Lektsii (1) / Lecture 6

ICEF, 2012/2013 STATISTICS 1 year LECTURES

LECTURE 6

October 6, 2012

OTHER SAMPLING METHODS

Often SRS is extremely cost and time consuming. There are some other sampling method widely used in practice.

1.Systematic sampling: randomly listing the population in order and then picking every tenth, hundredth, thousandth, and so on, from the list.

2.Stratified sampling: the population is divided into representative groups, called strata, and random samples of persons from all strata are chosen.

3.Proportional sampling: the special case of stratified sampling, when the sizes of the random samples from each stratum depend on the proportion of the total population represented by the stratum.

4.Multistage sampling: divide the population into groupings, subdivide each grouping , select a random sampling of the subdivisions and finally pick a random sample of people from the selected subdivisions.

PLANNING AND CONDUCTING EXPERIMENTS

In an experiment we impose some change or treatment and measure the result or response. The goal of an experiment is to indicate the cause-and effect-relationship between treatment and response or explanatory factor (variable).

Main characteristics of an experimental design:

1.Experimental units. An experiment if performed on objects called experimental units, and the units are people, they are called subjects.

2.Treatment: an action for changing explanatory variable. Examples: new drug for pain relief; gymnastic exercises to improve flexibility; new fertilizer to increase the yield; etc.

3.Treatment level. Often the treatment may have different levels: different plants may be assigned different amounts of fertilizer; etc.

4.Treatment group and control group. The experimental units or subjects are typically divided into two groups. One group receives a treatment and is called the treatment group. Other group receives no treatment and is called control group. A comparison is made between the response noted in the treatment group and the response noted in the control group.

Placebo effect. Planning an experiment, a designer should keep in mind that many people respond to any kind of perceived treatment. This is called the placebo effect. For example, when given a sugar pill after surgery but told that it is a strong pain reliever, many patients feel immediate relief from the pain. Thus when responses are noted in any experiment, there is concern whether real physical responses are being caused by the psychological placebo effect.

Blinding and Double blinding. The typical tool to remove the placebo effect is blinding, when the subjects don’t know treatment or placebo they receive. Double blinding occurs if the response evaluators don’t know too.

Confounding. When there is uncertainty with regard to which variable is causing an effect, we say the variables are confounded. That is, when comparing two groups with regard to their response to some variable, if there is a lurking variable in regard to which the two groups also differ, this lurking variable may very well be confounded with the variable under consideration. For example, if you wish to test a new drug for decreasing cholesterol level, then age or gender of testing people may be confounded factors.

Randomization. Ideally in order to indicate the cause-and-effect relationship between treatment and explanatory variable it is desirable to have subjects with the same confounded factors. Then divide them into treatment and control groups, make a treatment, compare the values of explanatory variable in two groups. If there is significant difference between groups the cause- and-effect relationship is indicated. Because in practice this plan cannot be realized, in order to minimize the effect of confounding factor usually randomization is used to form the treatment and control groups. This means that the division into treatment and control groups should be made by using standard randomization tools like random digit table or computer.

Randomized Paired Comparison Design. Two treatments can be compared based on the responses of paired subjects, one of whom receives one treatment while other receives the second treatment. Often the paired subjects are really single subjects who are given both treatments, one a time.

Blocking. Due to confounding factors and natural difference of the subjects there is a variance of responses in treatment and control groups. In order to control the confounding factors and to decrease the variation of responses an experimental designer may use blocking. This means that before dividing into treatment and control groups the whole group of subjects is divided into blocks. Each block contains subjects having approximately coinciding confounding factors. Then every block is divided into treatment and control group using randomization. For example, testing a new skin cream a researcher may assume that it can give different results for men and women (gender is a confounding factor). So, a researcher makes two separate blocks (men and women) and designs treatment and control group within each block using randomization. The number of blocks may be arbitrary. There may be many types of blocking factors: age, weight, health level, etc. Paired comparison design is a special case of blocking in which each pair can be considered as a block.

Self control

1.What is Census Sample Experiment

Observational study

2.What is the main difference between Experiment and Observational study

3.What is

Simple random sample

Sample bias

Non-response bias

Voluntary response bias

Convenience bias

Undercoverage bias

Response bias

4. What is

Systematic sampling Stratified sampling Proportional sampling Multistage sampling

5. What is

Treatment and treatment level Control group

Placebo effect

Blinding and Double blinding Confounding

Randomization Blocking