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Purpose of this student corner
The purpose of this corner is to give students a brief explanation of what statistics is all about. It includes a brief description of the processes and concepts involved in statistics. The student corner will be upgraded as and when needed, in order to cover the widest range of topics of interest to its users.
Why do we need Statistics?
We need statistics for the following reasons:
it informs us about the society, that is, helps us to better understand the world;
it helps us to take the right decision;
it helps us to design/evaluate/monitor a project;
good national statistics leads to good Government policies and better development progress which benefits our people;
statistics also improve the transparency and accountability of policy-making;
perhaps the most valuable contribution that statistics can make is to help ensure that our limited resources are used in the best way.
Use of Statistics in Mauritius
Mauritius enjoys a relatively high level of statistical awareness. Most stakeholders as well as the media look forward to the regular, periodic release of economic and social statistics, particularly on economic growth, unemployment and inflation. These data are used every year to determine the quantum of salary compensation. Poverty and income statistics play an important role in determining policies relating to social aid, whilst NGOs use mapping of local area relative development indices, based on census data, for poverty alleviation initiatives. Data from the Census of Economic Activities are used by the National Empowerment Foundation and Enterprise Mauritius to develop and promote programmes for small and medium enterprises. Population estimates for local authority areas are the basis for allocation of financial grants by Central Government. The Central Bank uses inflation as well as statistics of exports and imports among others, to inform decisions of the Monetary Policy Committee. The CSO participates actively in developing performance indicators and targets which are used by development partners such as the World Bank and the European Union for release of funds for budget support. As from 2009 the CSO will be more and more involved in measuring the satisfaction of users of services of various ministries and agencies.
What are the procedures involved in statistics?
Statistics is primarily concerned with the collection, compilation and the analysis of data. The information thus obtained from the analysis of the data is then interpreted and disseminated to users in the form of reports.
Data types and sources
Data can be classified into two main types, namely, primary and secondary. Primary data are collected through censuses and surveys. For this purpose a questionnaire is prepared that comprises all the data items of interest that need to be collected. (CENSUS & SURVEY QUESTIONNAIRES) Secondary data are obtained from administrative sources. The data are called secondary because they are primarily meant for administrative purposes.
Censuses provide first hand primary data at source. The population and housing census is generally conducted every ten years in order to collect data on the economic, social and demographic situation of the population. It is a complete count of all entities in the population. It gives a snapshot of the conditions of the population at a particular point in time. The information is necessary for planning purposes and policy-making.
Contrary to a census, a survey collects data from only sample of the population under study. The need for a survey arises given that the cost for conducting a complete census is too expensive. Also a survey project can be implemented in a shorter lapse of time so that the results are available more quickly. The estimates obtained from the sample are then generalized for the entire population. The sample, however, has to be representative of the population, that is, has to be a miniature replica of the population. The sampling theory enables us to construct confidence intervals for the estimate. For example let’s assume that in a particular survey the estimated proportion of overweight people is x%. Sampling theory enables us to say, for instance, that the actual proportion in the population falls in the range x-a to x+a, where a can be calculated, with a confidence of 95%.
Samples when properly designed sometimes give a better precision than a census. This is because with a survey, the logistics required is much less so that there is more control over the resources. For example, training of field staff can be made more rigorous, given the small workforce required for a survey.
The CSO has a regular programme of sample surveys covering household and enterprise income and expenditure and labour force. These surveys are conducted at periodic intervals and provide an important source of data to planners. Furthermore, in order to address the demand for more social indicators, a Continuous Multipurpose
Household Survey has been conducted since the year 1999 and is meant to be an on-going exercise covering various topics of interest.
As a result of their routine administrative activities, most government ministries and departments generate various types of information that can be used as primary sources for statistics, depending on their relevance, consistency, coverage, completeness and accuracy. The main organisations whose record systems are exploited routinely to yield substantial statistical output are:
• Civil Status Division of the Prime Minister's Office (vital statistics)
• Mauritius Revenue Authority (MRA) (trade, income tax & VAT statistics)
• Judicial Department (judicial activities)
• Ministry of Education, Culture and Human Resources (education statistics)
• Ministry of Finance and Economic Empowerment (Government Finance statistics)
• Ministry of Local Government, Rodrigues and Outer Islands (licensing statistics)
• Ministry of Social Security, National Solidarity & Senior Citizen Welfare and Reform Institutions (pension contributions and benefits)
• National Transport Authority and Traffic Management Unit (road transport statistics)
• Passport and Immigration Office (statistics of international travel and tourism)
Problems of data collection
(a) Response problems
In spite of provisions made in the Statistics Act 2000 to safeguard the interest of respondents, there are always some respondents who feel reluctant to provide data requested by the CSO. The main reasons for this reluctance are twofold: on the one hand there is the response burden imposed on respondents who have to make special efforts and find the time to assemble the information, and on the other, there is the fear that the data may be used for purposes other than statistical, especially taxation.
Because of these restrictions, CSO assists ministries and Government departments to collect data under their own legislation. Besides, the Statistics Act 2000 makes provision for the joint collection of data by the Central Statistics Office and any other Ministry of Government Department, local authority or statutory body.
(b) Other problems
Many research institutes or private firms are conducting surveys for market research or opinion polls, thus increasing the burdens on would be respondents who may be selected in more than one survey at a time. Some people may not be able to differentiate between questionnaires for an official survey conducted by the CSO and those carried out by private organisations.
Data collected from administrative sources are not devoid of problems. The forms and documents which have been established independently of the CSO, may lead to inconsistencies and incomplete coverage. Besides, these organisations may be using non-standard definitions and methods and this necessitates careful putting together to have meaningful statistics.
Sampling is the process whereby a sample of respondents is selected from the population for the purpose of the survey. Sampling theory enables us to determine the optimum sample size in order to achieve the required precision.
Usually researchers have a restricted budget for a survey. With the available budget they would attempt to get the highest precision. This would depend on the cost per questionnaire, or indirectly the sample size and the sampling design. The cost per questionnaire would itself depend on the complexity of the questionnaire and on the cost involved in locating a respondent. It should be recalled that the bigger the sample, the higher will be the precision but the cost of the survey will also be higher. Therefore a balance needs to be established between the precision required and the cost of the survey.
Various sampling designs are available that give different precisions for a specified sample size. The choice of design will depend on various considerations, including the precision required and the cost per questionnaire.
Types of sampling design
Simple random sampling
In this design, every unit in the population has an equal and non-zero chance of being selected. To ensure equal chance of selection, a random selection of the units can be done. This method is suitable only if the population is small and that there is a complete listing of all members present in the population (sample frame). If the population is large, however, this method may result in respondents being widely dispersed. This would tend to increase the cost of reaching them.
This design also requires a complete population frame. This frame might take the form of a register containing a list of names. The process of selection involves the selection of the nth unit from the list provided that the first element is randomly selected. The value n is a constant and is related to the sample size by the following formula: sample size = P/n where P is the population size.
Stratified sampling could be a viable design in situations where the population can be divided into distinct strata due to the heterogeneity of the population. The factor(s) of stratification need to have an important bearing on the responses of the respondents. Sampling is usually done in such a way as to keep the probability of selection of any unit from any stratum to be constant. The stratification helps to ensure representativeness of the sample and at the same time increases the precision of the sample.
One of the advantages of this technique is that it does not require a sampling frame. Also, it helps in reducing cost per unit by concentrating fieldwork in a few selected areas. The method involves breaking down the area under study into smaller areas or clusters. A sample of clusters is then randomly selected. Within each selected clusters, every unit e.g. household may be selected, else a sample of units is interviewed in which case it will be a multi stage sampling.
Multi stage sampling
As the name itself implies, sampling is done in stages. It usually starts with a sampling of clusters followed by sampling of units within the clusters adopting one or more of the techniques described above. These procedures essentially cut down cost of the survey by reducing fieldwork in a few selected clusters.
Quota sampling, in contrast with all the techniques described above, is a non-random sampling procedure. This means that all members of the population do not have an equal and non-zero chance of selection. The peculiarity with this technique is that the final choice of respondents rests with the interviewer. He has to select respondents according to a given set of criteria. For example the interviewer may be instructed to interview 10 males and 10 females above 20 years of age, among whom, 16 is working. This procedure reduces the cost of the survey considerably by imposing no condition on geographical coverage and eliminates the problem of call backs and refusals as encountered with other techniques. Commercial firms usually use this technique to do market research.
Given the non-random nature of this technique, the precision of its estimates cannot be assessed statistically. That is, no confidence intervals can be built for its estimates. For this reason, this technique is criticized by professional statisticians.
Types of errors
The estimates obtained from a sample survey are influenced by two types of errors: the sampling error and the non-sampling error. It should be recalled that non-sampling errors occur in censuses also. The sampling error arises from the fact that we are not taking the whole population but just a fraction of it. Errors from this source are dealt with by sampling theory, which gives a confidence interval for the sample estimates.
Some examples of non-sampling errors are as follows: (a) coverage error or errors due to incomplete coverage of the population under study (b) response errors that is responses are incorrectly recorded by the interviewer (c) Errors in data processing operations such as coding, keying, verification, tabulation etc. (d) Errors during presentation and publication of tabulated results. The best way to control non-sampling errors is to follow the right procedures for all survey activities from planning to the analysis of results.
Both sampling and non-sampling errors need to be controlled and reduced to a level at which their presence does not defeat or obliterate the usefulness of the final sample results.
Main steps in data processing include the following:
Data should be edited before being presented as information. This action ensures that the information provided is accurate, complete and consistent.
There are several situations where errors can be introduced into the data, and the following list gives some of them:
A respondent could have misunderstood the question
A respondent or an interviewer could have checked the wrong response
An interviewer could have miscoded or misunderstood a written response
An interviewer could have forgotten to ask a question or record the answer
A respondent could have provided inaccurate responses
In brief, the main objectives of data editing are:
to ensure the accuracy of data
to establish the consistency of data
to determine whether or not the data are complete
to obtain the best possible data available
Coding is the conversion of data/information into meaningful codes that can be processed electronically. The codes can either be devised by the Statistician or, if available, taken from an international source. The Central Statistics Office uses latest revisions of standard international codes as far as possible. Examples are:
NSIC: National Standard Classification adapted from the UN International Standard Industrial Classification of Economic Activities (ISIC)
ISCO: International Standard Classification of Occupation (UN)
ISCED: International Standard Classification of Education
SITC: Standard International Trade Classification
CPC: Central Product Classification
The next step in data processing is data capture, which consists in entering the coded data into a computer.
This is the process by which data are transferred from a paper copy (questionnaires and survey responses) to a database file.
After editing, data may be processed further to produce a desired output. The computer software used to process the data will depend on the size of database and form of output required.
The primary outputs are a series of tables cross-classified by selected variables. The job of statistician is to extract meaningful information from these tables and present them in a form understandable by users so that they may use them efficiently for planning and policy making.
Steps towards optimizing use of statistics
The office is investigating ways and means to make statistics more useful to users. Among the steps taken are:
to conduct user surveys /user-producer consultation to assess the needs of users in order to provide them with statistics that are most relevant to them
provide statistics in a more user-friendly format
market the products of the CSO through its website
promote public understanding of statistics among the population at large
Confidentiality, privacy and security
The Central Statistics Office takes special care to prevent published statistics from being used to derive information about a particular individual or company
In order to protect privacy, personal information must not be used for purposes other than those for which its collection was authorized.
Under the Statistics Act 2000 “No person shall be required to supply any information under this Act which involves the disclosure of any technical process or trade secret in or relating to the undertaking of which he is the owner or in the conduct or supervision of which he is engaged”.
CAST, (Computer Assisted Statistics Teaching) is a series of electronic statistics textbooks. (For more information please click here)