# Non-probability sampling

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The difference between probability and non-probability sampling has to do with a basic assumption about the nature of the population under study. In probability sampling, every item has a chance of being selected. In non-probability sampling, there is an assumption that there is an even distribution of characteristics within the population. This is what makes the researcher believe that any sample would be representative and because of that, results will be accurate. For probability sampling, randomization is a feature of the selection process, rather than an assumption about the structure of the population.

In non-probability sampling, since elements are chosen arbitrarily, there is no way to estimate the probability of any one element being included in the sample. Also, no assurance is given that each item has a chance of being included, making it impossible either to estimate sampling variability or to identify possible bias.

Reliability cannot be measured in non-probability sampling; the only way to address data quality is to compare some of the survey results with available information about the population. Still, there is no assurance that the estimates will meet an acceptable level of error. Statisticians are reluctant to use these methods because there is no way to measure the precision of the resulting sample.

Despite these drawbacks, non-probability sampling methods can be useful when descriptive comments about the sample itself are desired. Secondly, they are quick, inexpensive and convenient. There are also other circumstances, such as in applied social research, when it is unfeasible or impractical to conduct probability sampling. Statistics Canada uses probability sampling for almost all of its surveys, but uses non-probability sampling for questionnaire testing and some preliminary studies during the development stage of a survey.

Most non-sampling methods require some effort and organization to complete, but others, like convenience sampling, are done casually and do not need a formal plan of action.

The most common types are listed below:

## Convenience or haphazard sampling

Convenience sampling is sometimes referred to as haphazard or accidental sampling. It is not normally representative of the target population because sample units are only selected if they can be accessed easily and conveniently.

There are times when the average person uses convenience sampling. A food critic, for example, may try several appetizers or entrees to judge the quality and variety of a menu. And television reporters often seek so-called ‘people-on-the-street interviews' to find out how people view an issue. In both these examples, the sample is chosen randomly, without use of a specific survey method.

The obvious advantage is that the method is easy to use, but that advantage is greatly offset by the presence of bias. Although useful applications of the technique are limited, it can deliver accurate results when the population is homogeneous.

For example, a scientist could use this method to determine whether a lake is polluted. Assuming that the lake water is well-mixed, any sample would yield similar information. A scientist could safely draw water anywhere on the lake without fretting about whether or not the sample is representative.

Examples of convenience sampling include:

• the female moviegoers sitting in the first row of a movie theatre
• the first 100 customers to enter a department store
• the first three callers in a radio contest.

## Volunteer sampling

As the term implies, this type of sampling occurs when people volunteer their services for the study. In psychological experiments or pharmaceutical trials (drug testing), for example, it would be difficult and unethical to enlist random participants from the general public. In these instances, the sample is taken from a group of volunteers. Sometimes, the researcher offers payment to entice respondents. In exchange, the volunteers accept the possibility of a lengthy, demanding or sometimes unpleasant process.

Sampling voluntary participants as opposed to the general population may introduce strong biases. Often in opinion polling, only the people who care strongly enough about the subject one way or another tend to respond. The silent majority does not typically respond, resulting in large selection bias.

Television and radio media often use call-in polls to informally query an audience on their views. The Much Music television channel uses this kind of survey in their CombatZone program. The program asks viewers to cast a vote for one of two music videos by telephone, e-mail or through their online website.

Oftentimes, there is no limit imposed on the frequency or number of calls one respondent can make. So, unfortunately, a person might be able to vote repeatedly. It should also be noted that the people who contribute to these surveys might have different views than those who do not.

## Judgement sampling

This approach is used when a sample is taken based on certain judgements about the overall population. The underlying assumption is that the investigator will select units that are characteristic of the population. The critical issue here is objectivity: how much can judgment be relied upon to arrive at a typical sample? Judgement sampling is subject to the researcher's biases and is perhaps even more biased than haphazard sampling. Since any preconceptions the researcher may have are reflected in the sample, large biases can be introduced if these preconceptions are inaccurate.

Statisticians often use this method in exploratory studies like pre-testing of questionnaires and focus groups. They also prefer to use this method in laboratory settings where the choice of experimental subjects (i.e., animal, human, vegetable) reflects the investigator's pre-existing beliefs about the population.

One advantage of judgement sampling is the reduced cost and time involved in acquiring the sample.

## Quota sampling

This is one of the most common forms of non-probability sampling. Sampling is done until a specific number of units (quotas) for various sub-populations have been selected. Since there are no rules as to how these quotas are to be filled, quota sampling is really a means for satisfying sample size objectives for certain sub-populations.

The quotas may be based on population proportions. For example, if there are 100 men and 100 women in a population and a sample of 20 are to be drawn to participate in a cola taste challenge, you may want to divide the sample evenly between the sexes—10 men and 10 women. Quota sampling can be considered preferable to other forms of non-probability sampling (e.g., judgement sampling) because it forces the inclusion of members of different sub-populations.

Quota sampling is somewhat similar to stratified sampling in that similar units are grouped together. However, it differs in how the units are selected. In probability sampling, the units are selected randomly while in quota sampling it is usually left up to the interviewer to decide who is sampled. This results in selection bias. Thus, quota sampling is often used by market researchers (particularly for telephone surveys) instead of stratified sampling, because it is relatively inexpensive and easy to administer and has the desirable property of satisfying population proportions. However, it disguises potentially significant bias.

As with all other non-probability sampling methods, in order to make inferences about the population, it is necessary to assume that persons selected are similar to those not selected. Such strong assumptions are rarely valid.

Example 1: The student council at Cedar Valley Public School wants to gauge student opinion on the quality of their extracurricular activities. They decide to survey 100 of 1,000 students using the grade levels (7 to 12) as the sub-population.

The table below gives the number of students in each grade level.

Table 1. Number of students enrolled at Cedar Valley Public School, by grade
Grade level Number of students Percentage of students (%) Quota of students in sample of 100
7
150
15
15
8
220
22
22
9
160
16
16
10
150
15
15
11
200
20
20
12
120
12
12
Total
1,000
100
100

The student council wants to make sure that the percentage of students in each grade level is reflected in the sample. The formula is:

Percentage of students in Grade 10
= (number of students ÷ number of students) x 100%
= (150 ÷ 1,000) x 100
= 15%

Since 15% of the school population is in Grade 10, 15% of the sample should contain Grade 10 students. Therefore, use the following formula to calculate the number of Grade 10 students that should be included in the sample: