *could* be used for two groups (and would yield the same p-value as a t-test), the **t-test** is the more direct and appropriate choice for a two-group comparison. *Correlation analysis* - **Correlation analysis** measures the strength and direction of a **linear relationship between two continuous variables**. - It does not test for significant differences between group means but rather how two variables move together.

Question 816: From a population of 100,000, a sample of 100 women's hemoglobin is measured with a standard deviation of 2 gm%. What is the standard error of the mean?

A. 2 gm%
B. 1 gm%
C. 0.1 gm%
D. 0.2 gm% (Correct Answer)

Explanation: ***0.2 gm%*** - The **standard error of the mean (SEM)** is calculated by dividing the population **standard deviation (SD)** by the square root of the **sample size (n)**. - Given SD = 2 gm% and n = 100, the SEM = 2 / √100 = 2 / 10 = **0.2 gm%.** *1 gm%* - This value would be obtained if the standard deviation was 10 gm% or if the sample size was 4 (2/√4 = 1), which is incorrect. - It does not reflect the given standard deviation or sample size in the standard error formula. *0.1 gm%* - This value would be correct if the standard deviation was 1 gm% (1/√100 = 0.1 gm%). - It does not align with the provided standard deviation of 2 gm%. *2 gm%* - This value represents the original **standard deviation** itself, not the standard error of the mean. - The standard error should be smaller than the standard deviation when the sample size is greater than 1.

Question 817: In a clinical trial, the difference in mean blood pressure between the treatment and control groups is found to be statistically significant. Which statistical test is most likely used?

A. Chi-square test
B. t-test (Correct Answer)
C. ANOVA
D. Fisher's exact test

Explanation: ***Correct Answer: t-test*** - A **t-test** is used to compare the means of **two groups** (e.g., treatment and control) for a continuous variable, such as blood pressure. - The goal is to determine if the observed difference between the means is **statistically significant**, rather than due to random chance. - This is the **most appropriate test** for comparing mean blood pressure between two groups in a clinical trial. *Incorrect: Chi-square test* - The **Chi-square test** is used for analyzing **categorical data** (e.g., frequencies or proportions), not for comparing means of continuous variables like blood pressure. - It assesses whether there is a significant association between two or more categorical variables. *Incorrect: ANOVA* - **ANOVA (Analysis of Variance)** is used to compare the means of **three or more groups**, or when multiple factors are involved. - While it can technically be used for two groups, the **t-test is preferred** for simple two-group comparisons as it is more straightforward and provides equivalent results. *Incorrect: Fisher's exact test* - **Fisher's exact test** is similar to the Chi-square test and is used for **categorical data**, particularly when sample sizes are small in a 2x2 contingency table. - It is not appropriate for comparing the means of continuous variables across groups.

Question 818: A randomized controlled trial of antihypertensives shows a p-value of 0.04 for the difference in blood pressure reduction. What is the most accurate interpretation?

A. 4% chance of this or more extreme result if null true (Correct Answer)
B. 4% chance that the null hypothesis is true
C. 96% chance that the alternative hypothesis is true
D. 4% chance that the difference is due to random chance

Explanation: ***4% chance of this or more extreme result if null true*** - A **p-value of 0.04** signifies that if the **null hypothesis** (no true difference between treatments) were true, there would be a **4% probability** of observing results as extreme as, or more extreme than, those obtained in the study. - This value is often compared to a predetermined **significance level (alpha)**, typically 0.05. Since 0.04 < 0.05, the result is considered statistically significant, leading to the rejection of the null hypothesis. *4% chance that the null hypothesis is true* - This statement incorrectly interprets a p-value as the **probability of the null hypothesis being true**. A p-value is the probability of observing the data, or more extreme data, given that the null hypothesis is true, not the probability of the null hypothesis itself. - The p-value does not provide the **prior probability** or the **posterior probability** of the null hypothesis being true. *96% chance that the alternative hypothesis is true* - This is an incorrect interpretation; a p-value does not indicate the **probability of the alternative hypothesis being true**. It is a measure related to the evidence against the null hypothesis, assuming the null is true. - The complement of the p-value (1 - p) does not represent the probability of the alternative hypothesis or the **power of the study**. *4% chance that the difference is due to random chance* - This interpretation is close but not entirely accurate; the p-value represents the probability of observing the data (or more extreme data) by **random chance alone** *if the null hypothesis were true*. - It does not state that the observed difference *is* due to random chance, but rather quantifies how likely such a difference is under the assumption of **no true effect**.

Question 819: In a study of 100 patients, the standard deviation of their blood pressure measurements is found to be 10 mmHg. What is the standard error of the mean?

A. 1 (Correct Answer)
B. 10
C. 0.1
D. 2

Explanation: ***Correct Option: 1*** - The **standard error of the mean (SEM)** is calculated by dividing the **standard deviation (SD)** by the square root of the **sample size (n)**. - Formula: SEM = SD / √n - Given an SD of **10 mmHg** and a sample size of **100**, SEM = 10 / √100 = 10 / 10 = **1 mmHg**. *Incorrect Option: 10* - This value represents the **standard deviation** of the sample, not the **standard error of the mean**. - The standard error accounts for the variability of sample means around the true population mean, which is always smaller than the standard deviation for n > 1. *Incorrect Option: 0.1* - This value would result if the standard deviation was 1 and the sample size was 100, or if the standard deviation was 10 and the sample size was 10,000. - It does not correctly reflect the given data of **SD = 10** and **n = 100**. *Incorrect Option: 2* - This value would result if the standard deviation was 20 and the sample size was 100, or if the standard deviation was 10 and the sample size was 25. - It does not align with the provided **standard deviation of 10** and a **sample size of 100**.

Question 820: During a health survey, data was collected to calculate the prevalence of hypertension in a population. Which statistical measure is used to describe the central tendency of systolic blood pressure readings in this survey?

A. Mean (Correct Answer)
B. Median
C. Mode
D. Range

Explanation: ***Mean*** - The **mean** is the most common measure of central tendency for **continuously distributed data** like systolic blood pressure readings. - It uses all values in the dataset to calculate the average, providing a comprehensive representation of the central point. *Median* - The median represents the **middle value** in an ordered dataset and is more appropriate for **skewed distributions** or when outliers might disproportionately affect the mean. - While it describes central tendency, it does not use all data points in its calculation and is less sensitive to extreme values, which isn't the primary goal when describing the average blood pressure in a general population. *Mode* - The mode identifies the **most frequently occurring value** in a dataset and is primarily useful for categorical or discrete data. - For continuous data like blood pressure, the mode may not be unique or meaningful since exact repeated values are less common. *Range* - The range indicates the **spread or variability** of the data, calculated as the difference between the maximum and minimum values. - It is a measure of dispersion, not a measure of central tendency.

Practice by Chapter

Collection and Presentation of Data

Practice Questions

Measures of Central Tendency

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Measures of Dispersion

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Normal Distribution

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Sampling Methods

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Sample Size Calculation

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Hypothesis Testing

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Tests of Significance

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Correlation and Regression

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Survival Analysis

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Multivariate Analysis

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Statistical Software in Research

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