Biostatistics Practice Questions

Q: In a study, an investigator compared the mean blood pressure and standard deviation between two independent groups. Which of the following is the most appropriate statistical test to assess the significance of the difference between the two means?

Unpaired t-test. ***Unpaired t-test***- It is the most appropriate statistical test used to compare the means of two independent (unrelated) groups when the data is continuous (like **blood pressure**).- This test assesses the null hypothesis that there is no significant difference between the **population means** of the two comparison groups.*Paired t-test*- This test is specifically designed to compare means when the observations are dependent, meaning the data comes from the **same subjects** measured twice (e.g., pre-treatment and post-treatment).- It is used for **within-group comparisons** rather than comparisons between two independent cohorts, as requested in the scenario.*Chi-square test*- The chi-square test is used to determine the association between **two categorical variables** (e.g., proportions or frequencies).- It is unsuitable here because the variable being compared (blood pressure) is **continuous data**, and the study requires comparing means, not counted frequencies.*ANOVA*- ANOVA (Analysis of Variance) is used when comparing the means of **three or more** independent groups.- While acceptable for two groups (where it gives equivalent results to the t-test), the **unpaired t-test** is the most specific and standard test for comparing means of exactly two independent samples.

Q: In a study based in Delhi, doctors followed 100 people who did exercise for a year and later they checked who all had developed coronary heart disease. Which type of study is this?

Cohort study. ***Cohort study***- This study starts with a group of people free of the disease (**CHD**) and classifies them based on their exposure status (e.g., *exercise* vs. no exercise) and follows them forward in time (**prospectively**) to measure the incidence of the disease.- The study tracks the patients *forward* from exposure (**exercise**) to outcome (**CHD**) over a specified period (one year), which is the definitive characteristic of a **prospective cohort study**.*Case Control Study*- In this design, the study starts with the outcome (**CHD**) and retrospectively looks back (examining controls without CHD) to determine past exposure, making it unsuitable for this specific prospective tracking of exposure.- It is used primarily to estimate the **odds ratio** and is efficient for studying rare diseases; it does not measure incidence over time.*Prospective Study*- While this specific study is **prospective** (looking forward in time), this term describes the *timing* and direction of data collection, whereas **Cohort Study** is the most specific designation describing the fundamental design of following a defined exposed population.- A **prospective study** is a broad term, and the term **Cohort Study** most accurately describes the method of following an exposed group to measure disease incidence over time.*Cross Sectional Study*- This study type measures both the exposure (exercise) and the outcome (**CHD**) simultaneously at a **single point in time**, assessing prevalence rather than tracking incidence over one year.- It provides a **snapshot** and cannot establish the temporal relationship between exposure and outcome, failing to align with the follow-up design described.

Q: Which of the following is the formula for sensitivity?

TP/(TP+FN)x100. ***TP/(TP+FN)x100***- This is the formula for **sensitivity** (or True Positive Rate), which is the proportion of individuals who truly have the disease (**True Positives, TP**) who are correctly identified by the test.- The denominator $TP + FN$ accounts for all individuals who actually have the disease according to the **gold standard**, including those who tested negatively (**False Negatives, FN**).*TP/(TP+FP)x100*- This formula calculates the **Positive Predictive Value (PPV)**, which indicates the probability that a positive test result represents a true positive.- The denominator $TP + FP$ includes everyone who tested positive, regardless of their actual disease status (**True Positives** and **False Positives**).*TN/(TN+FP)x100*- This formula calculates **specificity** (or True Negative Rate), which is the proportion of individuals who are truly disease-free (**True Negatives, TN**) correctly identified by the test.- The denominator $TN + FP$ accounts for all individuals without the disease, including those who were incorrectly identified as positive (**False Positives, FP**).*TN/(TN+FN)x100*- This formula calculates the **Negative Predictive Value (NPV)**, which is the probability that a negative test result represents a true negative.- The denominator $TN + FN$ includes everyone who tested negative, reflecting the proportion of subjects with a negative test result who are truly disease-free.

Q: In a normal distribution, the mean value is 82, the SD is 1.5. Calculate the range of two standard deviations?

79-85. ***79-85***- For a **normal distribution**, the range covering two standard deviations (2 SD) is calculated using the formula: **Mean $\pm$ (2 $\times$ SD)**. The $2\sigma$ interval encompasses approximately **95.45%** of the data points.- Calculation: Lower limit $= 82 - (2 \times 1.5) = 82 - 3 = 79$. Upper limit $= 82 + (2 \times 1.5) = 85$. The correct range is **79-85**. *60-68*- This range is highly incorrect as it is centered far below the **mean of 82** and the width (8 units) is too wide for a total of 3 units (2 SD) dispersion. - The lower limit of 60 is over 14 standard deviations away from the mean, indicating it is an outlier range not relevant to the $2\sigma$ calculation. *50-57*- This range is excessively far from the **mean of 82** and its width (7 units) does not correspond to the required 3 units of dispersion needed for $\pm 2$ SD. - Ranges like this would include virtually none of the observations expected in a population with a mean of 82 and a small **standard deviation** of 1.5. *40-49*- This interval is centered around 44.5, which is highly divergent from the actual **mean of 82**, and therefore cannot represent the population's $\pm 2$ SD range. - In a normal distribution, the data is symmetric around the mean; any calculated range must therefore include the mean near its center, which this option fails to do.

Q: A total of 2000 patients were assessed for HIV. 200 were diagnosed positive. A new ELISA screening test was tested on the same group. It showed 260 as positive out of which only 130 had the disease. What is the specificity of the test?

96%. ***96%*** - **Specificity** is the ability of a test to correctly identify those *without* the disease (True Negatives) among all disease-free individuals: Specificity = TN / (TN + FP) - Given data: Total patients = 2000; Actual HIV positive = 200; Actual HIV negative = 1800 - Test showed 260 positives, of which 130 were true positives (TP) - False Positives (FP) = 260 - 130 = 130 - True Negatives (TN) = Total negatives - FP = 1800 - 130 = 1670 - **Calculated Specificity = 1670/1800 × 100 = 92.78%** - Among the given options, **96% is the closest** to the calculated value of 92.78% *80%* - This value is too low and does not match the calculated specificity - This might represent a miscalculation or confusion with sensitivity *72%* - This is significantly lower than the actual specificity of 92.78% - This does not correspond to any standard epidemiological measure from the given data *68%* - This is the lowest option and far from the correct calculation - This may result from calculation errors such as using wrong denominators or confusing different test parameters

Q: Calculate the relative risk for the given situation: Developed Malaria | Did Not Develop Malaria | Total Vaccinated 6 | 94 | 100 Non-vaccinated 12 | 88 | 100

0.5. ***Correct: 0.5*** **Relative Risk (RR)** is calculated as: RR = Risk in exposed group / Risk in unexposed group **Step-by-step calculation:** - Risk in **vaccinated group** = 6/100 = 0.06 - Risk in **non-vaccinated group** = 12/100 = 0.12 - **RR = 0.06 / 0.12 = 0.5** **Interpretation:** An RR of **0.5 indicates a protective effect** of vaccination. Vaccinated individuals have **half the risk** (50% reduced risk) of developing malaria compared to non-vaccinated individuals. *Incorrect: 2* This is the **inverse** of the correct RR, calculated as 0.12/0.06 = 2 (risk in non-vaccinated / risk in vaccinated). This would incorrectly suggest vaccination **doubles the risk** of malaria, which contradicts the data showing vaccination is protective. *Incorrect: 1.5* This value does not result from the correct RR formula using the given incidence rates (0.06 vs 0.12). This may arise from incorrect formula application or confusion with other epidemiological measures like the **Odds Ratio**. *Incorrect: 1.7* This is not the result of standard RR calculation based on the incidence rates of 0.06 and 0.12. It represents a **calculation error** and has no epidemiological meaning in this context.

Q: The urban area of Delhi has 4000 people with different religions. Research is being done to study the dietary habits of the population. Which of the following techniques can be used to obtain a study sample?

Stratified random sampling. ***Stratified random sampling.***- This technique divides the population (Delhi area) into homogeneous subgroups (strata) based on the defining characteristic, which in this case is **religion**, to ensure proportional representation. - Since dietary habits are likely to vary significantly across different religious groups, stratification ensures that the study sample accurately reflects the **dietary heterogeneity** of the urban area. *Cluster random sampling*- **Cluster sampling** is typically used when the population is large and geographically dispersed; the basic unit sampled is a group (cluster), not the individual.- Selecting entire geographical clusters might not capture the full diversity of religious dietary habits, potentially leading to increased **sampling error**. *Simple random sampling*- **Simple random sampling** selects individuals purely randomly, irrespective of their subgroup (religious) membership.- This method risks selecting an inadequate number of individuals from smaller religious groups, thereby failing to accurately represent the **dietary practices** of the entire population. *Systematic random sampling*- **Systematic sampling** involves selecting every 'n'th member from a list and is logistically simple, but it does not account for the intrinsic heterogeneity (religion) of the population.- If the initial list is arranged in a pattern related to religious groups, this method could introduce a **hidden bias**, compromising the representativeness of the sample.

Q: Which of the following is the correct order of steps for conducting a research study? 1. Define the problem/hypothesis 2. Design the study methodology 3. Data collection and execution 4. Data analysis and interpretation

1,2,3,4. **1,2,3,4** - The correct research process begins with **defining the problem or hypothesis (1)**, which sets the foundation and direction for the entire study. - This is sequentially followed by **designing the study methodology (2)**, actual **data collection and execution (3)**, and finally, **data analysis and interpretation (4)**. *1,3,2,4* - Although starting correctly with **defining the research question (1)**, this sequence erroneously jumps to **data collection (3)** before finalizing the **study design (2)**. - Proper research requires the protocol, inclusion criteria, and sample size calculations (all part of **design 2**) to be complete prior to implementation. *2,1,4,3* - This sequence is illogical because it requires designing the study (**step 2**) before knowing what the study aims to achieve (**research question/step 1**). - Furthermore, **data analysis (4)** cannot proceed before all the necessary **data collection (3)** has been performed. *4,3,2,1* - This sequence is the complete reverse of scientific methodology, starting with the final step of **data interpretation and analysis (4)**. - A research study must always originate from a defined **research question (1)** and detailed planning, making this proposed order incorrect.

Q: In a Primary Health Centre (PHC), a study was done on diabetic patients. Mean weight was recorded before and after 6 months of dietary intervention. Which statistical test should be used to determine significance?

Paired t-test. ***Paired t-test*** - This test is appropriate for comparing the means of **two related samples** or measurements taken from the **same subjects** at two different time points (before and after intervention). - The study involves recording the mean weight of the *same* diabetic patients before and after a 6-month dietary intervention, making the samples dependent (paired). *Unpaired t-test* - The unpaired t-test (or Student's t-test) is used to compare the means of **two independent (unrelated) groups** (e.g., comparing the mean weight of patients in Group A vs. Group B). - It is unsuitable here because the measurements are taken from the same set of individuals, meaning the data points are related, not independent. *ANOVA* - **Analysis of Variance (ANOVA)** is used to compare the means of **three or more** independent groups (e.g., comparing mean weight across three different regions). - It is used when there are multiple levels of a factor or multiple independent variables, which is not the case when comparing two time points. *Chi-square test* - The Chi-square test is primarily used to analyze **categorical data** (frequencies or proportions) to determine if there is a significant association between two variables (e.g., relationship between gender and diabetes status). - It is unsuitable for comparing numerical values like mean weight measurements, which are continuous data.

Q: Which of the following is incorrectly matched with respect to the statistical parameter?

Mean, median - Dispersion. ***Mean, median - Dispersion*** - This statement is **incorrect** because the **mean** and **median** are measures of **central tendency** (location) of a distribution, not dispersion. - Measures of dispersion quantify the spread of data, such as **standard deviation**, range, and interquartile range. ***Standard error - Variation*** - **Standard error** is a measure of the **variation** (or dispersion) of sample means around the true population mean, making this a correct match. - Specifically, it estimates how much the sample mean is likely to deviate from the population mean. ***Correlation coefficient - Relationship*** - The **correlation coefficient** (e.g., Pearson's r) measures the **strength and direction of the linear relationship** between two variables, making this a correct match. - Its value ranges from -1 (perfect negative relationship) to +1 (perfect positive relationship). ***Moments - Skewness*** - **Moments** are specific mathematical calculations used to describe the shape and characteristics of a distribution; the **third moment** is specifically used to calculate **skewness**. - **Skewness** describes the asymmetry of the distribution (whether it leans left or right), and the third moment helps quantify this.

Question 1

In a study, an investigator compared the mean blood pressure and standard deviation between two independent groups. Which of the following is the most appropriate statistical test to assess the significance of the difference between the two means?

Accepted Answer

Unpaired t-test

Answer

Chi-square test

Answer

ANOVA

Answer

Paired t-test

Question 2

In a study based in Delhi, doctors followed 100 people who did exercise for a year and later they checked who all had developed coronary heart disease. Which type of study is this?

Accepted Answer

Cohort study

Answer

Case Control Study

Answer

Prospective Study

Answer

Cross Sectional Study

Question 3

Which of the following is the formula for sensitivity?

Accepted Answer

TP/(TP+FN)x100

Answer

TN/(TN+FP)x100

Answer

TP/(TP+FP)x100

Answer

TN/(TN+FN)x100

Question 4

In a normal distribution, the mean value is 82, the SD is 1.5. Calculate the range of two standard deviations?

Accepted Answer

79-85

Answer

60-68

Answer

40-49

Answer

50-57

Question 5

A total of 2000 patients were assessed for HIV. 200 were diagnosed positive. A new ELISA screening test was tested on the same group. It showed 260 as positive out of which only 130 had the disease. What is the specificity of the test?

Accepted Answer

96%

Answer

68%

Answer

72%

Answer

80%

Question 6

Calculate the relative risk for the given situation:

Developed Malaria | Did Not Develop Malaria | Total
Vaccinated                 6          |          94             |  100
Non-vaccinated            12          |          88             |  100

Accepted Answer

0.5

Answer

1.5

Answer

2

Answer

1.7

Question 7

The urban area of Delhi has 4000 people with different religions. Research is being done to study the dietary habits of the population. Which of the following techniques can be used to obtain a study sample?

Accepted Answer

Stratified random sampling

Answer

Simple random sampling

Answer

Systematic random sampling

Answer

Cluster random sampling

Question 8

Which of the following is the correct order of steps for conducting a research study?
1. Define the problem/hypothesis
2. Design the study methodology
3. Data collection and execution
4. Data analysis and interpretation

Accepted Answer

1,2,3,4

Answer

1,3,2,4

Answer

2,1,4,3

Answer

4,3,2,1

Question 9

In a Primary Health Centre (PHC), a study was done on diabetic patients. Mean weight was recorded before and after 6 months of dietary intervention. Which statistical test should be used to determine significance?

Accepted Answer

Paired t-test

Answer

Chi-square test

Answer

Unpaired t-test

Answer

ANOVA

Question 10

Which of the following is incorrectly matched with respect to the statistical parameter?

Accepted Answer

Mean, median - Dispersion

Answer

Moments - Skewness

Answer

Standard error - Variation

Answer

Correlation coefficient - Relationship

Biostatistics — MCQs

Biostatistics — MCQs

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