PART THREE STATISTICAL ANALYSIS FOR DECISION MAKING

Why Sample

In this brief scenario, we are introduced to one of the most important tools in the decision making process of the business community—the survey. Although often treated with disdain, it can be highly informative and of enormous assistance to everyone from the multinational executive officer to the small retailer in Oshkosh, Wisconsin.Perhaps, the survey represents the outstanding example of using sampling techniques to make inferences about populations.

But why sample? Why not target a particular population in which we are interested and then conduct a census of this population ? Certainly it would remove the uncertainty that inevitably accompanies drawing inferences from samples.

Example

Statistics on the U.S.population have been collected and published decennially（every 10 years）ever since 1790, generally with increasing amounts of detail.The decennial census attempts to count every person, household, and so forth, in the population.It is designed to be the most complete census of the entire population. Perhaps because it is the biggest, it best illustrates the problems with census taking and why sampling is probably, even here, the best way to collect data.

Let's look at the 1980 census and some of the problems associated with an attempt to measure every member of a population and, thus, obtain the actual parameters, not just estimates from samples.

Because the population is so very large, and, in some cases, scattered, the cost of the 1980 census will well exceed $1 billion! The massive undertaking officially got under way in the spring. On March 28,1980, census forms were sent through the mail.Let's look at some of the problems that arose from the system used to collect the data.First, many citizens reported that they never received the form in the March mailing.The U.S.Postal Service said that the mailing lists were filled with errors.For example,13 percent of the census forms in Manhattan were undeliverable because of bureau errors.Approximately 85 percent of the mailed forms were filled out and returned.Since the census attempts a complete count of all citizens, over 300,000 workers were recruited and paid to follow up mailed forms and to contact residents of out-of-the-way places. Think of the monetary expenses involved here!

Timeliness, as we know, is a key factor.Unfortunately, the 1980 census found itself embroiled in legal difficulties. Thus, not only was there a significant time delay, but one can well imagine the impact these litigations will have on the final costs.

Then, of course, census officials encountered the usually types of problems associated with any census.Many members of the population were inaccessible, unavailable, or simply unresponsive. Although the law provides penalties for not giving the bureau required information, one census bureau supervisor reported, “It's very difficult to count people who don't want to be counted.”He indicated that such people include illegal aliens, welfare cheats, tax evaders, and others who feel the census invades their privacy.This particular type of problem—dealing with the part of the population that is not included—has already led to various legal skirmishes.For example, a federal judge upheld Detroit's contention that its residents had been undercounted.New York city officials claim that the 1980 census missed at least 800,000 of its citizens.In recent years, big cities have asserted that the bureau has missed huge numbers of blacks and Hispanics because its approach to counting citizens is antiquated.As of September 1980, the bureau faced lawsuits filed by cities（other than Detroit）such as New York, Philadelphia, Chicago, and Newark.According to The Wall Street Journal, all the suits are aimed at a readjustment of the 1980 figures.

Thus, we see, even the biggest census of them all has its problems.Later, we shall examine some of the errors associated with these government censuses.The director of the National Opinion Research Center at the University of Chicago said, “Maybe [the Census Bureau]can count noses, but the more people they have to count, the less chance there is that they'll do it right.”

Let's look at a few additional examples that illustrate why we sample.

The cost per minute of television advertising is determined by such factors as the time of the day, the day of the week, and the size of the estimated audience viewing a particular program. With approximately 98 percent of all U.S.homes owning at least one TV set, it is unthinkable that the TV viewing practices of the residents of all 75,000,000 homes could be obtained.The population is simply too large.Even if it were not, the cost would be prohibitive and the time required to collect and analyze the data might make the results as timely as last week's newspapers.

In order to assess the risk of serious injury or death to drivers and passengers in a given model compact car, the car is driven into a concrete wall at 35 miles per hour.A dummy, wired with sensitive electronic equipment, provides data on the possible consequences of the impact.Since the test involves the destruction of the vehicle, few cars would be available at the dealership if the entire population were tested in this way.

A government agency authorizes a study to determine the principal causes of mine disasters.The total population is not available since the sites of some of the disasters may be buried under tons of dirt and water.Or, a college is interested in the income and occupations of its alumni.For a variety of reasons, it may be impossible to query some members of this population.They may be dead, institutionalized, or inaccessible because they hold high political offices or for various other reasons.Hence, a sample must suffice to represent the population.

We have attempted to illustrate that there are a number of factors that make it necessary for us to sample rather than to attempt to measure the entire population.

In brief, the reasons for sampling are：

1.Economy.The larger and less accessible the population of interest, the greater the cost of obtaining a census vis à vis collecting a sample. There are times, however, where the population is sufficiently small and accessible that cost differences are negligible.

2.Timeliness.Generally, it requires less time to collect, analyze, and report the data from a sample than to perform similar operations with a census. If the survey is required in order to make a timely decision, the sample survey has a distinct advantage.Again, if the population is sufficiently small and accessible, this advantage will be diminished.I should be emphasized that inferential statistical procedures are not required following the collection of census data.A mean or proportion is a parameter and is not an estimate.

3.Destruction of item.When testing destroys or impairs the operation of an item, there is no real choice but to sample.

4.Infinite population.When the population is unlimited, such as that resulting from an ongoing production process, sampling must be undertaken since a census is impossible.

5.Accuracy.Paradoxically, a sample may be more accurate than a census.This is especially the case in surveys that require much information from the respondents.Because of cost and time factors, a sample may permit detailed probing whereas a census frequently involves yes-no types of responses.

Richard P.Runyon and Audrey Haber, Business Statistics © 1982, pp.158161.Reprinted by permission of Richard D.Irwin, Inc., Homewood, Illinois.

KeyTerms and Concepts

sample to draw data as an example to represent the population in a given research work so as to make inferences about population.

survey statistical investigation.

population the total collection of elements or items that fall into the scope of a statistical investigation.

dummy an artificial human form electronically wired to measure force impact,used in automotive crash testing.

mean A mean is the sum of the values of a set of observations divided by the number of observations.

estimate the numerical value of the statistic used to estimate a parameter.