Parametric tests Versus Non parametric tests

Prepared on 24^th July 2009

“Fewer or weaker are the assumptions, the more general are the conclusions”.

In statistics, unfortunately the most powerful tests are those which have extensive and stringent assumptions. With this assertion, I will be presenting the most prominent discussion of Parametric vs. Non parametric tests very briefly. The following write up reflects my personal (with nascent knowledge) bias for non parametric tests.

Parametric tests (t test and f test) are the tests that have certain assumptions about the population from which the samples are drawn. The strength of the results of such tests depends on the validity of those stringent conditions/assumptions. The prominent among them are.

• Observations must be independent
• Observations must be drawn from normally distributed populations
• Those populations must have same variance
• Variables are measured at least in an interval scale

Non parametric tests are the tests that make no assumption about the populations, but share few relatively weak assumptions with the parametric tests. They are:

• Observations must be independent
• Variables under study have underlying continuity.

However the concept of power of efficiency (by increasing the sample size) ensures that non parametric tests achieve the same strength as parametric test. Moreover the criticism of the non parametric tests over their usage of information (some non parametric tests ignores the sign, some convert the scale into ranks) may be answered by eliciting the answers to the following questions.

Ø How important is it that the conclusions drawn from the research are applicable to the generally rather than only to the populations with normally distributions?

Ø Which tests of the parametric and non parametric tests use the information appropriately?

The potential answer to the former question is presented in itself. The answer to the later one may be viewed from the perspective of possible assumptions one makes about the potentially unknown populations one deals with. The issue of comparing the parametric and non parametric tests may be highlighted by presenting the short summary of the advantages and disadvantages of the non-parametric test.

Advantages of Non-parametric tests:

ü The probability statements obtained from the non parametric tests are the exact ones, regardless of the shape of the underlying population.

ü For the very small samples (say N=8), there is no other alternative other than non parametric tests unless the parameters of the underlying population are known exactly.

ü Non parametric tests are suitable in the case of the samples that are drawn from various populations with different variances.

ü No other alternative than non parametric tests in the case of the samples involving nominal data.

Disadvantages of the non-parametric tests

• In the case of the samples that satisfy the underlying assumptions of the parametric tests, application of non-parametric tests is of wasteful given their power of efficiency
• Unstructured availability of literature about the non parametric tests may confine the researcher to employ the parametric tests though their validity is vague.

The author has heavily benefited from the extensive and provocative discussions with his fellow doctoral student Yoonus C. A at IFMR, Chennai; and the writings of Sidney Siegel. The comments on the draft by Nandhini R. are highly commendable. Finally, the author is solely responsible for any mistakes and constructive comments are highly respected.

Corporate Bankruptcy Law in India

In India, there is no comprehensive law or market mechanism that governs corporate bankruptcy. The way it has been defined, ‘industrial sickness’ goes beyond the general understanding of ‘bankruptcy’. It has been defined as the extreme state where accumulated losses exceed the net worth. The stringent policies that dealt with the industrial undertakings until late 1980s fueled the persistence of industrial sickness in the country. The MRTP act (1969) prevented the private sector companies from attaining globally competitive scales of operation through its stringent definition of ‘dominant undertaking’. The FERA (1973) and Import Substitution policies that were adapted created the insurmountable hurdles to the domestic entities in acquiring the innovative technologies and forced them far behind in modernization process. This resulted in the widespread industrial sickness thereby blocking of scarce resources in unviable activities. To deal with the industrial sickness, the Government of India took various ad-hoc measures such as constituting Industrial Reconstruction Corporation of India Ltd (IRCI) in 1971; setting up of state level inter institutional committees (1980) to provide rehabilitation assistance to sick and closed units. These ad-hoc measures were not effective as they could not forge the coordinated approach to deal with the problem. In 1981, the RBI set up a committee under the chairmanship of T. Tiwari to suggest on the possible legal options/mechanisms to effectively deal with the problem of industrial sickness.

Based on the recommendations of the Tiwari committee, the Government of India enacted the Sick Industrial Companies Act (SICA) in 1985. The purpose of SICA has been the early detection of sick or potential sick companies; determination of the potential viability and timely provision of remedial measures. The economic underpinning behind the purpose of SICA is to unveil the scarce resources that were hitherto blocked with the unviable unit. In order to implement various provisions of SICA, Board of Industrial and Financial Reconstruction (BIFR) was set up in January 1987 and became functional from May 1987. Initially BIFR covered only private entities, the government companies were brought under the BIFR jurisdiction in July 1991. The SICA applies to the companies satisfying the following criteria:

• Companies specified in the First Schedule to the Industries (D & R) Act, 1951, except the industries relating to ships and other vessels drawn by power
• Companies not being ‘small scale industrial undertakings or ancillary industrial undertakings’ as defined in Industries Act, 1951.

The criteria that BIFR follows in determining the sickness of a particular company is as follows:

• The accumulated losses of the company to be equal to or more than its net worth.
• The company should have completed five years after incorporation under Companies act, 1956. (before July, 1991 it was seven years)
• The company should have 50 or more workers on any day of the 12 months preceding the end of the financial year.
• It should have a factory license.

The companies satisfying the above criterion are reviewed by the body of experts who determines the viability of the company. Based on the observations, unviable companies are winded up and potentially viable companies are recommended for the re-organization process. The companies that underwent the re-organization process will be declared as ‘no longer sick’ as and when their viability is established (as and when their net worth becomes positive).

Reference:

- T.C.A. Anant and Omkar Goswami (1997), “Getting Everything Wrong: India’s Policies Regarding ‘Sick’ Firms” in Dilip Mukharjee (ed), Indian Industry: Policies and Performance, OUP, New Delhi.

- www.bifr.nic.in.

Suggestions and comments will be encouraged!