Sampling Errors


0
SAMPLING ERRORS

Whatever kind of sample is taken and whatever the sample size there will always be error arising from the sampling process. The extent of such error may be defined as the difference between a sample result, and the result that would have been achieved by undertaking a complete census. Such errors arise because particular types of cases are under-represented or over-represented in the sample compared with the population as a whole. If, for example, the cases are individual consumers, then the under- or over- representation of the sexes, ages or social classes will affect the measurement (and, more importantly, the estimates made from them) of a large number of variables. Lack of representation in the appropriate quantities may be a product of two factors: systematic error (or bias) and random error (or variance).

Systematic error

Bias arises when the sampling procedures used bring about over- or under- representation of types of cases in the sample, which is mostly in the same direction. This may happen because:

• the selection procedures are not random,

• the selection is made from a list that does not cover the population, or uses a procedure that excludes certain groups,

• non-respondents are not a cross-section of the population.

 

If the selection procedures are not random then it means that human judgement has entered into the selection process. For example, interviewers may be asked to choose respondents at some geographical location or to select households in specified streets. The result is likely to be that certain kinds of people or households or organizations are excluded from the sample. Thus choosing respondents in a shopping centre will miss out people who seldom or never go shopping; the selection of households by an interviewer may result in the omission of flats at the tops of stairs.

 

If the Electoral Register is used to select adults aged 16 or over, then, as indicated earlier, 16 and 17 year-olds and many of the 18 year-olds will be missing from the list and will be under-represented in the final sample. The use of telephone directories will under represent certain social groups less likely to be in the telephone book (or those who are ex-directory). Duplication in lists, for example in the Yellow Pages, may result in some over-representation. If we try to estimate sales of soap from a sample of private households, then all users in institutions of various kinds will be excluded.

 

Non-response is a problem for both censuses and samples. For censuses it means that the enumeration will be incomplete. If large numbers are missing, it would be inappropriate to treat those successfully contacted as a represen­tative sample’. For samples, it means that estimates made from the sample will he biased if non-respondents are not themselves representative of the popula­tion. If they are representative, then non-response is not so much of a pro­blem; but it may still mean that analyses are made on the basis of too small a sample.

 

Whatever the reason for the systematic error, the effect will be that all samples that could be drawn from a population will tend to result in the same direction of over- or under-representation. The average of all these samples will then not be the same as the real population average or proportion. Thus if we took lots of samples using a procedure that tended to omit working mothers with young children, then all the samples will manifest such under-representation rather than some over-representing them and some under-representing them so that the average of all samples was very close to the real population proportion.

 

Systematic errors cannot be reduced simply by increasing the sample size. If certain kinds of people are not being selected, cannot be contacted or are not responding, it will not be ‘solved’ by taking a bigger sample. Indeed, some kinds of errors -will increase with more interviewers, more questionnaires and greater data-processing requirements. All the researcher can do is minimize the likelihood of bias by using appropriate sample designs. Biases for some variables can be checked, for example against Census data or data from other sources. Sometimes attempts are made to discover the characteristics of non-responders, for example by sending out interviewers to non-respondents to a postal survey, taking ‘late’ responders as typical of non-responders, or gaining demographic data from the results of another survey that the non-responders have taken part in.

 

Random error

If we took a number of random, unbiased samples from the same population there will almost certainly be a degree of fluctuation from one sample to another. Over a large number of samples such errors will tend to cancel out, so that the average of such samples will be close to the real population value However, we usually take only one sample, and even a sample that has used unbiased selection procedures will seldom be exactly representative of the population from which itwas drawn. Each sample will, in short, exhibit a degree of error. Such error is often called ‘sampling error’, ‘hut it would he clearer to think of it as ‘random sampling error’ to distinguish it from bias (which some statisticians and some textbooks, confusingly, categorize as ‘non-sampling’ error).

 

Unlike bias, which affects the general sample composition and relates to each variable being measured in unknown ways, random sampling error will differ from variable to variable. The reason for this is that the extent of such error will depend on two factors:

• the size of the sample – the bigger the sample, the less the random sampling error (but by a declining amount),

• the variability in the population for that particular variable – a sample used to estimate a variable that varies widely in the population will show more random sampling error than for a variable that does not.

 

These two factors are used as a basis for calculating the likely degree of variability in a sample of a givensize for a particular variable. This, in turn, is used as an input for establishing with a specified probability the range of accuracy of sample estimates, or that sample findings are only random sam­pling fluctuations from a population of cases in which the findings are untrue.


Like it? Share with your friends!

0
BMS Team

We, at BMS.co.in, believe in sharing knowledge and giving quality information to our BMS students. We are here to provide and update you with every details required by you BMSites! If you want to join us, please mail to [email protected].

4 Comments


Warning: Undefined array key "html5" in /home/bmsnewco/public_html/wp-content/plugins/facebook-comments-plugin/class-frontend.php on line 140

Facebook comments:

This Website Is For Sale. Email us an offer we cannot refuse on [email protected] :)

X
Choose A Format
Personality quiz
Series of questions that intends to reveal something about the personality
Trivia quiz
Series of questions with right and wrong answers that intends to check knowledge
Poll
Voting to make decisions or determine opinions
Story
Formatted Text with Embeds and Visuals
List
The Classic Internet Listicles
Countdown
The Classic Internet Countdowns
Open List
Submit your own item and vote up for the best submission
Ranked List
Upvote or downvote to decide the best list item
Meme
Upload your own images to make custom memes
Video
Youtube and Vimeo Embeds
Audio
Soundcloud or Mixcloud Embeds
Image
Photo or GIF
Gif
GIF format