# Statistical Sampling

Statistical sampling techniques are the strategies applied by researchers during the statistical sampling process.

Concerns in Statistical Sampling

Representativeness – This is the primary concern in statistical sampling. The sample obtained from the population must be representative of the same population.

This can be accomplished by using randomized statistical sampling techniques or probability sampling like cluster sampling and stratified sampling.

The reason behind representativeness being the primary concern in statistical sampling is that it allows the researcher to draw conclusions for the entire population. If the sample is not representative of the population, conclusions cannot be drawn since the results that the researcher obtained from the sample will be different from the results if the entire population is to be tested.

Practicability – Practicability of statistical sampling techniques allows the researchers to estimate the possible number of subjects that can be included in the sample, the type of sampling technique, the duration of the study, the number of materials, ethical concerns, availability of the subjects/samples, the need for the study and the amount of workforce that the study demands.

All these factors contribute to the decisions of the researcher regarding to the study design.

Sampling Risks – There are two types of sampling risks, first is the risk of incorrect acceptance of the research hypothesis and the second is the risk for incorrect rejection. These risks pertain to the possibility that when a test is conducted to a sample, the results and conclusions may be different from the results and conclusions when the test is conducted to the entire population.

The risk of incorrect acceptance pertains to the risk that the sample can yield a conclusion that supports a theory about the population when it is actually not existent in the population. On the other hand, the risk of incorrect rejection pertains to the risk that the sample can yield a conclusion that rejects a theory about the population when in fact, the theory holds true in the population.

Comparing the two types of risks, researchers fear the risk of incorrect rejection more than the risk of incorrect acceptance. Consider this example; an experimental drug was tested for its debilitating side effects. With the risk of incorrect acceptance, the researcher will conclude that the drug indeed has negative side effects but the truth is that it doesnâ€™t. The entire population will then abstain from taking the drug. But with the risk of incorrect rejection, the researcher will conclude that the drug has no negative side effects. The entire population will then take the drug knowing that it has no side effects but all of them will then suffer the consequences of the mistake of the researcher.

Random Sampling

A random sample is obtained by using methods such as random numbers, which can be generated from calculators, computers, or tables. In random sampling, the basic requirement is that, for a sample of size n, all possible samples of this size have an equal chance of being selected from the population. But before the correct method of obtaining a random sample is explained, several incorrect methods commonly used by various researchers and agencies to gain information are discussed. To meet the requirement of having an equal chance of being selected. either of the two methods can be used

• The first method is to number each element of the population and then place the numbers on cards. Place the cards in a hat or fishbowl, mix them, and then select the sample by drawing the cards. When using this procedure, researchers must ensure that the numbers are well mixed. On occasion, when this procedure is used, the numbers are not mixed well, and the numbers chosen for the sample are those that were placed in the bowl last.
• The second and preferred way of selecting a random sample is to use random numbers.

The theory behind random numbers is that each digit, 0 through 9, has an equal probability of occurring. That is, in every sequence of 10 digits, each digit has a probability of occurring. This does not mean that in every sequence of 10 digits, you will find each digit. Rather, it means that on the average, each digit will occur once. For example, the digit 2 may occur 3 times in a sequence of 10 digits, but in later sequences, it may not occur at all.

To obtain a sample by using random numbers, number the elements of the population sequentially and then select each person by using random numbers.

Sampling Bias

Bias in sampling is the tendency for samples to differ from the corresponding population in some systematic way. Bias can result from the way in which the sample is selected or from the way in which information is obtained once the sample has been chosen. The most common types of bias encountered in sampling situations are selection bias, measurement or response bias, and non-response bias.

Selection bias (sometimes also called undercoverage) is introduced when the way the sample is selected systematically excludes some part of the population of interest. For example, a researcher may wish to generalize from the results of a study to the population consisting of all residents of a particular city, but the method of selecting individuals may exclude the homeless or those without telephones. If those who are excluded from the sampling process differ in some systematic way from those who are included, the sample is virtually guaranteed to be unrepresentative of the population. If this difference between the included and the excluded occurs on a variable that is important to the study, conclusions based on the sample data may not be valid for the population of interest. Selection bias also occurs if only volunteers or self-selected individuals are used in a study, because self-selected individuals (e.g., those who choose to participate in a call-in telephone poll) may well differ from those who choose not to participate.

Measurement or response bias occurs when the method of observation tends to produce values that systematically differ from the true value in some way. This might happen if an improperly calibrated scale is used to weigh items or if questions on a survey are worded in a way that tends to influence the response.

Other things that might contribute to response bias are the appearance or behavior of the person asking the question, the group or organization conducting the study, and the tendency for people not to be completely honest when asked about illegal behavior or unpopular beliefs.

Non-response bias occurs when responses are not obtained from all individuals selected for inclusion in the sample. As with selection bias, non-response bias can distort results if those who respond differ in important ways from those who do not respond. Although some level of non-response is unavoidable in most surveys, the biasing effect on the resulting sample is lowest when the response rate is high. To minimize non-response bias, it is critical that a serious effort be made to follow up with individuals who do not respond to an initial request for information.

The non-response rate for surveys or opinion polls varies dramatically, depending on how the data are collected. Surveys are commonly conducted by mail, by phone, and by personal interview. Mail surveys are inexpensive but often have high non-response rates. Telephone surveys can also be inexpensive and can be implemented quickly, but they work well only for short surveys and they can also have high non-response rates. Personal interviews are generally expensive but tend to have better response rates.