________________
2.5x2 +7.5x4
5.0+30.0
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6
6
6
This is not the same as the first mean, which is 5.5 Where is the error? As a matter of fact, the error lies in the non-fulfillment of a particular assumption for grouped frequency distribution. All items within a group should be uniformly and normally distributed. This particular assumption was not verified while using the grouped frequency distribution and hence the error. Likewise, there are certain assumptions with all statistical formulae. Sometimes assumptions are not valid for the situation and sometimes they are not verified to be present, yet the formula is used leading to an error.
A statement about the population is generally verified through the study of sample. In hypothesis testing, we pass on judgement about population parameters through the corresponding measures calculated for a sample drawn from the population. However carefully you draw a sample, there is no guarantee that it will be an appropriate representative of population; for example, from a population of 100 people consisting of 50 male and 50 female, you draw a sample of 10 by using random methods. All the 10 may turn out to be either male or female. The sample was without any bias, yet it did not turn out to be representative sample. If the sample is changed, findings may change. Researchers try to solve this problem by resolving to the techniques of stratified random sampling. Even a stratified random sampling is not necessarily 100 % representative. By stratified random sample, no doubt, representativeness of the sample is ensured up to certain extent. From a population, if you draw two non-biased samples of the same size using the same techniques, they will not necessarily lead to the same result. If the sample size is changed then the findings are also likely to change. Hence, for the same population, with different samples of the same size and different samples of different sizes varied results are likely to be there. Statistical techniques, thus, may induce certain amount of error. So, should we give up statistical techniques? No, use them with caution and never consider your findings as ultimate truth. Researchers' Mindset
= 5.83
If the same sample, data and statistical calculations are given to many researchers, all of them will not reach to the same conclusions and inferences. The researchers have different perception, attitude and mindset. They cannot completely get over this. Their psychology, up to some extent will definitely be reflected in the conclusions and inferences that they draw and the recommendation that they make.
This is yet another source of error in data base social science researches. So, should we say good-bye to research and research methodology, which is supposed to be systematic way of conducting the research? No, it gives bad answers to questions which otherwise would have worst answers.
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