Statistics Can Lead to Errors
The use of statistics can often lead to wrong conclusions or wrong estimates. For example, we may want to find out the average savings by individual investors in 1994-95. Hence, we would have to question every investor in our population or some sample of such investors. In either case, the average savings calculated may not be the true average savings for the population. This is basically due to the occurrence of errors. Errors may be classified into two categories.
Such errors are caused by deficiencies in the collection and editing of data. Three reasons for such errors include Procedural Bias, Biased Observations and Non-Response Bias. Such errors may occur in a sample or in a census.
Procedural bias is the distortion of the representativeness of the data due to the procedure adopted in collecting the data.
For instance in our retailers example, Procedural Bias may creep in, if the retailer excludes all customers making purchases under Rs.2,000. In effect she will then study only high value customers, not all customers.
Suppose data is being collected about the rent levels in a city. The question “How much rent do you pay for accommodation?” can introduce a Procedural Bias because the rent may be for accommodation without furniture, etc. or for accommodation with furniture. In some cases the rent may include charges of the co-operative housing society for maintenance, etc. In other cases it may be a composite rent including even electricity and water charges. Hence, the above question must necessarily be supplemented by questions about what is included and excluded from the rent.
Unless questions are correctly framed, a procedural bias can creep into the investigation.
Absence of response can lead to Non-Response Bias.
In the retailers case, she may ask the customers for their suggestions for better products and services. The customers would require some time for thinking about this and may not be able to give an immediate answer. But, once they leave the shop they may forget all about responding. It is not possible to conclude that the customers do not have any suggestion for improving the service.
For another example, investors may be asked “How much do you expect to invest in shares in 1998 if the Sensex rises to 6000 by the end of the year?” If a significant proportion, say 60% of the investors, do not reply then there will be significant Non-Response Bias. It cannot be assumed that those who did not respond will not invest in shares in 1998. Nor can it be assumed that those who did not respond will invest in the same way as those who responded.
Here the observations do not correctly reflect the characteristics of the population being studied. The retailer may exclude important information like the quantity and type of equipment purchased, etc. and only concentrate on the bill amount. Hence, a purchaser of a number of low value items would be treated on the same footing as a purchaser of a single high value item. This may be unjustified as the two purchasers are likely to have distinctly different needs.
For another example, a study may be conducted to find out the annual earnings of various types of finance executives as compared with their qualifications. In such a case if all CFAs and CAs are grouped together as professionals then there is Biased Observation. This is because each of these qualifications is distinct and many executives may have more than one of the above qualifications.