Data analysis and interpretation using Student’s t-test is essential for B.Pharm students analyzing experimental and clinical data. This concise introduction covers core concepts: hypothesis testing, one-sample, independent and paired t-tests, assumptions (normality, equal variances), degrees of freedom, t-statistic, p-value, confidence intervals, effect size (Cohen’s d), and choosing Welch’s correction. Understanding calculation steps, result interpretation, and common pitfalls prepares students for pharmacology, formulation studies, and biostatistics. Practical emphasis on sample size, statistical power, and software implementation enhances reproducibility and evidence-based decisions in pharmaceutical research. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. Which t-test is most appropriate to compare mean systolic blood pressure before and after administration of a drug in the same group of patients?
- Independent two-sample t-test
- One-sample t-test
- Paired t-test
- Chi-square test
Correct Answer: Paired t-test
Q2. What does the t-statistic measure in a Student’s t-test?
- The probability of the null hypothesis being true
- The standardized difference between sample mean(s) and population mean under the null
- The correlation between two variables
- The sample variance only
Correct Answer: The standardized difference between sample mean(s) and population mean under the null
Q3. Which assumption is required for the validity of the classical Student’s t-test?
- Large sample size only
- Normal distribution of the data (or approximately normal) in each group
- Categorical outcome variables
- Homogeneity of regression slopes
Correct Answer: Normal distribution of the data (or approximately normal) in each group
Q4. When should Welch’s t-test be used instead of the pooled Student’s t-test?
- When sample sizes are equal and variances are equal
- When variances between two groups are unequal
- When comparing more than two groups
- When data are categorical
Correct Answer: When variances between two groups are unequal
Q5. What is the null hypothesis for an independent two-sample t-test comparing mean drug absorption between groups A and B?
- Mean absorption in A is greater than in B
- Mean absorption in A is less than in B
- Mean absorption in A equals mean absorption in B
- Variances of absorption in A and B are equal
Correct Answer: Mean absorption in A equals mean absorption in B
Q6. How are degrees of freedom (df) calculated for a simple two-sample pooled t-test with sample sizes n1 and n2?
- df = n1 + n2
- df = n1 + n2 – 1
- df = n1 + n2 – 2
- df = (n1 – 1)(n2 – 1)
Correct Answer: df = n1 + n2 – 2
Q7. Which result indicates statistical significance at alpha = 0.05 in a two-tailed t-test?
- p-value = 0.08
- p-value = 0.05 exactly
- p-value = 0.03
- p-value = 0.10
Correct Answer: p-value = 0.03
Q8. What does a 95% confidence interval for mean difference that does not include zero imply?
- The sample means are identical
- The mean difference is not statistically significant
- The mean difference is statistically significant at the 5% level
- The assumption of normality is violated
Correct Answer: The mean difference is statistically significant at the 5% level
Q9. Which t-test compares a sample mean to a known population mean?
- Paired t-test
- Two-sample t-test
- One-sample t-test
- ANOVA
Correct Answer: One-sample t-test
Q10. What is Cohen’s d used for in the context of t-tests?
- Estimating sample size only
- Measuring effect size (standardized mean difference)
- Testing equality of variances
- Adjusting p-values for multiple comparisons
Correct Answer: Measuring effect size (standardized mean difference)
Q11. In a paired t-test, what is analyzed to compute the test statistic?
- The sum of all observations
- The differences between paired observations
- The ratio of variances
- The correlation coefficient
Correct Answer: The differences between paired observations
Q12. Which choice best describes a one-tailed t-test?
- Tests for any difference between means, either direction
- Tests for a difference in a specified direction only
- Used only when variances are equal
- Equivalent to a two-sample F-test
Correct Answer: Tests for a difference in a specified direction only
Q13. When sample size is small, which condition makes the t-test more robust?
- Severe skewness in data
- Moderate departures from normality with symmetric distribution
- Presence of multiple outliers
- Highly unequal sample sizes and variances
Correct Answer: Moderate departures from normality with symmetric distribution
Q14. Which alternative test is appropriate if t-test assumptions are violated and data are ordinal?
- Paired t-test
- Mann–Whitney U test (Wilcoxon rank-sum)
- Two-sample pooled t-test
- Z-test
Correct Answer: Mann–Whitney U test (Wilcoxon rank-sum)
Q15. How does increasing sample size affect the t-statistic, assuming the observed mean difference remains constant?
- It tends to decrease the t-statistic
- It tends to increase the t-statistic (improves precision)
- It has no effect on t-statistic
- It always makes p-value larger
Correct Answer: It tends to increase the t-statistic (improves precision)
Q16. Which value of t (absolute) corresponds to stronger evidence against the null hypothesis?
- Smaller absolute t
- t near zero
- Larger absolute t
- Negative t only
Correct Answer: Larger absolute t
Q17. In pharmacokinetic studies comparing Cmax between two formulations with unequal variances, which test is recommended?
- Pooled Student’s t-test
- Welch’s t-test
- One-sample t-test
- Chi-square test
Correct Answer: Welch’s t-test
Q18. Which of the following affects the width of a confidence interval for a mean difference?
- Sample size, variability, and chosen confidence level
- Only the p-value
- Only the mean of the combined samples
- Only the number of groups
Correct Answer: Sample size, variability, and chosen confidence level
Q19. What is the primary consequence of multiple t-tests without correction when comparing many groups?
- Decreased power
- Increased type I error rate (false positives)
- Guaranteed normality
- Lowered sample variance
Correct Answer: Increased type I error rate (false positives)
Q20. Which step is first when performing a t-test?
- Calculate Cohen’s d
- State null and alternative hypotheses
- Report p-value
- Compute degrees of freedom
Correct Answer: State null and alternative hypotheses
Q21. How is the pooled standard deviation used in the two-sample pooled t-test?
- As a weighted average of group standard deviations to estimate common variance
- As the maximum of the two variances
- As the geometric mean of variances
- It is not used in pooled t-test
Correct Answer: As a weighted average of group standard deviations to estimate common variance
Q22. Which p-value interpretation is correct?
- p-value is the probability that the null hypothesis is true
- p-value is the probability of observing the data (or more extreme) assuming the null hypothesis is true
- p-value indicates effect size directly
- p-value equals alpha multiplied by power
Correct Answer: p-value is the probability of observing the data (or more extreme) assuming the null hypothesis is true
Q23. Which software output is most useful for deciding between pooled t-test and Welch’s t-test?
- Levene’s test or variance equality test
- Histogram of individual observations only
- Correlation matrix
- ANOVA table without variance info
Correct Answer: Levene’s test or variance equality test
Q24. For small samples, why is the t-distribution used instead of the normal distribution?
- T-distribution has heavier tails to account for extra uncertainty due to estimating the population standard deviation
- T-distribution has lighter tails and narrower center
- Normal distribution cannot be used at all
- T-distribution is discrete
Correct Answer: T-distribution has heavier tails to account for extra uncertainty due to estimating the population standard deviation
Q25. Which practice improves the robustness of t-test results in presence of mild non-normality?
- Ignore assumptions and proceed
- Use log transformation or nonparametric tests
- Reduce sample size
- Switch to chi-square test
Correct Answer: Use log transformation or nonparametric tests
Q26. What is the effect of removing outliers on t-test results?
- Always increases p-value
- May change mean, variance, and significance; must be justified and documented
- Has no statistical impact
- Automatically valid without reporting
Correct Answer: May change mean, variance, and significance; must be justified and documented
Q27. Which statement about statistical power in t-tests is true?
- Power decreases with larger effect size
- Power increases with larger sample size and larger effect size
- Power is independent of alpha
- Power equals the p-value
Correct Answer: Power increases with larger sample size and larger effect size
Q28. When interpreting a non-significant t-test (p>0.05), which conclusion is correct?
- The null hypothesis is proven true
- There is insufficient evidence to reject the null; consider power and sample size
- The alternative hypothesis is true
- The data are invalid
Correct Answer: There is insufficient evidence to reject the null; consider power and sample size
Q29. Which approach helps control type I error when making multiple pairwise t-test comparisons?
- Bonferroni correction or other multiplicity adjustments
- Increase alpha for each test
- Ignore p-values and report means only
- Use only one sample in all tests
Correct Answer: Bonferroni correction or other multiplicity adjustments
Q30. Which practical tip is best for reporting t-test results in a B.Pharm research paper?
- Report only p-values without context
- Report test type, t value, degrees of freedom, p-value, confidence interval, and effect size
- Report means only and avoid statistics
- Report raw data without summary statistics
Correct Answer: Report test type, t value, degrees of freedom, p-value, confidence interval, and effect size
I am a Registered Pharmacist under the Pharmacy Act, 1948, and the founder of PharmacyFreak.com. I hold a Bachelor of Pharmacy degree from Rungta College of Pharmaceutical Science and Research. With a strong academic foundation and practical knowledge, I am committed to providing accurate, easy-to-understand content to support pharmacy students and professionals. My aim is to make complex pharmaceutical concepts accessible and useful for real-world application.
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