Biostatistics Practice Questions

Q: All are true about the Chi-Square test except?

The lowest expected frequency should be less than 5.. ### Explanation The **Chi-Square ($\chi^2$) test** is a fundamental statistical tool used in medical research to analyze categorical data. **1. Why Option D is the correct answer (The Exception):** For a Chi-Square test to be valid, a key assumption is that the **expected frequency in any cell should not be less than 5**. If the expected frequency is less than 5, the test becomes inaccurate because the distribution no longer approximates the Chi-Square distribution. In such cases, **Fisher’s Exact Test** is preferred (for $2 \times 2$ tables) or **Yates’ Correction** is applied. **2. Analysis of Incorrect Options:** * **Option A:** Chi-Square is indeed a **non-parametric test** because it does not assume a normal distribution of the underlying population and deals with frequencies rather than mean/standard deviation. * **Option B:** It is the primary test used to assess the **association between qualitative (categorical) variables** (e.g., comparing the incidence of a disease between smokers and non-smokers). * **Option C:** Like most statistical tests, the validity of the Chi-Square test relies on the assumption that the **sample is randomly selected** and observations are independent. **3. NEET-PG High-Yield Pearls:** * **Degrees of Freedom (df):** Calculated as $(r-1) \times (c-1)$, where $r$ = rows and $c$ = columns. * **Null Hypothesis ($H_0$):** Assumes there is no association between the variables. * **Fisher’s Exact Test:** Use this instead of Chi-Square when the sample size is very small or expected cell frequency is $<5$. * **McNemar’s Test:** A variation of Chi-Square used for **paired data** (e.g., before-and-after studies).

Q: Which measure of central tendency is best determined for the following set of data: 18, 20, 22, 24, 26, 28, 30?

Mean. **Explanation:** The correct answer is **Mean (Arithmetic Average)**. **1. Why Mean is the Correct Choice:** The provided data set (18, 20, 22, 24, 26, 28, 30) follows a **Normal (Symmetrical) Distribution**. The values are evenly spaced with a constant difference of 2, and there are no extreme values or outliers. In a normal distribution, the **Mean** is the most preferred and powerful measure of central tendency because it utilizes every value in the data set and is mathematically stable for further statistical analysis (like calculating Standard Deviation). **2. Why Other Options are Incorrect:** * **Median:** While the median (24) is also accurate here, it is primarily the "measure of choice" for **skewed distributions** or data containing outliers (e.g., income levels or incubation periods), as it is not affected by extreme values. * **Mode:** The mode is the most frequently occurring value. In this data set, every value appears only once (no mode). Mode is best suited for **nominal/categorical data** (e.g., most common blood group). **3. High-Yield Clinical Pearls for NEET-PG:** * **Normal Distribution:** Mean = Median = Mode. The Mean is the best measure. * **Skewed Distribution:** The **Median** is the best measure of central tendency. * **Qualitative Data:** The **Mode** is the best measure. * **Most Sensitive to Outliers:** The Mean (it shifts towards the tail). * **Least Sensitive to Outliers:** The Mode and Median. * **Relationship in Positive Skew:** Mean > Median > Mode. * **Relationship in Negative Skew:** Mean < Median < Mode.

Q: What does it indicate when the highest mean and lowest mode are observed?

Positive skewing. ### Explanation In biostatistics, the relationship between the measures of central tendency (Mean, Median, and Mode) determines the shape of the distribution curve. **1. Why Positive Skewing is Correct:** In a **Positively Skewed Distribution** (also known as Right-skewed), the tail of the distribution extends toward the higher values on the right side. * The **Mode** represents the peak of the curve (the most frequent value) and remains at the lowest numerical value. * The **Mean** is highly sensitive to extreme values (outliers) in the tail, which pulls it toward the right. * Therefore, the relationship is: **Mean > Median > Mode**. Since the Mean is the highest and the Mode is the lowest, this perfectly describes positive skewing. **2. Why the Other Options are Incorrect:** * **Negative Skewing (Left-skewed):** The tail extends toward the lower values. Here, the Mean is pulled down by outliers, resulting in **Mode > Median > Mean**. The Mean is the lowest value, not the highest. * **Normal/Symmetrical Distribution:** In a perfectly symmetrical bell-shaped curve, the Mean, Median, and Mode are all equal (**Mean = Median = Mode**). There is no "highest" or "lowest" value among them. **3. Clinical Pearls & High-Yield Facts for NEET-PG:** * **Memory Aid:** In **P**ositive skew, the Mean is more **P**ositive (greater). In **N**egative skew, the Mean is more **N**egative (smaller). * **Median:** Always stays in the middle in both types of skewed distributions. It is the best measure of central tendency for skewed data. * **Sensitivity:** The Mean is the most affected by outliers; the Mode is the least affected. * **Example:** Income distribution in a population or incubation periods of most infectious diseases usually follow a positive skew.

Q: What is the definition of statistical power?

The ability to reject a false null hypothesis.. **Statistical Power** is a fundamental concept in clinical research that measures a study’s ability to detect an effect (or difference) when one truly exists. ### Why Option B is Correct Statistical Power (represented as **1 – β**) is the probability that a test will correctly **reject a false null hypothesis**. In clinical terms, if a new drug is truly effective (the null hypothesis is false), power is the likelihood that the study will yield a statistically significant result confirming that effectiveness. A power of 0.80 (80%) is generally considered the minimum acceptable level for clinical trials. ### Explanation of Incorrect Options * **Option A:** Rejecting a *true* null hypothesis is a **Type I Error (α)**. This is a "false positive," where you claim a difference exists when it actually does not. * **Option C:** Correctly accepting (or failing to reject) a *true* null hypothesis is known as **Confidence Level (1 – α)**. * **Option D:** Accepting (failing to reject) a *false* null hypothesis is a **Type II Error (β)**. This is a "false negative," where the study fails to detect a real effect. ### NEET-PG High-Yield Pearls * **The Relationship:** Power is inversely related to Type II error (**Power = 1 – β**). As the risk of a false negative decreases, the power of the study increases. * **Factors Increasing Power:** 1. **Increased Sample Size (N):** The most common way to boost power. 2. **Increased Effect Size:** Larger differences are easier to detect. 3. **Decreased Standard Deviation:** Less "noise" in the data makes the "signal" clearer. 4. **Increased Alpha (α):** Though rarely done, increasing the significance level (e.g., from 0.05 to 0.10) increases power.

Q: Observing alcohol intake over 20 years and its association with the occurrence of liver disease is an example of what type of study?

Cohort study. ### Explanation **Why Cohort Study is Correct:** A **Cohort study** is a longitudinal, observational study that starts with a group of individuals (the cohort) who are currently free of the disease but differ in their exposure to a potential risk factor. In this scenario, the researchers start with people based on their **exposure** (alcohol intake) and follow them forward in time (**prospective**) for 20 years to observe the **outcome** (liver disease). The key feature here is the direction of inquiry: **Exposure $\rightarrow$ Outcome**. This allows for the calculation of Incidence and Relative Risk (RR). **Why Other Options are Incorrect:** * **B. Case-control study:** This study starts with the outcome (people who already have liver disease) and looks backward in time (**retrospective**) to find exposures. The direction is **Outcome $\rightarrow$ Exposure**. * **C. Ecological study:** This uses **populations or groups** as the unit of study (e.g., comparing alcohol sales in different countries to liver cirrhosis rates) rather than tracking specific individuals over time. * **D. Randomized Controlled Trial (RCT):** This is an **experimental** study where the investigator intervenes (e.g., giving a drug). It would be unethical to intentionally assign individuals to consume alcohol to see if they develop liver disease. **NEET-PG High-Yield Pearls:** * **Incidence:** Can only be calculated from Cohort studies. * **Best for Rare Exposures:** Cohort Study. * **Best for Rare Diseases:** Case-control Study. * **Temporal Association:** Cohort studies are the best observational design to establish that the exposure preceded the disease (Temporality is the strongest Hill’s Criterion). * **Attrition Bias:** The biggest challenge in long-term (20-year) cohort studies is "loss to follow-up."

Q: If the coefficient of correlation between height and weight is 2.6, what is true?

The calculation of the coefficient is wrong. ### Explanation **1. Why the Correct Answer is Right:** The **Pearson Correlation Coefficient (r)** is a statistical measure that quantifies the strength and direction of a linear relationship between two continuous variables. A fundamental mathematical property of the correlation coefficient is that its value **must always lie between -1 and +1** ($-1 \leq r \leq +1$). * **r = +1:** Perfect positive correlation. * **r = -1:** Perfect negative correlation. * **r = 0:** No linear correlation. In this question, the value provided is **2.6**, which exceeds the maximum possible limit of +1. Therefore, such a value is mathematically impossible, indicating that the calculation is incorrect. **2. Why the Other Options are Wrong:** * **Option A (Positive correlation):** While a positive number usually indicates a positive correlation, the value must be $\leq 1$. Since 2.6 is invalid, we cannot conclude the nature of the correlation. * **Option B (No association):** No association is represented by $r = 0$. * **Option C (Negative correlation):** A negative correlation is represented by a value between 0 and -1. **3. Clinical Pearls & High-Yield Facts for NEET-PG:** * **Coefficient of Determination ($r^2$):** This is the square of the correlation coefficient. it represents the proportion of variance in one variable that is predictable from the other. (e.g., if $r = 0.6$, then $r^2 = 0.36$ or 36%). * **Independence of Units:** The value of 'r' is independent of the units of measurement (e.g., whether height is in cm or inches, 'r' remains the same). * **Scatter Diagram:** The best visual method to represent correlation. * **Regression vs. Correlation:** Correlation measures the *strength* of association, while Regression measures the *nature* of the relationship to predict the value of a dependent variable.

Q: Contraceptive efficacy is measured by?

Pearl index and Life table analysis. ### Explanation **1. Why the Correct Answer is Right:** Contraceptive efficacy refers to the ability of a method to prevent pregnancy under ideal or typical conditions. It is measured using two primary statistical tools: * **Pearl Index:** This is the most common method. It calculates the number of accidental pregnancies per 100 woman-years of exposure. * *Formula:* (Total accidental pregnancies × 1200) / (Total months of exposure). * **Life Table Analysis:** This is considered more accurate than the Pearl Index. It calculates the "failure rate" at specific intervals (e.g., at 6 months, 12 months). It accounts for "drop-outs" (people who stop using the method for reasons other than pregnancy), providing a more cumulative and realistic risk assessment over time. **2. Why Other Options are Wrong:** * **Option A (Pearl Index only):** While widely used, it is not the *only* measure. It fails to account for the fact that failure rates often decrease the longer a couple uses a method (the "selection effect"). * **Options C & D (Couple Protection Rate):** The **Couple Protection Rate (CPR)** is a management indicator used to monitor the performance of Family Welfare Programmes. It measures the percentage of eligible couples effectively protected against childbirth by various methods. It is a measure of **program coverage**, not the biological efficacy of the contraceptive itself. **3. High-Yield Facts for NEET-PG:** * **Pearl Index of Common Methods:** * No Method: 80–90 * OCPs (Typical use): 9 * Copper T 380A: 0.8 * Vasectomy: 0.1 (Most effective) * **Net Reproduction Rate (NRR):** The goal of the National Health Policy is to achieve NRR = 1 (replacement level fertility). * **Eligible Couple:** A currently married couple where the wife is in the reproductive age group (15–49 years).

Question 1

All are true about the Chi-Square test except?

Accepted Answer

The lowest expected frequency should be less than 5.

Answer

It is a non-parametric test of significance.

Answer

It is used to test the significance of association between two or more qualitative characteristics.

Answer

The sample must be randomly selected.

Question 2

Which measure of central tendency is best determined for the following set of data: 18, 20, 22, 24, 26, 28, 30?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

None

Question 3

Which of the following is NOT true about a cohort study?

Accepted Answer

Is time-consuming.

Answer

Requires a large number of subjects.

Answer

Is expensive.

Answer

Is suitable for studying common diseases.

Question 4

On a given day, a hospital had 50 admissions with about 20 girls and 30 boys. Out of these, 10 girls and 20 boys needed surgery. What is the probability of picking a person requiring surgery?

Accepted Answer

2/5

Answer

1/3

Answer

1/2

Answer

3/5

Question 5

What does it indicate when the highest mean and lowest mode are observed?

Accepted Answer

Positive skewing

Answer

Negative skewing

Answer

Normal distribution

Answer

Symmetrical distribution

Question 6

What is the definition of statistical power?

Accepted Answer

The ability to reject a false null hypothesis.

Answer

The ability to reject a true null hypothesis.

Answer

The ability to accept a true null hypothesis.

Answer

The ability to accept a false null hypothesis.

Question 7

Observing alcohol intake over 20 years and its association with the occurrence of liver disease is an example of what type of study?

Accepted Answer

Cohort study

Answer

Case control study

Answer

Ecological study

Answer

Randomized controlled trial (RCT)

Question 8

If the coefficient of correlation between height and weight is 2.6, what is true?

Accepted Answer

The calculation of the coefficient is wrong

Answer

Positive correlation

Answer

No association

Answer

Negative correlation

Question 9

Contraceptive efficacy is measured by?

Accepted Answer

Pearl index and Life table analysis

Answer

Pearl index only

Answer

Life table analysis and Couple protection rate

Answer

Pearl index and Couple protection rate

Question 10

In a certain population, there were 4050 births in the last one year. There were 50 stillbirths, 50 infants died within 7 days, and 150 died within 28 days. What is the neonatal mortality rate?

Accepted Answer

50

Answer

62.5

Answer

12.5

Answer

49.4

Biostatistics — MCQs

Biostatistics — MCQs

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