Sampling

Introduction to Sampling

Population (universe)--any group or objects which are similar in one or more ways, and which form the subject of study in a particular survey.

Populations may be finite or infinite, depending on the type of research.

Census--when a population or universe is examined in its entirety.

Sample--a number of sampling units is drawn from a population and examined in detail. A sample should be representative of the population on a whole from which it is drawn.

Elementary sampling units (ESU)--an individual element of the population to be sampled, e.g. a certain type of person (age, income, etc.).

Sampling frame--lists, indexes, maps, or other records of a population from which a sample can be drawn, e.g. zip code sampling frame.

Statistic--also known as ‘estimator’; refers to any quantity calculated from a sample to estimate a population parameter.

Parameter--the value of a variable (or attribute) calculated in the population, e.g. the average or mean.

Sampling variability (experimental error)--different samples drawn from a fixed population generally have different statistics.

Sampling distribution--refers to a frequency distribution based on a number of samples, e.g. 12 samples, their means calculated and listed in a frequency distribution.

Stratified distribution--this is a sampling technique where certain known characteristics in the population under survey are represented in certain proportions.

Two broad types of sample:

Random--’probability’: occurs where each element of a population from which the sample is chosen has a known (and non-zero) chance of being selected.

Quota--’non-probability’; type of stratified sampling in which selection of sampling units within strata, e.g. age, sex, social group is done by interviewers on a non-random basis, controlled to some extent by quotas allocated to the different strata.

Sampling error--difference between a sample estimate and the value of the population parameter obtained by a complete count or census.

Sample cells--these are formed when the strata of a sample are further divided, resulting in two or more subdivisions of the sample with common characteristics, e.g population divided into two main strata by sex, further divided into specific age groups, 21 and over, and under 21.

Be sure to familiarize yourself with the statistical symbols found on page 69 of the text. You will be running across them often.

Remember that Greek letters=descriptions of populations and Roman letters=samples.

There are two types of error which may bias sample estimates:

Experimental Error--arising from the differences in estimates that occur if repeated samples are taken from the same population. The degree of experimental error is affected by the variability present in the population and by the size of the sample drawn from it.

Systematic Error--arises from deficiencies in selection and measurement techniques, such as derives from an in efficient sampling frame or from a badly phrased questionnaire.

Sampling theory is concerned with the study of the relationships existing between a population and the samples drawn from it.

As Ferber states: "The very concept of sampling is based on the probability that one member will represent a group; on the probability that a number of members selected at random from a population will be so distributed as to provide a miniature re presentation of that population; on the probability that estimates drawn from this miniature will differ from the true population values only by a certain (measurable) amount attributable to the vagaries of a sample selection."

Statistical sampling theory is based strictly on the mathematics of probability.

We especially look to Estimation and Hypothesis testing in Market Research.

Estimation allows estimates of population parameters, such as the population mean and variance to made from sample statistics such as sample mean , variance etc.

Hypothesis testing enables certain probability statements, based on samples, about characteristics of a population to be tested statistically.

Saves Money

Saves Time

Enables data of high quality to be collected

Few people need to collect and analyze data

Lack of bias--for there to be a lack of bias the the value of an estimate must be equal to the population parameter. In short, a sample should be representative of the population it is taken from.

Consistency--The probability that the sample average approaches the population average as the sample size increases.

Efficiency--involves the comparison between estimators and is stated in relative terms.

Confidence intervals--deals with how close a sample comes to the population.

By using Confidence limits (fiducial limits)a sample estimate of a population parameter can be given which is likely to occur within a given interval.

See book page 74 for further explanation and examples.

One note: as the sample size is increased, the sampling error is decreased, and the confidence limits become narrower.

A sampling frame is a definition of the population to be studied.

There are five criteria useful in evaluating sampling frames:

Adequacy--a sample frame should cover the population to be surveyed.

Completeness--it must cover all units of a population.

No duplication--a unit must not be entered more than once.

Accuracy--it must not include non-existent units.

Convenience--must be accessible and be arranged for easy use.

No sampling frame meets all of these requirements perfectly.