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An Introduction to Statistics - Lesson 2

The How and Why of Statistical Sampling

Lesson Overview

Points to Consider

Before analyzing data statistically, it is important to consider if the data were collected appropriately. Many years of labor and even careers have been virtually wasted because of fundamental flaws in the data collection step. The statistical analysis will only likely be a minor part of the total expense of a properly conducted experiment, so time, effort, and money spent ensuring the data are collected appropriately is certainly well spent. The computer adage Garbage In, Garbage Out or GIGO is rather apropos.

Ensure that the sample size is large enough.

Although a large sample is no guarantee of avoiding bias, too small a sample is a recipe for disaster. How to determine minimum sample size goes beyond the scope of this introduction, but suffice it to say there are well established techniques to determine such. These techniques are based on the Central Limit Theorem and some information can be found in Probabilities and Distributions lesson 12.

Better results are obtained by measuring instead of asking.

A good classroom example would be to collect people's heights. We expect might be randomly distributed. Asking will result in several sources of error. Perhaps the most common being exaggeration, rounding, hair style, and shoe heel variation or even complete absence of shoes. Were you instead to measure each individual, these sources of error could be reduced. You may still encounter systematic errors. Following are some sources of systematic error. Perhaps your measuring device is defective. Specific examples might include the common fact that rulers often don't start exactly at zero, but have a little extra margin. Maybe the measuring tape is marked off in inches on one side and tenth's of a foot on the other and sometimes the wrong side is read. Tape measures can become kinked or even tangled (especially surveying caves). Perhaps being a Center students correlates with being shorter or taller for some unknown reason. This might only be a problem if you were to use your data to represent a larger population.

The medium used (mail, phone, personal interview) is important.

Surveys are a very popular method of data collection for social issues. Mail surveys tend to have a lower response rates which will distort and hence flaw a sample. Although telephone surveys may be relatively efficient and inexpensive, the more time consuming and correspondingly expensive personal interview allows more detailed and complex data to be collected. Be not called by telemarketers.

Be sure the sample is representative of the population.

An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. An experiment deliberately imposes some treatment on individuals in order to observe their responses. Observational studies are then a poor way to gauge the effect of an intervention. When our goal is to understand cause and effect, experiments are the only source of fully convincing data. However, imposing treatments may produce some ethical concerns. See more below under experimental design.

Before we move on to the next point, we should note that some studies are retrospective, or involve looking back at past events, whereas others are prospective or track groups forward in time.

Methods of Sampling

Sampling is the fundamental method of inferring information about an entire population without going to the trouble or expense of measuring every member of the population. Developing the proper sampling technique can greatly affect the accuracy of your results.

Statisticians have classified sampling into five common types, as follows.

Random Sampling: Members of the population are chosen in such a way that all have an equal chance to be measured.

Other names for random sampling include representative and proportionate sampling because all groups should be proportionately represented. Consider what might happen if a telephone directory were used as a source for randomly selecting survey participants. Some people have no phone, others have multiple phones and corresponding listings. Still others have unlisted phone numbers. In affluent areas unlisted phone numbers may approach half the population! Now-a-days many are giving up lands lines and use cell phone exclusively. Cell phone directories are controversial at best. Pollsters commonly use computers to generate and dial phone numbers in an attempt to circumvent these problems. However, many people consider such use of the telephone as an invasion of their privacy and refusals or hang-ups may well significantly influence the outcome. Some of us have learned to recognize these computer dialers and quickly hang up. Such are the pitfalls which must be carefully considered in designing an experiment, study, or survey.

Systematic Sampling: Every kth member of the population is sampled.

The historic event leading to the word decimate, where every 10th Roman soldier was killed, is a gruesome example of systematic sampling.

Stratified Sampling: The population is divided into two or more strata and each subpopulation is sampled (usually randomly).

Stratum is the singular form of the word strata which means to spread out. One of the word's most common usage is in geology to describe the layers of sedimentary rocks which have formed during the earth's history. Gender and age groups would be commonly used strata. Classes is another term for strata. Each stratum must share the same characteristic. Random sampling may well be used to select a certain number of data points from each stratum. This is often the most efficient sampling method.

Cluster Sampling: A population is divided into clusters and a few of these (often randomly selected) clusters are exhaustively sampled.

Exhaustively means considering all elements. Cluster sampling is used extensively by governmental and private research organizations.

Convenience Sampling: Sampling is done as convenient, often allowing the element to choose whether or not it is sampled.

Convenience sampling is the easiest and potentially most dangerous. Often good results can be obtained, but perhaps just as often the data set may be seriously biased. Consider collecting GPA information from students in detention. It may be convenient, but perhaps not representative of the entire student body!

Be wary of convenience sampling.

Sampling Error

We have listed above several sources of sampling error. One of the most famous sampling errors occurred in 1948 when the Gallup poll predicted Dewey would be elected president over Truman. The day after the election, such an announcement made the front page of a major newspaper! Gallup then abandoned the quota system and instituted random sampling based on clusters of interviews nationwide. Sample subjects should be selected by the pollster. They should not select themselves as they do via mail or perhaps telephone surveys. The systematic errors listed above are examples of nonsampling errors.

Of great debate recently was what to do with the errors which arise in the decennial US Census. Considerable time was spent by all three branches of our government addressing this issue.

Question Types

Some questions are classified as open, whereas other questions are classified as closed. Open questions elicit open-ended responses and thus work best in a personal interview. Multiple-choice or true/false questions are a type of closed question. Closed questions can thus more easily be coded and analyzed by a computer.

Record Keeping

In science especially, a detailed lab notebook is important for serious work. Standards will vary with the institution, level, and seriousness of the work. Some common requirements are as follows.
  1. Records should be kept in a bound notebook of quality paper.
  2. Entries should be made in ink with each page numbered (and none missing).
  3. Each page should be signed and dated by the principle participants.
  4. A full account of each experiment should be given, including set-up, procedure, original data, analysis, and conclusions.
  5. Establish beforehand who will retain the notebook.
If surveys are used be sure to include the survey sponsor, the date the survey was conducted, the size of the sample, the nature of the population sampled, the type of survey used, and the exact wording of the survey questions. Other important issues include: assessing the risk to those surveyed, the scientific merit of the survey, and the guarantee of the subject's consent to participate. An example of risk might be the hazard of planting ideas (rape, murder, suicide, etc.) in someone's head or reviving suppressed memories (abuse) while asking related questions. Nuclear poisoning/fallout from the 1950's and associated cancer deaths would be another example of risk which was recently (Sep. 2000/1998) in the news.

Lab notebooks and other sources have commonly been used to establish priority and patent claims. This may occur long after the records were made, so detail and clarity are important to remember. Patents and associated royalties for the transistor, the laser, and even computers have depended on such records. Lab write-ups are an essential part of any science experiment and will provide practice in this area.

The principle author has done original research in several different fields (Chemistry, Mathematics, Physics, and Computer Science) at various times in his career. Organization has been a key factor in such an achievement. Without it, the ability to move between fields would be severely hampered. Detailed records were certainly important when accusations of embezzlement arose!

Fabrication or falsification of data, although rare, is a serious breach of ethics. It can easily result in the end of a career however promising it might have been. Such record keeping can be extremely important in trying to reproduce someone else's findings. You might consider it a sort of professional diary. Classic scientific failures include evidence of a fifth force (antigravity) and cold fusion (now known as low energy nuclear reactions or LENR). Differentiating between being mislead and fabrication can be very important.

Experimental Design

More information on experimental design (treatments, factors, blocking, double blind, latin square, randomized complete block, matched pairs, replication, and simulation) should be included here but isn't. Consult any good Statistics book or take the AP Statistics course for more information.

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