Vinod Anand | 16 Oct 2009


(PART 4)                                                                                                              
Practically speaking, exact determination of sample size basically depends, apart from other factors, on the standard deviation of the population from which the sample has to be drawn, and also on the probability error.
In most of the cases the population standard deviation is not known, and, hence, sample size cannot be exactly fixed. Even when the population standard deviation is known, researchers do not much bother about the exact sample size because of their own convenience both in terms of time and cost.
But no matter what it is, statistical methodology and, therefore, statistical analysis is subject to many unreal assumptions. Some of the contexts of these assumptions are briefly mentioned below:
·        Construction of Frequency Distributions: Once the data-set is available, it has to be condensed by some method of ranking or classification before its characteristics can be comprehended. This method of ranking or classification of a given variable (continuous or discrete) takes the form of what is termed as frequency distribution of the given variable, which spells the manner in which class-frequencies are distributed over the class-intervals of that variable. This involves fixing the scale class-interval, and also the position of intervals. It is then that the observations are classified. They are also then graphically represented through frequency curves, polygons and histograms. These various steps in the construction of frequency distributions involve many assumptions, which may not be true in real life.
·        Types of Frequency Distributions: There are four broad categories of frequency distributions: the symmetrical, the moderately symmetrical or skew, the extremely symmetrical or J-shaped, and the U-shaped. We do find examples of these in real life, but they sometimes occur in an incomplete form because of certain limitations on the range of the variate, resulting in truncated forms. We also sometimes get complex distributions, which are a distorted mix of other normal varieties. We also get examples of pseudo-frequency distributions where the variate is s not strictly speaking measurable, as in psychology or even economics.
·        Theoretical Distributions: Frequency distributions are normally constructed from a given set of data, but it is also possible to mathematically deduce what the frequency distributions of certain population should be, subject to certain general hypotheses. Such distributions are called theoretical distributions. We have three such distributions in statistics, which are of prime importance in statistical analysis. They are: the Binomial distribution, the Normal distribution, and the Poisson distribution. They are also termed as classical distributions. Each one of them is subject to many assumptions. For example, the Binomial distribution is subject to assumptions like, an ideal coin (uniform, homogeneous circular disc) or an ideal die (perfect, uniform, and homogeneous cube), large number of throws, independent events, and so on. Likewise, the Normal distribution is subject to defining the mean, the standard deviation, and other parameters of the population. It is also symmetrical. The Poisson distribution is subject to the crucial assumption that one of the chances, say q, becomes indefinitely small and the total number of events (n) is increased sufficiently to keep nq finite, but not necessarily large. All these assumptions of the three theoretical distributions are just hypotheses, which do not have proper exactitude. The distributions, therefore, are just approximations, and do not always match with reality. The Tests of Significance (like, the t-test, the z-test, and the Chi-Square test) used variously to test the validity of the sample results for the given population, are, in fact, based on the given theoretical distributions, and are, as such, subject to the same and even other assumptions, which are also oblivious of reality.
We may, therefore, conclude that the final outcome of all quantitative economic analysis invariably fails to reflect what happens in real life.
The Final Word
Believing in the theory of the second best, the built-in difficulties of quantitative economics, as pointed out above, make us rely more on qualitative economics for better and effective diagnosis of the economic and social problems. Qualitative studies in economics are rather indicative. They optimally mix economic theory with the researcher’s own experience of the given context, perhaps through his insights and vision, and also on some kind of a feedback he gets from the concerned respondents.
But even qualitative studies have their own limitations, which can perhaps be easily avoided by taking little extra care. One of the crucial limitations is perhaps the intended indifference (and sometimes the ignorance) of researchers towards certain basic/built-in assumptions of the given context. In most of the cases, exclusion of these assumptions from the basic text, eventually lead to acute contradictions and inconsistencies between the stated goals and the actual policy. No matter what the context is, such built-in assumptions are always there.
For example, in the context of the informal sector studies the basic built-in assumptions, which are, by and large, ignored are:
·        The majority of the entrepreneurs (especially in the micro and small units of the informal sector) are poor, and, hence, apart from other concerns of this sector, one has to focus on the equity and empowerment of the poor entrepreneurs to enable them to share the benefits of growth and development so that they can voice their concerns and have a say in the formulation of policy programmes that directly affect them;
·        Informal sector connects economics to society. This reality has four basic dimensions. These are economic, social, fiscal and regulatory, and conditions of insufficiency. The economic dimension takes us beyond the normal indicators of economic measurement, human resource development, and labour market operations, which invariably neglect or incorrectly measure the activities in informal sector. The social dimension relates to gender issues, child labour issues, and dual burden of women as workers and housekeepers. The fiscal and regulatory dimension relates to minimum wages, hazardous and unsafe working conditions, environmental pollution, and child labour. The conditions of insufficiency are linked with the fact that conditions of work in informal sector are adverse both economically and environmentally;
·        Sufficient empowerment of the poor through asset building, and their involvement in the informal pursuits accelerates the pace of development; 
·        A paradigm shift from technology expansion to market expansion mindset, from production to productivity, and from all kinds of trade to selected unexploited sectors (like, export markets, mass markets) helps informal sector development.
We may, therefore, conclude to say that any policy package for informal sector is best created through qualitative studies provided it takes into account the built-in assumptions as mentioned above. This is equally true of other contexts also. Once this caution is exercised, the ex-ante becomes the ex-post.