A study of the Theoretical Framework of Parametric and non-Parametric Tests used Social Sciences


Ravindra Bhardwaj

Research Scholar, Institute of Business Management, CSJMU Kanpur



This paper analyses the concepts of parametric and non-parametric tests used and differentiated between them. The main problem of social science scholars does not know applications of these types of tests. Therefore, my endeavors to clarify the concepts of these tests. This paper is based on theories so secondary data used by secondary sources like internet websites, research papers etc. Parametric tests follow certain assumption where as non Parametric test don’t follow any certain assumptions. There is a wide range of statistical tests. The decision of which statistical test to use depends on the research design, the distribution of the data, and the type of variable. In general, if the data is normally distributed you will choose from parametric tests. If the data are non-normal you choose from the set of non-parametric tests. An application of parametric test the nature of data should follow a normal distribution curve, whereas in non parametric test nature of the data doesn’t follow the normal. This paper clearly defines the concept of parametric and non parametric test and their assumptions of application. In a typical research design there might be statistical errors and shortcomings due to the incorrect use of statistical tools and techniques thereby leading to incorrect result and conclusions. These incorrect results, conclusions may have a negative effect on the reliability, validity and verifiability of the research results. 


KEY WORDS: Statistical tools, Parametric Test, Non-Parametric Test, Research analysis, Inferential Statististics.



Statistics is the science of collecting, analyzing and making inference from data. Statistics is a particularly useful branch of mathematics that is not only studied theoretically by advanced mathematicians but one that is used by researchers in many fields to organize, analyze, and summarize data. Statistical methods and analyses are often used to communicate research findings and to support hypotheses and give credibility to research methodology and conclusions.  It is important for researchers and also consumers of research to understand statistics so that they can be informed, evaluate the credibility and usefulness of information, and make appropriate decisions. The evaluation of the quality of services available to a group or organization.


Methods are classified on the basis of what we know about the population we are studying.  Parametric methods are typically the first methods studied in an introductory statistics course.

The basic idea is that there is a set of fixed parameters that determine a probability model.


Parametric methods are often those for which we know that the population is approximately normal, or we can approximate using a normal distribution after we invoke the central limit theorem. There are two parameters for a normal distribution: the mean and the standard deviation.


To contrast with parametric methods we will define nonparametric methods. These are statistical techniques for which we do not have to make any assumption of parameters for the population we are studying. Indeed, the methods do not have any dependence on the population of interest. The set of parameters is no longer fixed, and neither is the distribution that we use.  It is for this reason that nonparametric methods are also referred to as distribution free methods.


Nonparametric methods are growing in popularity and influence for a number of reasons. The main reason is that we are not constrained as much as when we use a parametric method.  We do not need to make as many assumptions about the population that we are working with as what we have to make with a parametric method. Many of these nonparametric methods are easy to apply and to understand.



Hoel (1984) suggested that if there were too few runs, this would indicate positive autocorrelation, while too many runs would indicate negative autocorrelation. A slightly more complex but explicit nonparametric test for serial correlation of higher orders is given in.


Moorthy and Ratcliffe (1988) analyzed time series forecasts for an area of West Sussex, and Smith and Demetsky (1997) demonstrated application of a time series model to forecast traffic volumes on a freeway in Northern Virginia.


Bacchetti (2002) stated that Multiple comparisons occur when one considers a set or a family of statistical inferences simultaneously. These methods are used in the same context as ANOVA to check whether there exists a difference in population means between more than two populations. In contrast to ANOVA, which simply tests the null hypothesis that all means were equal, multiple comparison procedures help the researcher to determine where the difference among the means occur.

Higgins (2004) defines the method to perform the Wilcoxon rank-sum test is computed as follows. Let m be the sample size of the one group or treatment, and n be the sample size of another. Combine nm+ observations into one group, and rank the observations from smallest to largest. Let 1 be the rank of the smallest observation, 2 the rank of the next smallest observation, and so on. It is common to have ties among observations in a data set; that is, one or more observations may have the same value.


Warner (2007) stated that nonparametric methods should be used when the sample size is small, whereas parametric methods should be used when the sample size is large. Also when there is an outlier in the data, nonparametric methods are said to be preferable.


According to Tanis and Hogg (2008) when the population distribution is normal and the sample size n is as small as 4 or 5 the normal test should a very adequate approximation.


Nalou (2011) produced on different types of statistical techniques of which one has no statistical component. The purpose of this explanation is to acquaint researchers the different types of statistical techniques and the rate at which they are been used.



To study the concepts of Parametric and non-Parametric test used in Social Sciences.

To study the Differences between parametric and non Parametric test used in Social Sciences.



The present study is based on the collection of data from secondary sources. Secondary data is obtained from internet, various published and unpublished records, magazines, books and journals.


Different types of parametric and non parametric tests:


Parametric tests (means)

Nonparametric tests (medians)

1-sample t test

1-sample Sign, 1-sample Wilcoxon

2-sample t test

Mann-Whitney test


Kruskal-Wallis, Mood’s median test

Factorial DOE with one factor and one blocking variable

Friedman test



Fig-1 Different types of test used in social sciences



Differences between Parametric Tests and Non-Parametric Tests



Parametric Tests

Non-Parametric Test


Normality assumption is required.

Normality assumption is not required.


Uses the metric data.

Ordinal or interval scale data is used.


Can be applied for both small and large samples.

Can be applied for small   samples.


One sample using Z or t test

One sample using sign test.


Two independent samples using a t or Z test.

Two independent samples using the Mann-Whitney U statistics.


Two pair samples using a t of Z test.

Two pair samples using the sign test and wilcoxon matched pair rank test.


Randomness-no test in Parametric is available.

Randomness using runs test.


Several independent samples using F test in ANOVA.

Several independent samples using  Kruskal-Wallis test.



There are a wide range of statistical tools. The decision of which statistical tools to use depends on the  research design used in research papers or thesis, the distribution of the data, nature of data and the type of variable. In general, if the data is normally distributed you will select from the set parametric tests. If the data is non-normal you select from the set of non-parametric tests. Parametric test can perform quite well when they have been spread over and each group happens to be different. While these non parametric tests don’t true assume that the data follows a normal distribution, they do tend to have other ideas and assumptions which can become very difficult to meet. In every parametric test for example, you have to use statistics to estimate the parameter of the population. Because of such estimation, you have to follow a process which includes a sample as well as a sampling distribution and a population along with certain parametric assumptions which are required, which makes sure that all components are compatible with one another. An example can be used to describe this. Observations are first of all quite independent, the sample data doesn’t have any normal distributions and the scores in the different groups have some homogeneous variances.



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5.        Hoel, P.G. 1984. Introduction to Mathematical Statistics, 5th ed. New York, NY: Wiley and Sons.

6.        Hogg, Robert V., and Tanis, Elliot A. A Brief Course in Mathematical Statistics. Upper Saddle River, NJ: Pearson Prentice Hall, 2008.

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11.     Nalou, A. A. (2011). Assessing the Statistical Methodologies of Business Research in South Africa.

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Received on 18.06.2017

Modified on 25.06.2017

Accepted on 29.06.2017

© A&V Publications all right reserved

Research J. Humanities and Social Sciences. 8(2): April- June, 2017, 225-228.

DOI:  10.5958/2321-5828.2017.00034.1