Biostatistics — MCQs

Biostatistics Indian Medical PG Practice Questions and MCQs

Question 851: Which of the following statements about the population pyramid of India is incorrect?

A. India has narrow apex
B. Developing countries have bulge in the center
C. India has narrow base (Correct Answer)
D. India has broad base

Explanation: ***Correct Answer: India has narrow base*** - A **narrow base** in a population pyramid indicates a **low birth rate** and a small proportion of young people. - This statement is **INCORRECT for India**, as India's population pyramid has a **broad base** due to high birth rates and a large proportion of children and young people. - This is the correct answer because the question asks for the incorrect statement. *Incorrect Option: India has narrow apex* - A **narrow apex** signifies a **smaller proportion of older individuals**, indicating lower life expectancy. - This is TRUE for India's population pyramid, making it an incorrect answer choice. *Incorrect Option: Developing countries have bulge in the center* - A **bulge in the center** represents a larger cohort of working-age adults in developing countries undergoing demographic transition. - This reflects improvements in childhood survival and declining (but still substantial) birth rates. - This is TRUE, making it an incorrect answer choice. *Incorrect Option: India has broad base* - A **broad base** indicates a **high birth rate** and large proportion of young children in the population. - This is TRUE and characteristic of India's population structure, making it an incorrect answer choice.

Question 852: Which of the following statements is true for a left-skewed distribution?

A. Mean = Median
B. Mean>Mode
C. Median > Mean (Correct Answer)
D. Mean < Mode

Explanation: ***Median > Mean*** - In a **left-skewed distribution**, the bulk of the data is on the right, and the tail extends to the left, pulling the **mean** towards the lower values. - This pull results in the **mean** being less than the **median**, which is less affected by extreme values in the tail. *Mean = Median* - This relationship holds true for a **symmetrical distribution**, such as a **normal distribution**, where the data is evenly distributed around the center. - In a **skewed distribution**, the mean and median will diverge due to the presence of outliers or extreme values on one side. *Mean>Mode* - This statement is characteristic of a **right-skewed distribution**, where the tail extends to the right, pulling the **mean** to a higher value than the **mode**. - In a right-skewed distribution, typically **mode < median < mean**. *Mean < Mode* - This statement indicates that the **mode** (the most frequent value) is greater than the **mean**, which is not a defining characteristic of a left-skewed distribution. - While it can occur, the primary relationship for left-skewness is **mean < median**.

Question 853: In pediatric growth assessment, what is the typical relationship observed between height and weight in healthy children?

A. Negative Correlation
B. No Correlation
C. Inverse Relationship
D. Positive Correlation (Correct Answer)

Explanation: ***Positive Correlation*** - In healthy children, as **height increases**, **weight generally also increases** in a predictable pattern, demonstrating a **positive correlation** between these two variables. - This is a fundamental aspect of normal pediatric growth, where both height and weight increase together as children develop. - The **correlation coefficient** between height and weight in healthy children is typically **strong and positive** (r > 0.7). *Negative Correlation* - A **negative correlation** would imply that as height increases, weight decreases, which contradicts normal growth patterns in healthy children. - This relationship might be observed in certain pathological conditions (e.g., severe malnutrition with stunting) but is not characteristic of normal development. *No Correlation* - Stating **no correlation** would mean that changes in height have no predictable linear relationship with changes in weight, which contradicts well-established growth data. - Height and weight are both key anthropometric indicators that are inherently linked during normal growth. *Inverse Relationship* - An **inverse relationship** is synonymous with a negative correlation, suggesting that as one variable increases, the other decreases. - This is incorrect for normal pediatric growth, where height and weight generally trend upwards together throughout childhood.

Question 854: What does a highly sensitive test imply about its false negative rate?

A. High false positive rate
B. Low false negative rate (Correct Answer)
C. High true negative rate
D. High true positive rate

Explanation: ***Low false negative rate*** - A highly **sensitive test** is good at identifying true positives, meaning it correctly identifies most people who have the disease. - Sensitivity = TP/(TP+FN), so high sensitivity mathematically means few false negatives. - This characteristic directly translates to a **low false negative rate**, as few people with the disease will be missed. *High false positive rate* - A high **false positive rate** relates to **specificity**, not sensitivity. - False positive rate = FP/(FP+TN), which measures how many healthy people are incorrectly identified as diseased. - While some sensitive tests may have lower specificity (higher FP rate), this is not a direct implication of high sensitivity. *High true negative rate* - A high **true negative rate** is a characteristic of a highly **specific** test, which correctly identifies people who do **not** have the disease. - True negative rate = TN/(TN+FP) = Specificity. - **Sensitivity** and **specificity** are independent measures, so high sensitivity does not imply a high true negative rate. *High true positive rate* - High **true positive rate** is actually another term for high sensitivity (Sensitivity = TPR = TP/(TP+FN)). - While this is true of a sensitive test, the question specifically asks about the implication for the **false negative rate**. - The **most direct answer** regarding false negatives is "low false negative rate" rather than describing the true positive rate.

Question 855: Correlation between height and weight is measured by?

A. Coefficient of variation
B. Range of variation
C. Correlation coefficient (Correct Answer)
D. None of the options

Explanation: ***Correlation coefficient*** - The **correlation coefficient** specifically measures the strength and direction of a **linear relationship** between two variables, such as height and weight. - A positive coefficient indicates that as one variable increases, the other tends to increase, reflecting their interconnectedness. *Coefficient of variation* - The **coefficient of variation (CV)** is a measure of **relative variability** or dispersion, indicating the extent of variability in relation to the mean. - It defines how much dispersion exists in data relative to the mean, but does not describe the relationship between two different variables. *Range of variation* - The **range of variation** simply describes the difference between the **maximum and minimum values** within a single dataset. - It provides information about the spread of a single variable but does not measure any **relationship between two different variables**. *None of the options* - This option is incorrect because the **correlation coefficient** is indeed the appropriate statistical measure for assessing the relationship between height and weight.

Question 856: An investigator wants to know the similarity of the mean peak flow of expiratory rates among non-smokers, light smokers, moderate smokers, and heavy smokers. Which statistical test of significance is appropriate?

A. One way ANOVA (Correct Answer)
B. Two way ANOVA
C. Student-t test
D. Chi square test

Explanation: ***One way ANOVA*** - This test is appropriate for comparing the means of **three or more independent groups** (non-smokers, light, moderate, heavy smokers) on a **single quantitative dependent variable** (peak flow of expiratory rates). - It determines if there's a statistically significant difference between the means of these groups, indicating at least one group mean is different from the others. *Two way ANOVA* - This test is used when there are **two independent categorical variables** (factors) influencing a single continuous dependent variable. - In this scenario, there is only one independent categorical variable (smoking status) with multiple levels. *Student-t test* - The Student-t test is used to compare the means of **only two groups**. - Since this question involves comparing the means of four groups of smokers, a t-test would not be appropriate. *Chi square test* - The Chi-square test is used for analyzing the association between **two categorical variables**. - Here, one variable (peak flow) is continuous, making the Chi-square test unsuitable.

Question 857: What is the most appropriate statistical test to test the statistical significance of the change in blood cholesterol levels after a month's treatment with atorvastatin?

A. Paired t-test (Correct Answer)
B. Unpaired or independent t-test
C. Analysis of variance
D. Chi-square test

Explanation: ***Paired t-test*** * A **paired t-test** is appropriate when comparing two means from the **same group of subjects** measured at two different time points (before and after treatment). * In this scenario, a single group's blood cholesterol levels are measured *before* and *after* atorvastatin treatment, making the observations dependent. *Unpaired or independent t-test* * An **unpaired t-test** is used to compare the means of two *independent* groups. * It would be used, for instance, if cholesterol levels were being compared between a group receiving atorvastatin and a separate control group. *Analysis of variance* * **Analysis of variance (ANOVA)** is used to compare **three or more means**. * It would be appropriate if there were multiple treatment groups or multiple time points for comparison beyond just two. *Chi-square test* * The **Chi-square test** is used to examine the association between **categorical variables**. * It would not be suitable here, as blood cholesterol level is a continuous numerical variable, not a categorical one.

Question 858: For testing the statistical significance of the difference in heights among different groups of school children, which statistical test would be most appropriate?

A. Student's t test
B. chi-square test
C. Paired 't' test
D. ANOVA (Correct Answer)

Explanation: ***ANOVA (Analysis of Variance)*** - **ANOVA** is used to compare the means of **three or more independent groups** simultaneously. In this scenario, you are comparing heights across "different groups" of school children, implying more than two groups. - It tests whether there are any significant differences between the means of these groups, using the **F-statistic**. *Student's t test* - The **Student's t-test** is designed to compare the means of **only two groups**. It would be inappropriate for comparing more than two groups. - Applying multiple t-tests for several groups would increase the risk of **Type I error** (false positive). *chi-square test* - The **chi-square test** is used for analyzing **categorical data** (frequencies or proportions), not for comparing means of continuous data like height. - It determines if there is a significant association between two categorical variables. *Paired 't' test* - A **paired t-test** is used when comparing the means of two related groups or when measurements are taken from the **same subjects at two different times** (e.g., before and after an intervention). - This scenario involves independent groups of children, not paired or repeated measures.

Question 859: What is the 95% confidence interval for the intraocular pressure (IOP) in the 400 people, given a mean of 25 mm Hg and a standard deviation of 10 mm Hg?

A. 22-28
B. 23-27
C. 21-29
D. 24-26 (Correct Answer)

Explanation: ***24-26*** - This is the correct 95% confidence interval calculated using the formula: **mean ± (Z-score × standard error of the mean)**. - For a 95% confidence interval, the **Z-score is 1.96**. - The **standard error of the mean (SEM)** = standard deviation / √(sample size) = 10 / √400 = 10 / 20 = **0.5**. - Therefore: 25 ± (1.96 × 0.5) = 25 ± 0.98 = **24.02 to 25.98**, which rounds to **24-26**. *22-28* - This interval is too wide for a 95% confidence interval with the given parameters. - An interval of ±3 would correspond to a Z-score of 3/0.5 = 6, which is far beyond the **1.96 required for 95% confidence**. - This would represent a much higher confidence level (>99.9%). *23-27* - This interval is slightly too wide, implying a larger margin of error than calculated. - A range of ±2 would require a Z-score of 2/0.5 = 4 times the SEM, which **overestimates the 95% confidence interval**. - This would correspond to approximately 99.99% confidence. *21-29* - This interval is significantly too wide for a 95% confidence interval. - An interval of ±4 would require a Z-score of 4/0.5 = 8 times the SEM, which would correspond to an **extremely high confidence level** (virtually 100%). - This dramatically exceeds what is needed for 95% confidence.

Question 860: This study found a correlation coefficient of +0.7 between self-reported work satisfaction and life expectancy in a random sample of 5,000 corporate workers, with a p-value of 0.01. This means that:

A. Correlation does not imply that 70% of people who enjoy work shall live longer.
B. Correlation coefficient of +0.7 indicates a moderate positive relationship, not a percentage.
C. Work satisfaction is moderately associated with life expectancy.
D. Strong statistically significant (+) association between work satisfaction and life expectancy. (Correct Answer)

Explanation: ***Strong statistically significant (+) association between work satisfaction and life expectancy.*** - A **correlation coefficient** of **+0.7** indicates a strong positive linear relationship between two variables. - A **p-value of 0.01** (which is less than 0.05) indicates that the observed association is **statistically significant**, meaning it's unlikely to have occurred by chance. *Correlation does not imply that 70% of people who enjoy work shall live longer.* - A **correlation coefficient** is a measure of the strength and direction of a linear relationship, not a percentage of a population. - Saying "70% of people" implies a proportional relationship, which is an incorrect interpretation of a correlation coefficient. *Correlation coefficient of +0.7 indicates a moderate positive relationship, not a percentage.* - A correlation coefficient of **+0.7** is generally considered a **strong positive relationship**, rather than moderate. - This statement correctly clarifies that a correlation coefficient is not a percentage, but mischaracterizes the strength of the given correlation. *Work satisfaction is moderately associated with life expectancy.* - A **correlation coefficient of +0.7** signifies a **strong positive association**, not a moderate one. - The term "moderately" underestimates the strength of the relationship indicated by a correlation coefficient of 0.7.

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Collection and Presentation of Data

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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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