5.07c-f Single-sample, paired-sample and rank-sum tests Quiz: OCR Further Maths, Unit 2

The 20 questions

1. Which population parameter is tested in a standard single-sample sign test?

   • Standard deviation
   • Population mean
   • Population variance
   • Population median

2. What assumption must be met to use a Wilcoxon signed-rank test?

   • Equal variances
   • Symmetric distribution
   • Normal distribution
   • Linear relationship

3. How are zero differences handled when carrying out a paired Wilcoxon signed-rank test?

   • Keep as zero
   • Discard them
   • Assign rank one
   • Split equal ranks

4. In a sign test with 12 positive and 4 negative differences, what is $n$?

   • 12
   • 4
   • 8
   • 16

5. In a single-sample sign test, what does the test statistic S represent?

   • Number of positive signs
   • Total sample size
   • Difference in medians
   • Sum of positive ranks

6. For differences +3, +5, -2, +1, -4, +6, what is the sign test statistic $S$?

   • 2
   • 4
   • 6
   • 9

7. How are absolute differences ranked in the Wilcoxon signed-rank test?

   • In descending order
   • By raw value
   • By sign group
   • In ascending order

8. If the ranks of positive differences are 2, 4, and 7, what is $T_+$?

   • 13
   • 7
   • 3
   • 28

9. What is the maximum possible sum of ranks for $n = 6$ non-zero differences?

   • 15
   • 21
   • 36
   • 6

10. Which test is used to compare medians of two independent continuous samples?

    • Wilcoxon signed-rank test
    • Paired sign test
    • Single-sample t-test
    • Wilcoxon rank-sum test

11. Two independent samples have sizes $m = 4$ and $n = 6$. How many total ranks are given?

    • 24
    • 5
    • 10
    • 2

12. Which distribution approximates the test statistic for large sample non-parametric tests?

    • Binomial distribution
    • Normal distribution
    • Poisson distribution
    • Exponential distribution

13. What continuity correction is used when approximating a discrete rank statistic using a normal distribution?

    • 0.25
    • 0.1
    • 0.5
    • 1.0

14. For a Wilcoxon signed-rank test with $n = 10$, what is the expected value $\text{E}(T_+)$?

    • 5
    • 55
    • 27.5
    • 25

15. What does the null hypothesis state in a two-sample Wilcoxon rank-sum test?

    • Identical population distributions
    • Different population medians
    • Normally distributed data
    • Equal population variances

16. In a Wilcoxon rank-sum test, sample 1 has $n_1 = 4$. What is the minimum possible rank sum?

    • 20
    • 10
    • 4
    • 15

17. In a signed-rank test with $n = 8$, the sum of positive ranks is 10. What is $T_-$?

    • 26
    • 36
    • 28
    • 18

18. Before ranking data in a paired-sample Wilcoxon test, what calculation is performed first?

    • Square all values
    • Calculate sample means
    • Combine both samples
    • Calculate paired differences

19. Why choose a non-parametric test over a parametric equivalent test?

    • Higher statistical power
    • Unknown underlying distribution
    • Data is categorical
    • Larger sample size

20. What is the variance $\text{Var}(T_+)$ for a Wilcoxon signed-rank test with $n = 6$?

    • 22.75
    • 10.5
    • 21
    • 15.75

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