INTRODUCTION TO NONPARAMETRIC TECHNIQUES Noor Jannah Yob
Lesson outcomes At the end of this lecture, you should be able to: • • • •
Define the nonparametric tests Identify the advantages and disadvantages of the nonparametric tests Identify the type of nonparametric tests Conduct the statistical techniques and interpret the results
RECAP: PARAMETRIC TECHNIQUES
1. Data
2. Tests
One sample
One sample t-test
Two samples
Paired sample t-test
K-sample test
Analysis of variance (ANOVA)
Independent sample t-test
3. Objective
Comparison Relationship
Assumptions Stringent
OVERVIEW: NONPARAMETRIC TECHNIQUES
Data Data measured on any scale
Distribution •
Do not involve population parameter
•
If the data are not normally distributed, there are two options:
1.
Use a non-parametric test
2.
Transform the dependent variable
Not normal
3. Objective
Generic assumptions Assumptions Less stringent
Random samples
Independent observations Each person or case can be counted only once, they cannot appear in more than one category or group
The data from one subject cannot influence the data from another.
The exception to this is the repeated measures techniques
(McNemar’s Test
Wilcoxon Signed Rank Test
Friedman Test)
4. Choose the statistical test:
Dependent Data (Response)
Depends on measurement scale of the dependent variables
Normally distributed Parametric test
Categorical
Scale
Skewed data Non-parametric
Ordinal:
Nominal:
Non-parametric
Chi-squared
Comparison Nonparametric
Parametric
Data must be continuous
Involved population parameter
Stringent assumptions
Interval
Mean
Random sampling
Ratio
Standard deviation Variance
Normality
Data
Population
Assumptions
Any scale of data
Distribution-free methods
No assumptions about population
Medians
Less stringent assumptions
Independent Ranks
Homogeneity of variance
Definition •
The idea of nonparametric statistics (the term nonparametric was first used by Wolfowitz, 1942)
•
Nonparametric methods do not rely on the estimation of parameters describing the distribution of the variable of interest in the population
•
Called parameter-free methods or distribution-free methods
Advantages •
Nonparametric tests are easier to perform (they do not require normally distributed populations).
•
They can be applied to categorical data (such as genders of survey responds).
•
They are less efficient than parametric tests.
•
Stronger evidence is required to reject a null hypothesis.
•
One of the easiest nonparametric tests to perform is the sign test.
Tests
Two samples n≥30
Independent t-test Equal variance
Independent Normally distributed
2 groups
Not normally distributed n≥30
Transform t
Paired t-test Normally distributed
Paired
Equal n’s Not equal variance
n<30 Number of groups
Independent t-test
n<30
Paired t-test Transform t
Not Wilcoxon signed ranks
Independent t-test Transform t
Not Wilcoxon rank-sum
k samples 1 factor
Independent groups Number of groups
3 or more groups
Normally distributed
Number of factors
Not normally distributed
Kruskal-Wallis â&#x20AC;&#x201C; 1 factor
Normally distributed
Repeatedmeasures
Not normally distributed
Friedman test
Paired
2 or more factors
One-way ANOVA Two-way ANOVA Other ANOVA
Summary
Concept: Nonparametric Test
Sort
Rank
Data are sorted when they are arranged according to some criterion.
A rank is a number assigned to an individual sample item according to its order in the sorted list.
Such as smallest to the largest or best to worst.
1st item is assigned a rank of 1, 2nd item is assigned a rank of 2 and so on.
Original variable
Ranking raw data
Nonparametric techniques are usually based on ranks or signs
Scale data is ordered and ranked
Analysis is carried out on the ranks rather than the actual data
www.statstutor.ac.uk
Rank of subject
Example Sorted Data
Preliminary Ranking
Rank
1
4
1
5
5
2 3 4
10
5
5
11
6
6
12
7
5
12
Mean is 3.
8
3 3 3
7.5
Mean is 7.5.
7.5
Handling Ties in Ranks • Find the mean of the ranks involved and assign this mean rank to each of the tied items.