Statistics of Non-Parametric test Biostat

1. Non-Parametric test

2. Introduction
• Biostatistics
• Importance of biostatistics
• Types of statistical test and differences
• Requirement of non parametric test
• Types of non parametric test

3. Types of Statistical test
• Parametric test
• Non –Parametric test

4. Difference
Parametric test
• Data
• Observation form
• Scales
• E.g. - Student ‘ t-test’
-ANOVA( Analysis of
variance)
Non-Parametric test
• Data
• Observation form
• Scales
• E.g. - Chi- square test
-Fisher’s Exact test
-Sign test
-Wilcoxon signed rank test
- Wilcoxon rank sum test

5. • Requirement of non- parametric test ?
Types of non – parametric test:
• Chi- square test
• Fisher’s Exact test
• Mann Whitney ‘U’ test
• Sign test
• Wilcoxon signed rank test
• Spearman rank order test

6. • Chi-square (χ2) :
• It is used to examine
group differences between
categorical variables
• Developed by Karl
Pearson
• Calulated using the
formula
• χ2 = Ʃ( O – E)2
__________
E

7. • Application of Chi-square :
• Test of association
• Test of proportion
• Chi square for goodness of fit
• Yates correction

8. Fischer’s Exact test
• This is applied when
sample size is (<5 )

9. Mann Whitney U test
• This test is similar to wilcoxon signed rank test except the
samples are independent and not paired
• This test is applied for large sample size (n>100)
• It is calculated by :
U = N1* N2 + Nx(Nx +1) –Rx ( Rx is the larger rank
total)
2
__________

10. • Examples :
• 10 dieters followed Atkin’s diet
• 10 dieters followed Jenny Craig diet
• Atkins group losses weight of – 34.5 lbs
• J Craig group losses weight of --18.5 lbs
• Conclusion : Atkins is better ?

11. • Atkins change in weight
• +4, +3, 0, -3, -4, -5, -11, -14, -15, -300
Rank: 1 2 3 4 5 6 9 11 12 20 = 73 ( rank was
summed)
• Craigs change in weight
• -8, -10, -12, -16, -18, -20, -21, -24, -26, -30
Rank : 7 8 10 13 14 15 16 17 18 19 = 137 ( rank
was summed)
Means Craig was better than Atkins , null hypothesis rejected

12. Sign test
• it is easy and simple to interpret
• Used for paired data , can be ordinal or continuous
• Eg. Children in an orthodontia study were asked to rate
how they felt about teeth on a 5 point scale
• Survey done before and after treatment

13. • Here sign test is used to
evaluate whether these
data provide evidence
that orthodontic
treatment improves
children’s image of their
teeth .

14. Wilcoxon Signed Rank Test
• It is applied for paired
data.
• Similar to sign test
• The sum of positive
rank is equal to sum of
negative rank.
(1892-1965)

15. • Example : The 14 difference scores in BP among
hypertensive patient after giving drug A were :
• -20, -8, -12, -14, -26, +6, -18, -10, -12, -10, -8, +4, +2, -18
• It is calculated by sum of positive rank is equal to sum of
negative rank
• The smaller of the two value is considered.

16. • Sum of positive rank=6
• Sum of negative rank=99
• T= 6
• For N= 14 , the critical
value of T=21
• If T is ≤ to T critical, null
hypothesis is rejected , i.e.
Drug A decreases BP in
hypertensive patients

17. Spearman rank order test
• It is used to assess the
relationship between two
ordinal variable or two
skewed continuous
variable
• It is a relative measure
which varies from
-1(perfect negative
relationship) to +1(perfect
positive relationship)

18. Conclusion
• Application of biostastics is important in community and
public health care and management
• They have a great utility in hospitals, nursing homes and in
academics , hence a great asset in research in medical
practice
• Non –parametric test is based on ranks rather than raw
scores
• These test are advised when scores are ordinal
• If the data meet the assumption of parametricity, these test
have more power

19. THANK
YOU