Biostatistics Practice Questions

Q: Which of the following is true about the box plot shown?

Mean = median, not equal to mode. ***Mean = median, not equal to mode*** - A **perfectly symmetrical distribution** (represented by a **symmetrical box plot without whiskers extending further in one direction**) indicates that the **mean and median are equal**. - However, the mode, which is the most frequent value, is not necessarily equal to the mean and median in all symmetrical distributions, especially if it's **not unimodal or not centered at the mean/median**. When depicted using a boxplot, we cannot ascertain the mode simply by looking at where the median lies. *Mean = median = mode* - While the **mean and median are equal** in a symmetrical distribution, the **mode is not explicitly represented** in a box plot. - The mode is the most frequently occurring value, and a box plot primarily shows quartiles and spread, not individual frequencies. *Mean = mode, not equal to median* - In a symmetrical distribution, the **mean and median are equal**. - Therefore, this option is incorrect as it states the mean is not equal to the median. *Mean, median and mode are not equal* - The **symmetrical nature** of the box plot strongly suggests that the **mean and median are equal**. - This option is therefore incorrect, as at least two of the measures of central tendency are equal.

Q: Which is incorrect about the image shown below?

75 % values are above 25 mg. ***75 % values are above 25 mg*** - This statement is incorrect. In a box plot, the **second quartile (Q2)** or **median** represents the 50th percentile. The upper boundary of the lower box (Q2) is at 23 mg, meaning 50% of values are above 23 mg. - The upper boundary of the upper box (Q3) is at 35 mg, meaning 25% of values are above 35 mg. Therefore, it is incorrect to say 75% of values are above 25 mg. *Negatively skewed* - The long **tail of the distribution** is on the left side, as indicated by the lower whisker extending further from the box than the upper whisker, and the lower half of the box being larger than the upper half. - In a negatively skewed distribution, the **mean is typically less than the median**, and the bulk of the values are concentrated on the higher end. *Positively skewed* - This statement is incorrect. A **positively skewed** distribution would have a longer tail on the right side, meaning the upper whisker would be longer than the lower whisker and the upper box larger than the lower box. - The provided image shows the opposite, with the longer tail towards the lower values. *Median is 50 mg* - The **median** is represented by the line dividing the lower and upper halves of the box. In this box plot, the median line is at approximately **23 mg**, not 50 mg. - The box itself represents the **interquartile range (IQR)**, with the median dividing it.

Q: A study was conducted to evaluate the diagnostic accuracy of ECG for detecting myocardial infarction. The results are shown in the 2x2 table below: Myocardial Infarction Present Absent Total ECG Positive 45 8,000 8,045 ECG Negative 5 32,000 32,005 Total 50 40,000 40,050 Consider the following statements: I. Sensitivity is 90%. II. Specificity is 80%. Which of the statements given above is/are correct?

Both I and II. **Both I and II** - **Sensitivity** = True Positives / (True Positives + False Negatives) = 45 / (45 + 5) = 45/50 = **0.90 or 90%** ✓ - **Specificity** = True Negatives / (True Negatives + False Positives) = 32,000 / (32,000 + 8,000) = 32,000/40,000 = **0.80 or 80%** ✓ - Both calculations are correct based on the 2×2 contingency table - **Sensitivity** measures the ability of the test to correctly identify those with disease (true positive rate) - **Specificity** measures the ability of the test to correctly identify those without disease (true negative rate) *I only* - Incorrect because Statement II (Specificity = 80%) is also correct, not just Statement I *II only* - Incorrect because Statement I (Sensitivity = 90%) is also correct, not just Statement II *Neither I nor II* - Incorrect because both statements are mathematically correct based on the given data

Q: A surgical department of a premier medical college conducted a study on rates of post-operative wound infection. The results of the study were negative for the proposed hypothesis. What should the department do with the results?

Report the negative results. **Report the negative results** - All research findings, whether positive or negative, contribute to the body of scientific knowledge and should be **ethically reported** to prevent publication bias. - Reporting negative results helps other researchers avoid duplicating efforts and can inform future study designs, potentially leading to a better understanding of the topic. *Label them as worthless* - Labeling negative results as "worthless" contradicts the principles of **scientific integrity** and promotes publication bias, where only positive findings are disseminated. - Even negative findings can provide crucial insights, indicating that a particular intervention or hypothesis is not supported, thus saving time and resources for future research. *Redo the study with a new hypothesis* - While forming new hypotheses may be necessary in some cases, redoing the study with a completely new hypothesis without reporting the initial negative results would be **unethical** and contribute to the problem of **publication bias**. - **New hypotheses** should ideally be formulated based on a comprehensive understanding of existing research, including negative findings. *Redesign the study and increase the sample size* - While redesigning the study and increasing sample size might be appropriate after the initial results have been reported and analyzed, the **immediate and ethical step** is to report the existing negative findings. - A larger sample size alone does not guarantee positive results; careful reevaluation of the methods and hypothesis is needed if the initial study was well-conducted.

Q: Cross-over type of study designs are those in which each subject serves as his/her own control. In which of the following conditions is a cross-over study not suitable ?

If the drug of interest cures the disease. ***If the drug of interest cures the disease*** - A **crossover study** relies on subjects experiencing both treatment and control conditions, which is **not possible** if a drug cures the disease, as the initial treatment would eliminate the condition for the second phase. - The carryover effect of a cure would invalidate the comparison between the treatment and control periods, making subsequent observations on the same subject non-independent. *If the disease changes radically during the period of time required for the study* - **Radical changes in disease progression** would introduce significant **confounding variables**, making it difficult to attribute changes in outcome solely to the intervention. - The **baseline state** for the second treatment period would be vastly different from the first, violating the assumption of comparable conditions inherent in crossover designs. *None of the options* - This option is incorrect because there is a specific scenario among the choices where a crossover study is unsuitable, as detailed in the correct answer. *If the drug is effective during all stages of the disease* - A drug's effectiveness across all disease stages would actually **make a crossover study more suitable**, as the treatment effects could be consistently observed regardless of when the intervention is given. - This scenario would reduce the variability in response due to disease progression, allowing for a clearer comparison between treatment and control periods.

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.

Question 1

Which of the following is true about the box plot shown?

Accepted Answer

Mean = median, not equal to mode

Answer

Mean = median = mode

Answer

Mean = mode, not equal to median

Answer

Mean, median and mode are not equal

Question 2

Which is incorrect about the image shown below?

Accepted Answer

75 % values are above 25 mg

Answer

Negatively skewed

Answer

Positively skewed

Answer

Median is 50 mg

Question 3

A study was conducted to evaluate the diagnostic accuracy of ECG for detecting myocardial infarction. The results are shown in the 2x2 table below:

Myocardial Infarction
                    Present    Absent    Total
ECG Positive         45       8,000     8,045
ECG Negative          5      32,000    32,005
Total                50      40,000    40,050

Consider the following statements:
I. Sensitivity is 90%.
II. Specificity is 80%.

Which of the statements given above is/are correct?

Accepted Answer

Both I and II

Answer

Neither I nor II

Answer

II only

Answer

I only

Question 4

A surgical department of a premier medical college conducted a study on rates of post-operative wound infection. The results of the study were negative for the proposed hypothesis. What should the department do with the results?

Accepted Answer

Report the negative results

Answer

Label them as worthless

Answer

Redo the study with a new hypothesis

Answer

Redesign the study and increase the sample size

Question 5

Cross-over type of study designs are those in which each subject serves as his/her own control. In which of the following conditions is a cross-over study not suitable ?

Accepted Answer

If the drug of interest cures the disease

Answer

If the disease changes radically during the period of time required for the study

Answer

None of the options

Answer

If the drug is effective during all stages of the disease

Question 6

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 7

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 8

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 9

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 10

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.

Biostatistics — MCQs

Biostatistics — MCQs

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