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Distinguish Between Parametric and Nonparametric Statistics and Discuss When to Use Each Method in Analysis of Data

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DISTINGUISH BETWEEN PARAMETRIC AND NONPARAMETRIC STATISTICS AND DISCUSS WHEN TO USE EACH METHOD IN ANALYSIS OF DATA
The word parametric comes from “metric” meaning to measure, and “para” meaning beside or closely related. The combined term refers to the assumptions about the population from which the measurements were obtained.
The two classes of statistical tests are:
 Parametric Statistics
 Nonparametric Statistics

i. Parametric Statistics:
Parametric statistics are statistical tests for population parameters such as means, variances and proportions that involve assumptions about the populations from which the samples were selected. These assumptions include:
 Observations must be independent i.e. when values in one set are different and unrelated from another set
 Observations must be drawn from normally distributed populations
 The populations must have the same variances
 The sample must be random
Use of Parametric Statistics in Data Analysis:
Parametric tests are used when the above parametric assumptions are met.
Parametric tests are also used to analyze interval and ratio data. Interval data are numerical data in which we not only know the order but also the exact differences between the values e.g. the time interval between the starts of years 1981 and 1982 is the same as that between 1983 and 1984 which is 365 days. Ratio data on the other hand describe measurements with attributes that have the qualities of nominal, ordinal and interval data and a true zero point can be defined e.g. height and weight.
Examples of parametric tests include t-test, f test and z test. ii. Nonparametric Statistics:
Nonparametric statistics are used when the population from which the samples are selected is not normally distributed. These statistics are also known as distribution free statistics. Nonparametric statistics can also be used to test hypotheses that do not involve specific population parameters.
Use of Nonparametric Statistics in Data Analysis:
Nonparametric tests are used when assumptions of nonparametric tests cannot be met, when very small numbers of data are used and when no basis exists for assuming certain types or shapes of distribution.
They can also be used for nominal and ordinal levels of measurement. Nominal data is a set of data in which values or observations belonging to it can be assigned a code or a label, e.g. In a data set, males could be coded as 0, females as1; marital status of an individual could be coded as ‘Y’ if married and ‘N’ if single. Ordinal data on the other hand is a set of data in which the values or observations belonging to it can be ranked or have a rating scale attached e.g. a set of survey answers can be listed as very satisfactory, satisfactory, neutral, unsatisfactory, very unsatisfactory. As a result, nonparametric tests can be used if data can only be classified, counted or ordered.
Examples of nonparametric tests include Wilcoxon Mann-Whitney Test, Sign Test and Ruskal-Wallis Test.
Advantages of nonparametric statistics:
 Nonparametric tests are simple and easy to understand
 They are designed for small numbers of data
 Nonparametric statistics do not involve complicated sampling theories
 No assumption is made regarding the parent population
 Nonparametric statistics can be used when data is nominal or ordinal
 They can be used to test population parameters when the variable is not normally distributed
 They can be used effectively for determining relationships and significance of differences using behavioral research methods
Disadvantages of nonparametric statistics:
 They are less efficient than parametric tests when the assumptions of the parametric methods are met.
 They tend to use less information than parametric tests
 They are less sensitive that parametric tests when the assumptions of the parametric methods are met.

iii. Differences between Parametric Tests and Nonparametric Tests:
Parametric Tests Nonparametric Tests
Information about the population is completely known Information about the population is not completely known
Specific assumptions are made regarding the population No assumptions are made regarding the population
Null hypothesis is made on parameters of the population distribution The null hypothesis is free from parameters
Test statistics is based on the distribution Test statistics is arbitrary
No parametric tests exist for nominal data Nonparametric tests exist for nominal and ordinal data

References:
Allan G. Bluman. (2004) Elementary Statistics, A Step by Step Approach, 5th Edition
Angela Hebel. (2002) Parametric versus Nonparametric statistics- when to use them and which is more powerful. [Presentation] University of Maryland Eastern Shore, 5th April.
Sai Prakesh (n.d) Parametric and Nonparametric Test. [Presentation] MBA Insurance Management, Pondicherry University.
L. Don Lehmukhul. (1996) Nonparametric Statistics: Methods for Analyzing Data Not Meeting Assumptions Required for the Application of Parametric Test. [Online] 8 (3).…...

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