Least significant difference (LSD) method MCQs With Answer

Least significant difference (LSD) method MCQs With Answer provides B. Pharm students a focused review of the LSD post-hoc test used after ANOVA for pairwise comparisons. This introduction covers key concepts such as pooled error variance, MSE, t-critical values, significance level (alpha), protection by overall F-test, and practical applications in pharmacology, bioassay, formulation studies and experimental design. Understanding assumptions, limitations (inflated Type I error), calculation formula and interpretation of results prepares students for data analysis in drug research. These targeted MCQs reinforce theory, calculations, software output interpretation and decision-making for laboratory studies. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. What is the primary purpose of the Least Significant Difference (LSD) method?

• To test for normality of residuals
• To perform pairwise comparisons after a significant ANOVA
• To replace ANOVA for overall group differences
• To estimate sample size for experiments

Correct Answer: To perform pairwise comparisons after a significant ANOVA

Q2. Which statistic is central to the LSD formula for pairwise mean comparisons?

• Mean square between groups (MSB)
• Mean square error (MSE)
• Coefficient of variation (CV)
• Standard error of the mean (SEM) only

Correct Answer: Mean square error (MSE)

Q3. The formula for LSD (two-sample equal n) commonly includes which of these components?

• t-critical × sqrt(2 × MSE / n)
• z-critical × sqrt(MSB / n)
• F-critical × sqrt(MSE / 2n)
• Chi-square × sqrt(MSE / n)

Correct Answer: t-critical × sqrt(2 × MSE / n)

Q4. When is it appropriate to apply Fisher’s LSD without adjustment?

• Always, regardless of ANOVA outcome
• Only after a significant overall F-test in ANOVA
• Only for non-parametric data
• When sample sizes vary widely

Correct Answer: Only after a significant overall F-test in ANOVA

Q5. Which assumption is NOT required for valid LSD comparisons?

• Independence of observations
• Homogeneity of variances across groups
• Normality of residuals
• Equal group means before testing

Correct Answer: Equal group means before testing

Q6. What is a main limitation of the LSD method in multiple comparisons?

• It is overly conservative and misses true differences
• It inflates Type I error rate when many comparisons are made
• It requires extremely large sample sizes
• It only works for two-group experiments

Correct Answer: It inflates Type I error rate when many comparisons are made

Q7. In a pharmacology bioassay with four treatments (n per group = 6), which degrees of freedom are used to find t-critical for LSD?

• df = number of treatments – 1
• df = total sample size – number of treatments
• df = total sample size – 1
• df = number of pairwise comparisons

Correct Answer: df = total sample size – number of treatments

Q8. What does “protected LSD” refer to?

• Applying LSD only when overall ANOVA F-test is significant
• Using LSD without checking assumptions
• Using LSD with Bonferroni correction
• Applying LSD before running ANOVA

Correct Answer: Applying LSD only when overall ANOVA F-test is significant

Q9. How does unequal sample size (n) between groups affect the LSD calculation?

• It has no effect; formula is unchanged
• The pooled variance is not estimable
• The LSD uses sqrt(MSE × (1/n1 + 1/n2)) instead of 2/n
• LSD cannot be computed for unequal n

Correct Answer: The LSD uses sqrt(MSE × (1/n1 + 1/n2)) instead of 2/n

Q10. Which post-hoc test is more conservative than LSD for controlling family-wise error?

• Tukey’s HSD
• Unprotected LSD
• Pairwise t-tests without adjustment
• No post-hoc test is more conservative

Correct Answer: Tukey’s HSD

Q11. In LSD, the t-critical value is taken from which distribution?

• Chi-square distribution
• t-distribution with pooled error df
• F-distribution with (k-1, N-k) df
• Normal distribution (z)

Correct Answer: t-distribution with pooled error df

Q12. If MSE = 4, n = 5 per group, and t-critical = 2.571, what is the LSD value for pairwise means?

• 2.571 × sqrt(2 × 4 / 5) = 3.646
• 2.571 × sqrt(4 / 5) = 2.304
• 2.571 × sqrt(2 / 5) = 1.628
• 2.571 × sqrt(8 / 5) = 3.646 (duplicate)

Correct Answer: 2.571 × sqrt(2 × 4 / 5) = 3.646

Q13. In B. Pharm research, a significant LSD difference between formulations indicates what?

• The formulations are clinically equivalent
• There is a statistically significant difference in the measured response
• The experiment must be repeated due to Type II error
• No conclusion can be drawn without Bonferroni correction

Correct Answer: There is a statistically significant difference in the measured response

Q14. Which software output element is essential to compute LSD manually?

• Total sum of squares only
• Mean square error (MSE) and error degrees of freedom
• Group means only
• R-squared value only

Correct Answer: Mean square error (MSE) and error degrees of freedom

Q15. When comparing many treatments, which strategy reduces the risk of inflated Type I error compared to unadjusted LSD?

• Performing only the largest pairwise differences
• Using more liberal alpha (e.g., 0.10)
• Using more conservative post-hoc tests (Tukey, Bonferroni)
• Reducing sample size

Correct Answer: Using more conservative post-hoc tests (Tukey, Bonferroni)

Q16. The LSD method assumes homogeneity of variances. Which test can check this assumption?

• Shapiro-Wilk test
• Levene’s test
• Kaplan-Meier test
• Cochran’s Q for paired data

Correct Answer: Levene’s test

Q17. If ANOVA F-test is not significant, what is the recommended action regarding LSD comparisons?

• Proceed with LSD regardless
• Avoid LSD pairwise tests as they are not protected
• Increase alpha for LSD
• Switch to non-parametric LSD

Correct Answer: Avoid LSD pairwise tests as they are not protected

Q18. For which experimental design is LSD applicable for pairwise comparisons?

• Only completely randomized designs
• Any design analyzed by ANOVA if assumptions met (CRD, RBD, factorial)
• Only paired t-test designs
• Only non-parametric designs

Correct Answer: Any design analyzed by ANOVA if assumptions met (CRD, RBD, factorial)

Q19. Which term describes the pooled estimate of within-group variability used in LSD?

• Between-group variance
• Mean square error (MSE)
• Total variance
• Group variance

Correct Answer: Mean square error (MSE)

Q20. In a bioassay comparing three dose levels, which pairwise result would be declared significant using LSD?

• Difference between means = 0.5 when LSD = 0.8
• Difference between means = 1.2 when LSD = 1.0
• Difference between means = 0.9 when LSD = 1.0
• Difference between means = 0.2 when LSD = 0.15

Correct Answer: Difference between means = 1.2 when LSD = 1.0

Q21. Which phrase best describes Fisher’s LSD compared to family-wise methods?

• More conservative and reduces Type I error
• Less conservative and more powerful but risks inflated Type I error
• Identical in error control to Bonferroni
• Not based on pooled variance

Correct Answer: Less conservative and more powerful but risks inflated Type I error

Q22. In reporting LSD results in a B. Pharm article, which information should be included?

• MSE, df for error, t-critical, LSD value and which comparisons were significant
• Only p-values without test statistics
• Only raw means without error estimates
• Only sample sizes without ANOVA details

Correct Answer: MSE, df for error, t-critical, LSD value and which comparisons were significant

Q23. If researchers apply LSD to exploratory data with many comparisons, what is a common recommendation?

• Report results as confirmatory without caution
• Use LSD and ignore family-wise error
• Label conclusions as exploratory and consider adjustment or replication
• Always prefer LSD over all other methods

Correct Answer: Label conclusions as exploratory and consider adjustment or replication

Q24. Which outcome from an ANOVA justifies conducting LSD tests?

• Non-significant F with p > 0.05
• Significant F with p < alpha
• High R-squared value only
• Significant Levene’s test

Correct Answer: Significant F with p < alpha

Q25. How does the number of treatments (k) affect the number of pairwise comparisons for LSD?

• Number of comparisons = k
• Number of comparisons = k – 1
• Number of comparisons = k(k – 1)/2
• Number of comparisons = 2^k

Correct Answer: Number of comparisons = k(k – 1)/2

Q26. In an ANOVA table, which value is directly used to compute MSE?

• Error sum of squares divided by error df
• Total sum of squares divided by total df
• Between treatments sum of squares divided by treatments df
• R-squared multiplied by variance

Correct Answer: Error sum of squares divided by error df

Q27. When comparing two means with unequal variances, the standard LSD is inappropriate. What is a remedy?

• Ignore variance inequality and proceed
• Use Welch’s t-test or adjust degrees of freedom for unequal variances
• Always increase sample size to equalize variances
• Use LSD with pooled variance regardless

Correct Answer: Use Welch’s t-test or adjust degrees of freedom for unequal variances

Q28. Which of the following best describes the role of LSD in factorial experiments?

• LSD cannot be used in factorial experiments
• LSD can compare main effect levels or interaction cell means after appropriate ANOVA
• LSD replaces interaction terms in the model
• LSD is used to test block effects only

Correct Answer: LSD can compare main effect levels or interaction cell means after appropriate ANOVA

Q29. If the pooled MSE decreases while other factors remain constant, what happens to the LSD value?

• LSD increases
• LSD decreases
• LSD remains unchanged
• LSD becomes infinite

Correct Answer: LSD decreases

Q30. Which interpretation is correct if a pairwise mean difference exceeds the LSD threshold?

• The difference is statistically significant at the chosen alpha
• The difference is not statistically significant
• The F-test must be non-significant
• No interpretation is possible without Bonferroni correction

Correct Answer: The difference is statistically significant at the chosen alpha

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