Lektsii (1) / Lecture 5

ICEF, 2012/2013 STATISTICS 1 year LECTURES

LECTURE 5

October 2, 2012

CHAPTER 2

PLANNING A STUDY

METHODS OF DATA COLLECTION

In studying statistics we learn how to estimate population characteristics by considering sample. For example, if we wish to know the average salary in a region we can select some people and as an estimate of average salary take the arithmetic mean of the salaries. To derive conclusion about the larger population we need to be confident that the sample we have chosen represents this population fairly. Nothing can help if the data are badly collected, even modern and powerful computers and software are useful. Remember: “Garbage in, garbage out”.

Collection: Census versus Sample

Census (перепись): complete enumeration of an entire population. Extremely cost and time consuming.

Sample. A sample survey aims to obtain information about a whole population by studying a part of it, i.e. sample. The goal is to gather information without disturbing or changing the population.

PLANNING AND CONDUCTING SAMPLESURVEY

For data collection to be useful, the resulting sample must be representative of the population under consideration.

Definition. A simple random sample (SRS) is a method of data collection in which every possible sample of the desired size has an equal chance of being selected.

The resulting sample obtained by using SRS is also called simple random sample.

Ideally SRS can be obtained by using the following procedure: to write the name of each member of the population on a card, to mix the cards in a large box, and to pull out a specified number of cards. If the size of a population is not large this method may be realized by using a random number table or special computer software.

Survey: Experiment versus Observational study

Experiment is a controlled study in which researcher can randomly divide subjects into appropriate groups. Some action (treatment) is taken on one or more group, and the response is observed. Experiments often have treatment group and control group. The examples of experiments are medical treatments (drug, special exercises, etc.).

In Observational studies there is no choice in regard to who goes into the treatment and control groups. For example if you want to study the relationship between family income and family vacation expenditure it is impossible to assign to some families one level of income and other level of income to the other group of families. You can only observe the households. Sample survey is an example of observational study.

Important. The main differences between Experiment and Observational study are the

following:

•In an experiment a researcher designs the treatment and control groups and determines the treatment level, while in observational study a researcher deals with given observations.

•The well-designed and well conducted experiment can indicate the cause-and-effect relationships while the observational study can indicate only relationships.

PLANNING AND CONDUCTING SAMPLE SURVEY

No matter how well-designed and well-conducted a survey is, it still gives a sample statistics as an estimate for population parameter. Different samples give different statistics, all of which are estimates for the same population parameter. So, error is naturally present in each sample survey. This error is called sampling error.

Important

•Sample error is always present when a sample survey is conducted.

•Sample error can be described using probability.

•Generally, a sample error is smaller when the sample size is large. However, the way the

data are obtained is crucial − a large sample size cannot make up for a poor survey design or faulty collection technique.

Example. Three organization based on independent polls report the average monthly in come in a region as 15 500 Rub, 16 100 Rub, and 15 700 Rub. All these figures are the estimates of (population) average monthly income in a region.

SOURCES OF BIAS IN SURVEYS

Poorly designed sampling techniques result in bias (смещение), that is, a tendency to favor the selection of certain members of a population.

There are different types of bias. Below is non-complete classification without explicit definition, illustrated by examples.

1.Non-response bias. This bias is present in most mail questionnaires. They tend to have very low response percentages, and it is often unclear which part of population is responding. In other words, those who respond cannot be considered as SRS.

2.Voluntary response bias. This bias is occurring when the conclusions base on individuals who prefer to participate, typically give too much emphasis to persons with strong opinions. For example, radio call-in programs about controversial topics such as gun control, smoking and alcohol restrictions do not produce meaningful data on what proportion of the population favor or oppose related issues.

3.Convenience bias. Convenience samples base on choosing individuals who are easily to reach. For example, interviews at university or church tend to produce data highly unrepresentative of the entire population.

4.Undercoverage bias. The samples in which certain people are left out consideration may result undercoverage bias. For example, telephone surveys simply ignore all those possible subjects who don’t have telephones.

The samples in 1 – 4 are not SRS. Usually a bias, that is occurring because a sample is not SRS, is called selection bias. So, 1 – 4 may be considered as the examples of selection bias.

5.Response or wording bias. People often don’t want to be perceived as having unpopular, unsavory, or illegal views and so may respond untruthfully when face to face with an interviewer or when filling out a questionnaire that is not anonymous.

Important. A concrete survey may have several sources of bias.

Exercises

1.Give the examples of samplings 1 – 5.

2.Give the example of sampling with several sources of bias.