Biostatistics Practice Questions

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 estimated mean age using class midpoints of the patients in this study?

5 years. ***5 years*** - To calculate the **estimated mean age using class midpoints** 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 estimated mean age using class midpoints: **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.

Q: For a screening test, 90% specificity means that 90% of non-diseased persons will give a

True negative result. ***True negative result*** - **Specificity** is defined as the proportion of **true negatives** among individuals **without the disease**. - A 90% specificity means that 90% of healthy individuals will correctly test negative for the disease. *False negative result* - A **false negative** occurs when a diseased person tests negative, which is related to the concept of **sensitivity**, not specificity. - This would imply missing actual cases of the disease. *True positive result* - A **true positive** occurs when a diseased person tests positive, which is also related to **sensitivity**. - This indicates accurate detection of the disease in affected individuals. *False positive result* - A **false positive** occurs when a non-diseased person inappropriately tests positive. - If 90% of non-diseased persons give a negative result (true negative), then 10% would give a **false positive result**.

Q: What is the method of sampling in which the units are picked up at regular intervals from the universe ?

Systematic random sampling. ***Systematic random sampling*** - This method involves selecting samples at a **fixed and regular interval** from a larger population after a random starting point is chosen. - It ensures representation across the entire population list by picking every nth unit, making it **efficient for large datasets**. *Stratified random sampling* - This method involves dividing the population into **homogeneous subgroups** (strata) and then drawing a random sample from each stratum. - It is used when there is a need to ensure **representation of specific subgroups**, which is not the primary characteristic described. *Snow-ball sampling* - This is a **non-probability sampling technique** where initial subjects recruit future subjects from among their acquaintances, typically used for hard-to-reach populations. - It relies on existing social networks and is not characterized by picking units at regular intervals. *Simple random sampling* - In this method, every member of the population has an **equal chance of being selected**, and selections are made fully at random. - While random, it does not involve the specific process of picking units at **regular, predetermined intervals**.

Q: A randomized trial comparing the efficacy of two drugs showed a difference between the two (p value < 0.05). However, in reality the drugs do not differ. This is an example of

Type I error. ***Type I error*** - A **Type I error** occurs when the **null hypothesis is incorrectly rejected**, leading to the conclusion that a significant difference exists when, in reality, there is no true difference. - In this scenario, the trial concluded a difference (p < 0.05), but the drugs are truly equivalent, which is precisely the definition of a **Type I error**. *Both type I and II error* - It is impossible to commit both a **Type I** and a **Type II error** simultaneously for the same statistical test. - A **Type I error** involves rejecting a true null hypothesis, while a **Type II error** involves failing to reject a false null hypothesis. *Random error* - **Random error** refers to unpredictable fluctuations in measurements or results, which can be minimized but not eliminated. - While random error can contribute to variability in data, it is not the direct statistical error of concluding a non-existent difference when analyzing the results, which is a **Type I error**. *Type II error* - A **Type II error** occurs when the **null hypothesis is incorrectly accepted** (or not rejected), meaning a real difference exists but the study fails to detect it. - This scenario describes the opposite: a difference was detected and concluded, but it was false.

Q: In a village, every fifth house was selected for a study. This is an example of

Systematic random sampling. ***Systematic random sampling*** - This method involves selecting subjects from a **ordered sampling frame** at regular intervals, such as every k-th item. - In this scenario, selecting every fifth house represents a fixed interval (k=5), which is characteristic of systematic random sampling. *Simple random sampling* - This method ensures that every member of the population has an **equal chance of being selected**, often through random number generation. - It does not involve a predetermined, fixed interval of selection from an ordered list. *Convenience sampling* - This technique involves selecting subjects who are **easily accessible or readily available**, without any systematic or random process. - It is prone to bias as it does not represent the entire population. *Stratified random sampling* - This method involves dividing the population into **homogeneous subgroups (strata)** and then conducting simple random sampling within each stratum. - The scenario does not describe dividing the village households into distinct subgroups before selection.

Q: The ability of a test to identify correctly those who do not have the disease is called its

Specificity. ***Specificity*** - **Specificity** is the proportion of **true negatives** correctly identified by the test. - It measures the ability of a test to correctly identify individuals who **do not have the disease**. *Sensitivity* - **Sensitivity** is the proportion of **true positives** correctly identified by the test. - It measures the ability of a test to correctly identify individuals who **do have the disease**. *Positive predictive value* - **Positive predictive value (PPV)** is the probability that a patient with a **positive test result** actually has the disease. - It depends on the **prevalence** of the disease in the population being tested. *Negative predictive value* - **Negative predictive value (NPV)** is the probability that a patient with a **negative test result** actually does not have the disease. - It also depends on the **prevalence** of the disease in the population.

Q: In a normal curve, how much per cent of the values will be included in the area between two standard deviations on either side of the mean (X ± 2σ) ?

95.4. ***Correct: 95.4*** - According to the **empirical rule** (also known as the 68-95-99.7 rule), approximately 95% of data falls within two standard deviations of the mean in a normal distribution. - More precisely, the area between **X ± 2σ** encompasses **95.4%** of the values. - This is a fundamental concept in biostatistics used for calculating confidence intervals and reference ranges. *Incorrect: 68.3* - This percentage represents the proportion of data within **one standard deviation** (X ± 1σ) of the mean in a normal distribution. - It is not the correct value for the range of two standard deviations. *Incorrect: 90.4* - This value does not correspond to any standard interval of standard deviations around the mean in a normal distribution. - It is not part of the empirical rule for common standard deviation ranges. *Incorrect: 99.7* - This percentage represents the proportion of data within **three standard deviations** (X ± 3σ) of the mean in a normal distribution. - It is a larger interval than what is asked in the question (two standard deviations).

Question 1

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 2

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

Accepted Answer

5 years

Answer

6 years

Answer

2 years

Answer

4 years

Question 3

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 4

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

Question 5

For a screening test, 90% specificity means that 90% of non-diseased persons will give a

Accepted Answer

True negative result

Answer

False negative result

Answer

True positive result

Answer

False positive result

Question 6

What is the method of sampling in which the units are picked up at regular intervals from the universe ?

Accepted Answer

Systematic random sampling

Answer

Stratified random sampling

Answer

Snow-ball sampling

Answer

Simple random sampling

Question 7

A randomized trial comparing the efficacy of two drugs showed a difference between the two (p value < 0.05). However, in reality the drugs do not differ. This is an example of

Accepted Answer

Type I error

Answer

Both type I and II error

Answer

Random error

Answer

Type II error

Question 8

In a village, every fifth house was selected for a study. This is an example of

Accepted Answer

Systematic random sampling

Answer

Simple random sampling

Answer

Convenience sampling

Answer

Stratified random sampling

Question 9

The ability of a test to identify correctly those who do not have the disease is called its

Accepted Answer

Specificity

Answer

Sensitivity

Answer

Positive predictive value

Answer

Negative predictive value

Question 10

In a normal curve, how much per cent of the values will be included in the area between two standard deviations on either side of the mean (X ± 2σ) ?

Accepted Answer

95.4

Answer

68.3

Answer

90.4

Answer

99.7

Biostatistics — MCQs

Biostatistics — MCQs

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