Statistical Surveys 1 Sampling Errors

Survey In a survey data are collected from the members of a population. Eg if we want to collect data on the money teenagers spend on clothes we will ask teenagers how much they spent on clothes last month.

Census A survey that includes every member of the population is called a census. Usually expensive and time consuming to carry out, and sometimes impossible to carry out. Often not necessary,as a sample survey will give good enough results.

Sample Survey The technique of collecting information from a portion of the population is called a sample survey. Providing the sample is properly selected the results from a sample survey may be just as good as from a census. Selecting shoppers from only St Luke’s shopping centre to establish how much they spend on a Valentine’s Day gift would not represent shoppers from the whole of Auckland.

Why take a sample? It is time consuming to carry out a census for a large population. By the time a census is complete the results may be out of date! The cost of collecting information about a large population may fall outside a budget. Sometimes it is impossible to locate every member of a population or in taking a census the population may be destroyed (eg testing icecream)

Representative Sample A sample that represents the characteristics of the population as closely as possible is called a representative sample. Taking a telephone sample would not produce a representative sample of the population as all those without landlines would be excluded.

Random Sample A sample drawn in such a way that each element of the population has a chance of being selected is called a random sample.

A Random Sample A Random Sample is a sample drawn in such a way that each member of the population has some chance of being included in the sample. In a non-random sample, some members of the population may not have the chance of being selected in the sample.

Errors The results from taking a sample will not give an exact estimate of the population parameters. The difference between the sample estimate and the population parameter is called the sampling error. The other type of error is based on the system we use to take the sample. We can try to minimise this.

Sampling Error Each sample taken from a population will give a different result. Also each sample will give a result that is different from a result from a census. The difference between the results obtained from a sample survey and the result that would have been obtained from the whole population is called sampling error.

Non-sampling Errors These errors occur in the collection, recording and tabulation of data. They are due to poor sample design, mistakes in collecting and recording data, and behaviour of people surveyed. There are several types of system error.

1. Selection error This occurs when the sampling frame, the list we take the sample from, leaves out many members of the population or includes individuals not in the population, eg if a homework survey was done when a large number of students were away at a sports event selection error would occur. It occurs when the sampling frame is not representative of the population.

2. Non-response error This occurs when many of the people in a sample do not respond to a survey. For example a door to door survey taken during a rugby match is likely to have non-response error. This will distort the results.

3. Response error This occurs when people do not give the correct response to a question in the survey. It refers to anything in the survey design that influences the result. It could be the wording of the question may be unclear, it could be that the interviewer influences the response, the question may be sensitive (eg about income or drug use or race relations), etc

4. Self selection error This error is caused if many members of the population do not respond to a survey because it is voluntary. eg if a magazine wants to survey its readers it is likely to have a large self selection error (also called voluntary response error) because not everyone who reads the magazine will take part. Usually only people with strong opinions will respond.

Bias A sample that does not represent the population in some important way is said to be biased. A sample may be biased because of one or more of the above errors.