Statistics of Non-Parametric test Biostat.ppt

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 (χ
2
) :
•It is used to examine
group differences between
categorical variables
•Developed by Karl
Pearson
•Calulated using the
formula
•χ
2
= 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 = N
1* N
2 + 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