#sampling error

To make accurate predictions of parameters, the sample used should be a representative sample of the population, where the sample is very reflective of the characteristics of the population. A good, representative sample provides the researcher with a "miniature mirror" to view an entire population.

There are two basic techniques for achieving representative samples: random sampling and stratified, or quota, sampling.

Random Sampling Random sampling is one of the media's misused terms. For example, newspapers claim to have selected a random sample of their readers, or television stations claim to have interviewed a random sample of city residents. However, all of these selections were done in an unorganized, careless way, which is not what random sampling does.

Random sampling requires that each member of an entire population has an equal chance of being included in the sample and no members of an entire population may be systematically excluded. If a researcher was trying to get a random sample of a population of students at a college, the researcher cannot simply select from the students who are free enough in the afternoon to meet with them. This would then exclude all of the students that are not free at that time. Unless the entire population is available for selection, the sample cannot be random.

For the researcher to obtain a random sample from the college, they would have to go to the registrar's office and get a list of names of the entire student population, then select at random the sample. Then the researcher must go out and find each student selected for the sample, because a sample can never be random if the subjects are allowed to select themselves. For example, instead of the researcher finding each student, they send each selected student an e-mail requesting to fill out a survey. However, only a few of the selected students fill out the survey. This is not a random sample, because the researcher allowed the subjects to select themselves on the basis of which the subjects decided whether or not they felt like filling out the survey. The subjects that did comply may have differed systematically on many other traits from the subjects who simply ignored the e-mail.

Stratified, or Quota, Sampling Another major technique for selecting a representative sample is known as stratified, or quota, sampling. This technique is sometimes combined with random sampling, where once the strata has been identified, random samples from each subgroup are selected. This is then called stratified random sampling.

To obtain a stratified sample, the researcher must know what some of the major characteristics are of the population, then deliberately select a sample that shares these characteristics in the same proportions. For example, if 35% of a student population are sophomores and 60% of those sophomores are majoring in business, then a quota sample of the population must have the same percentages.

Sampling Error Whenever a sample is selected, it must be assumed that the sample measures will not be quite exact as the measures obtained from the entire population.

To distinguish from the sample mean, M or x bar, the mean of the population is symbolized with the Greek letter mu, μ.

Then the sampling error is the difference between the sample mean and the population mean.

sampling error = M - μ

Note that the sample mean is expected to possibly deviate from the population mean; this is a normal, expected deviation. Sampling error is not a mistake, it is an expected amount of deviation. Additionally, sampling error should be random, where it can go either direction. The sample mean is just as often below the population mean as it is above the population mean. Therefore, if the means of 100 random samples from a given population were calculated, 50% of the resulting sampling errors will be positive (which is when the sample mean overestimates the population mean) and the other 50% of the resulting sampling errors will be negative (which is when the sample mean underestimates the population mean). Therefore, using probabilities, the probability of the sampling error being positive is P = 0.50 and the probability of the sampling error being negative is P = 0.50.

Outliers When one or two data values in a large random sample fall very far from the mean, such as 5 or 10 standard deviation units away, these data values are called outliers.

Outliers indicate either that the distribution is not normal or that some measurement error has occurred. When outliers occur, they can increase the standard deviation to more than one-sixth of the range, making the distribution look platykurtic. When it is clear that an outlier was not produced from bias, most researchers discard the outlier.

Bias Whenever the sample differs systematically from the entire population it was taken from, bias has occurred. Since researchers usually deal in averages, bias is defined as a constant difference in one direction between the mean of the sample and the mean of the population.

For example, the mean verbal S.A.T. score at a college is 500. If a researcher only selected for their sample students who did a poor performance in their English placement test, it will be likely that the mean verbal S.A.T. score among the sample is lower than the mean verbal S.A.T. score of the population.

Sampling error is a useful tool in the hands of anyone who routinely gathers data, which is pretty much anyone.  It has great value for two-year olds, who spend nearly all of their waking hours collecting data about the world.  It is equally as valuable to adult scientists whose working hours are generally spent recording data for a living.  Simply put, when the data humans gather doesn’t agree…

New Post has been published on http://sb.stakll.com/2014/04/17/in-u-s-blacks-most-likely-to-be-very-obese-asians-least-as-americans-enter-middle-age-they-become-more-likely-to-be-very-obese/

In U.S., Blacks Most Likely to Be Very Obese, Asians Least; As Americans enter middle age they become more likely to be very obese.

Synopsis: Blacks are the most likely in the U.S. to be very obese,

with 15% classified this way because their Body Mass Index is 35 or

higher. BMIs this high are common among the low-income and middle-aged

and least prevalent among Asians.

WASHINGTON, D.C. — Blacks are among the most likely in the United

States to be very obese, with about 9% falling into obese class II and

6% obese class III — the highest Body Mass Index (BMI) categories.

Asians are by far the least likely to fall into these two classes of

obesity. Hispanics are on par with whites for each obesity class.

Relationships by race and the others presented in this article hold

true even when controlling for age, ethnicity, race, marital status,

gender, employment, income, education, and region.

The findings are based on data collected as part of the

Gallup-Healthways Well-Being Index from Jan. 1, 2010 through May 31,

2012, and include interviews with more than 800,000 American adults aged

18 and older. Gallup calculates respondents’ BMIs using the

standard formula based on their self-reported height and weight.

An average of 26.3% of all respondents surveyed reported a height

and weight that led to a BMI calculation high enough to be categorized

as obese. Gallup and Healthways have been tracking Americans’ BMI

levels daily since January 2008 and find obesity is slightly higher now

than it was in 2008.

The World Health Organization defines a normal BMI range as being

18.50 to 24.99. It labels BMIs of 25.00 to less than 30.00 as

overweight/pre-obese. BMIs of 30.00 or higher fall into one of three

classes of obesity:

Those with BMIs of 40 or higher — obese class III — are also

frequently considered “morbidly obese.” Based on their

self-reports of height and weight, nearly 4% of American adults overall

are this obese, with a total of about one in 10 with BMIs high enough to

place them in the two highest obesity classes. However, all groups are

more likely to fall on the lower end of the obesity scale than the

higher end.

While men are more likely than women in general to be obese,

including obese class I, women and men are equally likely to fall into

obese class II — and women are, in fact, more likely than men to have a

BMI high enough to put them in obese class III. The U.S. Centers for

Disease Control and Prevention also previously found that women are more

likely than men to fall into obese class III, based on data from the

2007-2008 National Health and Nutrition Examination Survey, which

measured respondents’ actual height and weight.

As with obesity in general, each of the three classes of obesity

rise precipitously as Americans age — peaking in late middle-age — but

then drop off as Americans enter their 70s. Part of the drop-off as age

increases may be related to the shorter life expectancy among those who

are obese.

Income and education level are also related to Americans’

obesity levels. Those Americans with the lowest income levels and who

are the least educated are the most likely to be very obese.

About 5% of low-income Americans have BMIs high enough to put them

in obese class III, but that falls to 2.9% among those with annual

incomes of $36,000 to less than $90,000, and 1.8% among high-income

Americans ($90,000 or more per year).

Similarly, 4.4% of Americans with a high school education or less

are categorized as class III obese. That falls as education rises — to

3.6% among Americans with some college or vocational education, then to

2.3% among college graduates, and further to 1.8% among postgraduates.

Unemployed Americans are more likely than those who are employed to

have high enough BMIs to be in obese classes II and III. But, the

unemployed are only slightly more likely than the employed to be in

obese class I.

This finding expands on a recent Gallup analysis showing that the

unemployed are more likely than the employed to be obese in general. It

may reveal that a lower level of obesity isn’t as prohibitive to

working as the more severe classes of obesity can be.

Bottom Line

Obesity of all types is related to higher levels of chronic

conditions such as high blood pressure and diabetes as well as a lower

quality of life — including worse emotional health, more daily pain,

and more missed work. It is also tied to shorter life expectancy. The

more obese an individual is, the more likely he or she is to experience

these types of problems. And, those who are morbidly obese — with BMIs

of 40 or higher — are the most at risk.

Gallup-Healthways Well-Being Index data reveal that black,

low-income, middle-aged, less-educated, and unemployed Americans are the

most likely to be very obese, including morbidly obese. As government,

business, and healthcare leaders continue to try to develop policies and

programs to reduce obesity in the United States, they may need to target

specific efforts toward these high-risk groups. On the other hand, the

study of those groups that are less likely to be obese — including

Asians, very young and very old Americans, and those with higher

socioeconomic status — may provide insights into behaviors and

practices associated with a more normal weight.

The U.S. government is already taking steps to further address the

nation’s obesity problem, with the U.S. Preventative Services Task

Force putting out in June new guidelines for obesity screenings. The

task force is recommending that all adults get screened for obesity and

that doctors should refer patients with a BMI of 30 or higher to

“intensive, multicomponent behavioral interventions.”

As more Americans gain access to doctors through the 2010

Affordable Care Act, it is possible that guidelines such as these will

have an even greater impact on reducing obesity in the United States.

Gallup will be publishing an in-depth series further exploring why

certain groups — such as blacks and middle-aged Americans — are more

likely to be obese than others — such as Asians. The forthcoming

analysis will reveal the key predictors of obesity and will shed light

on what else can be done to reduce it.

Results are based on telephone interviews conducted as part of the

Gallup-Healthways Well-Being Index survey Jan. 1 2010-May 31, 2012, with

a random sample of 808,660 adults, aged 18 or older, living in all 50

U.S. states and the District of Columbia.

For results based on the total sample of national adults, one can

say with 95% confidence that the maximum margin of sampling error is 1

percentage point.

Interviews are conducted with respondents on landline telephones

and cellular phones, with interviews conducted in Spanish for

respondents who are primarily Spanish-speaking. Each sample includes a

minimum quota of 400 cell phone respondents and 600 landline respondents

per 1,000 national adults, with additional minimum quotas among landline

respondents by region. Landline telephone numbers are chosen at random

among listed telephone numbers. Cell phones numbers are selected using

random digit dial methods. Landline respondents are chosen at random

within each household on the basis of which member had the most recent

birthday.

Samples are weighted by gender, age, race, Hispanic ethnicity,

education, region, adults in the household, and phone status (cell

phone-only/landline only/both, cell phone mostly, and having an unlisted

landline number). Demographic weighting targets are based on the March

2011 Current Population Survey figures for the aged 18 and older

non-institutionalized population living in U.S. telephone households.

All reported margins of sampling error include the computed design

effects for weighting and sample design.

In addition to sampling error, question wording and practical

difficulties in conducting surveys can introduce error or bias into the

findings of public opinion polls.

For more details on Gallup’s polling methodology, visit