An introductory overview of Non-Parametric Tests. Resource taken from the work authored by S K Mangal.

1. Non-Parametric Tests
Unit 5

2. Sign Test Direction of difference between two observations
Hypothesis: increase (p) = decrease (q)
Computation:
No.of +ve(p) = 3
No.of -ve (q) = 1
Decision: Obtained value < or = the critical value → Reject H₀
Before
Treatment
After
Treatment
Direction of
difference
A 15 16 +
B 17 16 -
C 13 17 +
D 18 19 +
z= (X-pn) / √npq

3. When to use Sign Test?
● When you have infinite or undetermined scores
● No precise measurement
● Preliminary check before using other serious stats.
Limitations
● Takes into account only direction not magnitude. Unable to
make use of all available information.
● Less powerful compared to other tests.

4. Wilcoxon sign rank test Repeated-measures design
Hypothesis: Difference between two treatments
Computation:
∑R₊ = 16
∑R₋ =
T
Decision:Obtained value < or = the critical value → Reject H₀
5

5. Mann-Whitney u test Two different samples
Hypothesis: Difference between two groups; ranks in one group
systematically higher/lower than the other.
Critical value: n🇦, n🇧
Computation:
U🇦 = 30
U🇧 =
U
Decision: Obtained value < or =
the critical value → Reject H₀
6

6. Kruskal wallis test Two or more separate samples
Hypothesis: Difference between any groups; ranks in one group
systematically higher/lower than the other.
Critical value: df = k-1
Computation:
Decision: Obtained value < or = the critical value → Reject H₀

7. Friedman test Repeated-measures design (>3)
Hypothesis: Difference between any treatments; ranks in one group
systematically higher/lower than the other.
Critical value: df = k-1
Computation:
Decision: Obtained value < or = the critical value → Reject H₀