Biostatistics Practice Questions

Q: Consider the following statements about correlation between two variables : 1. The correlation is done between an independent variable X and a dependent variable Y. 2. The coefficient of correlation can range from -1 to ∞. 3. If coefficient of correlation (r) is equal to 1, it indicates there is no association between X and Y. 4. Correlation does not necessarily prove causation. Which of the statements given above are correct ?

4 only. ***Correct: 4 only*** - **Correlation** measures the strength and direction of a linear relationship between two variables, but it **does not imply that one causes the other**; other factors or confounding variables might be involved. - This statement is a fundamental principle in statistics, emphasizing that causality requires more rigorous evidence, such as controlled experiments, beyond a simple correlation. - **Only statement 4 is correct** among all the given statements. *Incorrect: 1 only* - While correlation is often explored between dependent and independent variables, it can also be used to assess the relationship between **any two quantitative variables**, whether one is clearly designated as independent or dependent. - Statement 1 is partially incorrect as correlation isn't exclusively between designated independent and dependent variables. *Incorrect: 1, 2 and 3* - Statement 1 is partially incorrect as correlation isn't exclusively between designated independent and dependent variables. - Statement 2 is incorrect because the **coefficient of correlation (r) ranges from -1 to +1**, not to infinity, with -1 indicating a perfect negative correlation and +1 a perfect positive correlation. - Statement 3 is incorrect because an **r equal to 1 indicates a perfect positive linear association** between X and Y, meaning they move in the same direction proportionally, not no association. *Incorrect: 1 and 4 only* - Statement 1 is incorrect because **correlation can be performed between any two variables** to assess their relationship, not just an explicitly independent and dependent pair. - While statement 4 is correct, the inclusion of statement 1 makes this option incorrect.

Q: The table below shows the results of ELISA test for HIV infection : Consider the following statements : 1. The sensitivity is 98%. 2. The specificity is 99%. Which of the statements given above is/are correct?

2 only. ***2 only*** - From the ELISA test table, we need to calculate sensitivity and specificity using standard formulas. - **True Positives (TP)** = Infected individuals who tested positive = **4900** - **False Negatives (FN)** = Infected individuals who tested negative = 5800 - 4900 = **900** - **True Negatives (TN)** = Non-infected individuals who tested negative = 95000 - 950 = **94050** - **False Positives (FP)** = Non-infected individuals who tested positive = **950** - **Sensitivity = TP / (TP + FN)** = 4900 / 5800 = **84.48%** (NOT 98%) - **Specificity = TN / (TN + FP)** = 94050 / 95000 = **99.0%** ✓ - **Statement 1 is INCORRECT** (sensitivity is 84.48%, not 98%) - **Statement 2 is CORRECT** (specificity is indeed 99%) *1 only* - This option is incorrect because statement 1 claims sensitivity is 98%, but the calculated sensitivity is only 84.48%. - The test correctly identifies only about 84.5% of infected individuals, missing approximately 15.5% (false negatives). *Both 1 and 2* - This option is incorrect because statement 1 is false. - While statement 2 regarding specificity (99%) is correct, statement 1 regarding sensitivity (98%) is incorrect. *Neither 1 nor 2* - This option is incorrect because statement 2 is correct. - The specificity calculation clearly shows 99%, so at least one statement is correct.

Q: While calculating the ‘total dependency ratio’, which one of the following is used in the denominator?

Population 15 to 64 years. ***Population 15 to 64 years*** - The **total dependency ratio** is calculated by dividing the sum of the **dependent population** (ages 0-14 and 65+) by the **working-age population** (ages 15-64). - Therefore, the **denominator** represents the segment of the population that is generally considered to be in their most productive working years. *Midyear population* - The **midyear population** refers to the population at the midpoint of a given year and is often used as a general denominator for various rates (e.g., birth rates, death rates). - However, in the context of the dependency ratio, a specific age group—the **working-age population**—is required in the denominator to reflect economic burden. *Population 14 to 70 years* - This age range does not accurately represent the standard definition of the **working-age population** or the traditional age groups used for calculating dependency ratios. - The internationally accepted age range for the working population is typically **15-64 years**. *Population 0 to 65 years* - This range includes both **dependent children** (0-14) and potentially some of the **elderly dependent population** (65 and over), thus it does not represent the **working-age population** for the denominator. - The denominator for the dependency ratio specifically excludes these dependent age groups.

Q: A researcher has obtained the country-level data on the average Body Mass Index (BMI) and the average sugar intake for 100 countries. Which among the following will be best suited to present the relationship between BMI and sugar intake in the 100 countries?

Scatter diagram. ***Scatter diagram*** - A **scatter diagram** is ideally suited for visualizing the relationship or **correlation** between two continuous variables, in this case, average BMI and average sugar intake per country. - Each point on the diagram represents a single country, with its coordinates determined by its corresponding BMI and sugar intake values, allowing for easy identification of patterns or trends. *Frequency polygon* - A **frequency polygon** is used to display the **frequency distribution** of a single continuous variable, showing the shape of the data. - It is not designed to show the relationship between two different variables. *Bar chart* - A **bar chart** is typically used to compare **categorical data** or show changes in a **single variable over time**. - It does not effectively display the relationship or correlation between two continuous variables like BMI and sugar intake. *Pie diagram* - A **pie diagram** is used to represent **proportions** or percentages of a whole for a single categorical variable. - It is not suitable for visualizing the relationship between two continuous quantitative variables.

Q: A town in the hills had a mid-year population of 250000 in the year 2021. During the same year, the death registry of the town recorded 1500 deaths due to tuberculosis in 365 calendar days. Given these facts, what is the specific death rate for tuberculosis in the town?

6. ***6*** - The **specific death rate** (also called cause-specific death rate) is calculated as **(Number of deaths from a specific cause / Mid-year population) × 1000** - For tuberculosis: (1500 deaths / 250,000 population) × 1000 = **6 deaths per 1000 population** - This represents the tuberculosis mortality rate in the community *10* - This incorrect value would be obtained if there were 2500 deaths due to tuberculosis instead of 1500 - Calculation error: (2500 / 250,000) × 1000 = 10 - Always verify the numerator (number of deaths) from the given data *60* - This is a common calculation error resulting from incorrect multiplication factor - May occur if using: (1500 / 250,000) × 10,000 = 60 (wrong multiplier) - Remember: specific death rate uses **per 1000** population, not per 10,000 *1* - This value results from calculation errors or incorrect rounding - May occur if dividing by wrong population figure or forgetting the multiplier - The actual rate (1500/250,000 = 0.006) must be multiplied by 1000 to get rate per 1000 population

Q: In a town, a study was carried out to determine the role of cigarette smoking in causation of lung cancer. It was found that a total of 7000 people in the town were smokers. Of them, 70 developed lung cancer. In the same town, 3000 people were non-smokers. Of them, 3 developed lung cancer. Given these numbers, what would be the attributable risk to cigarette smoking for lung cancer?

90%. **90%** - The **attributable risk** (AR) is calculated as the incidence in the exposed group minus the incidence in the unexposed group, divided by the incidence in the exposed group, all multiplied by 100%. - Incidence in smokers (Ie) = 70 cases / 7000 smokers = 0.01. Incidence in nonsmokers (Io) = 3 cases / 3000 nonsmokers = 0.001. AR = ((0.01 - 0.001) / 0.01) * 100% = (0.009 / 0.01) * 100% = 0.9 * 100% = **90%**. *30%* - This percentage is incorrect; it does not align with the formal calculation of **attributable risk** based on the given incidence rates in exposed and unexposed groups. - A value of 30% would imply a much smaller difference in incidence between smokers and non-smokers relative to the incidence in smokers. *10%* - This value might be obtained if the calculation confused **attributable risk** with the proportion of cases in the unexposed group or some other miscalculation. - It significantly underestimates the proportion of lung cancer in smokers directly attributable to their smoking status. *60%* - This answer is incorrect as it does not result from the appropriate application of the **attributable risk formula**. - The discrepancy between the incidence rate in smokers (0.01) and non-smokers (0.001) is much higher than what would lead to a 60% attributable risk.

Q: Forty patients with diarrhoeal diseases were studied. Their age distribution is given in the table below : What is the mean age of the patients in this study?

5 years. ***5 years*** - To calculate the **mean age** from grouped data, first find the midpoint of each age range. - The midpoints are: **2** for 0-4 years (22 patients), **7** for 5-9 years (12 patients), and **12** for 10-14 years (6 patients). - Multiply each midpoint by the number of patients in that range: (2 × 22) + (7 × 12) + (12 × 6) = 44 + 84 + 72 = **200**. - Divide the sum of these products by the total number of patients (**40**) to get the mean age: **200 / 40 = 5 years**. *2 years* - This is the **midpoint** of the first age group (0-4 years), not the mean of the entire dataset. - While 22 patients (the majority) fall in this age group, the mean must account for the **weighted distribution** across all age groups. - This would only be correct if all 40 patients were in the 0-4 years age group. *4 years* - This answer suggests an **incorrect calculation** of the weighted mean or an error in summing the products. - It does not match the correct weighted mean formula: Σ(midpoint × frequency) / total frequency. - May result from miscalculating the sum (200) or the total number of patients. *6 years* - This value is higher than the calculated mean and likely results from a **mathematical error**. - The correct calculation yields 5 years, not 6 years. - This might arise from rounding errors or incorrect midpoint selection.

Q: In a normal curve, the area of one standard deviation around the mean includes which of the following per cent of values in a distribution ?

68.3%. ***68.3%*** - In a **normal distribution**, approximately 68.3% of the data falls within **one standard deviation** (±1σ) of the mean. - This is a fundamental property of the **empirical rule** (68-95-99.7 rule) applied to normally distributed data. *95.4%* - This percentage represents the data within **two standard deviations** (±2σ) of the mean in a normal distribution. - It is often rounded to 95% for confidence intervals, but the precise value is 95.4%. *48.6%* - This value does not correspond to a standard interval around the mean in a **normal distribution**. - It might be a distracter derived from incorrectly calculating or misremembering the percentages of the empirical rule. *99.7%* - This percentage represents the data within **three standard deviations** (±3σ) of the mean in a normal distribution. - It indicates that almost all data points in a normal curve lie within this range.

Q: To understand the relationship between weight and height of a group of school children, the data can graphically be best depicted through

Scatter diagram. ***Scatter diagram*** - A **scatter diagram** (also called a scatter plot) is ideal for showing the relationship between **two continuous variables**, such as weight and height. - Each point on the graph represents an individual's paired values for weight and height, allowing visual identification of **patterns or correlations**. *Histogram* - A **histogram** is used to display the distribution of **a single continuous variable**, showing the frequency of data points within specific intervals or bins. - It would not effectively demonstrate the **relationship or correlation** between two variables simultaneously. *Bar diagram* - A **bar diagram** (or bar chart) is typically used for comparing **categorical data** or discrete values, showing frequencies or proportions for different categories. - It is not suitable for visualizing the relationship between **two continuous numerical variables** like weight and height. *Pictogram* - A **pictogram** uses images or symbols to represent data, often used for presenting simple statistics to a general audience. - It is generally used for **categorical data** or simple comparisons and lacks the precision needed to display the continuous relationship between weight and height.

Question 1

Consider the following statements about correlation between two variables :

1. The correlation is done between an independent variable X and a dependent variable Y.

2. The coefficient of correlation can range from -1 to ∞.

3. If coefficient of correlation (r) is equal to 1, it indicates there is no association between X and Y.

4. Correlation does not necessarily prove causation. Which of the statements given above are correct ?

Accepted Answer

4 only

Answer

1 only

Answer

1, 2 and 3

Answer

1 and 4 only

Question 2

The table below shows the results of ELISA test for HIV infection :

Consider the following statements :

1. The sensitivity is 98%.
2. The specificity is 99%.

Which of the statements given above is/are correct?

Accepted Answer

2 only

Answer

Both 1 and 2

Answer

Neither 1 nor 2

Answer

1 only

Question 3

While calculating the ‘total dependency ratio’, which one of the following is used in the denominator?

Accepted Answer

Population 15 to 64 years

Answer

Midyear population

Answer

Population 14 to 70 years

Answer

Population 0 to 65 years

Question 4

A researcher has obtained the country-level data on the average Body Mass Index (BMI) and the average sugar intake for 100 countries. Which among the following will be best suited to present the relationship between BMI and sugar intake in the 100 countries?

Accepted Answer

Scatter diagram

Answer

Frequency polygon

Answer

Bar chart

Answer

Pie diagram

Question 5

The following table shows the 'Total Fertility Rate (TFR)' by the Wealth Index, as per the National Family Health Survey, (NFHS–4) findings. Which among the following is/are correct about the information?

Accepted Answer

4. Each of the higher divisions of the Wealth Index had lower TFR than the previous (or lower) division.

Answer

2. The information given in the table can be presented as a pie chart.

Answer

1. The divisions of Wealth Index in the NFHS–4 can be called 'quartiles'.

Answer

3. The Wealth Index was calculated in NFHS–4 by asking about the per capita income.

Question 6

A town in the hills had a mid-year population of 250000 in the year 2021. During the same year, the death registry of the town recorded 1500 deaths due to tuberculosis in 365 calendar days. Given these facts, what is the specific death rate for tuberculosis in the town?

Accepted Answer

6

Answer

10

Answer

60

Answer

1

Question 7

In a town, a study was carried out to determine the role of cigarette smoking in causation of lung cancer. It was found that a total of 7000 people in the town were smokers. Of them, 70 developed lung cancer. In the same town, 3000 people were non-smokers. Of them, 3 developed lung cancer. Given these numbers, what would be the attributable risk to cigarette smoking for lung cancer?

Accepted Answer

90%

Answer

30%

Answer

10%

Answer

60%

Question 8

Forty patients with diarrhoeal diseases were studied. Their age distribution is given in the table below : What is the mean age of the patients in this study?

Accepted Answer

5 years

Answer

4 years

Answer

6 years

Answer

2 years

Question 9

In a normal curve, the area of one standard deviation around the mean includes which of the following per cent of values in a distribution ?

Accepted Answer

68.3%

Answer

95.4%

Answer

48.6%

Answer

99.7%

Question 10

To understand the relationship between weight and height of a group of school children, the data can graphically be best depicted through

Accepted Answer

Scatter diagram

Answer

Histogram

Answer

Bar diagram

Answer

Pictogram

Biostatistics — MCQs

Biostatistics — MCQs

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