QUOTA SAMPLING: METHOD, ADVANTAGES, DISADVANTAGES, EXAMPLES - DUDAS - 2025

The quota sampling is a non - probabilistic way to take data from a sample strata allocating quotas. The quotas must be proportional to the fraction that this stratum represents with respect to the total population and the sum of the quotas must be equal to the size of the sample.

The researcher is the one who decides which groups or strata will be, for example, he can divide a population into men and women. Another example of strata are age ranges, for example from 18 to 25, from 26 to 40 and from 40 onwards, which can be labeled like this: young, old and old.

Figure 1. The sampling quotas are segmented according to the differences in the total population. Source: Pixabay.

It is very convenient to know in advance what percentage of the total population represents each stratum. Then a statistically significant sample size is chosen, and proportional quotas are assigned to the percentage of each stratum with respect to the total population. The sum of the quotas per stratum must be equal to the total size of the sample.

Finally, the data of the quotas assigned to each stratum is taken, choosing the first elements that complete the quota.

It is precisely because of this non-random way of choosing the elements that this sampling method is considered non-probabilistic.

Steps to sample by quotas

Step 1

Segment the total population into strata or groups with some common characteristic. This characteristic will be previously decided by the statistical researcher conducting the study.

Step 2

Determine what percentage of the total population represents each of the strata or groups chosen in the previous step.

Step 3

Estimate a statistically significant sample size, according to the criteria and methodologies of statistical science.

Step 4

Calculate the number of elements or quotas for each stratum, so that they are proportional to the percentage that each one represents with respect to the total population and the total size of the sample.

Step 5

Take the data of the elements in each stratum until completing the quota corresponding to each stratum.

Practical case

Suppose you want to know the level of satisfaction with the metro service in a city. Previous studies on a population of 2000 people determined that 50% of users are young people between 16 and 21 years old, 40% are adults between 21 and 55 years old and only 10% of users are older than 55 years.

Taking advantage of the results of this study, it is segmented or stratified according to the age of the users:

-Young people: 50%

-Adults: 40%

-Elderly: 10%

As there is a limited budget, the study has to be applied to a small but statistically significant sample. A sample size of 200 is chosen, that is, the survey on the level of satisfaction will be applied to 200 people in total.

It now remains to determine the quota or number of surveys for each segment or stratum, which must be proportional to the size of the sample and the percentage per stratum.

Quota per stratum

The quota for the number of surveys per stratum is as follows:

Youth: 200 * 50% = 200 * (50/100) = 100 surveys

Adults: 200 * 40% = 200 * (40/100) = 80 surveys

Seniors: 200 * 10% = 200 * (10/100) = 20 surveys

Figure 2. Quotas in a sample of 200 individuals according to age stratum. Source: F. Zapata.

Note that the sum of the fees has to be equal to the sample size, that is, equal to the total number of surveys that will be applied. Then the surveys are passed until the quotas for each stratum are met.

It is important to note that this method is much better than taking all the surveys and passing them on to the first 200 people that appear, because according to previous data, it is very likely that the minority stratum will be left out of the study.

Applicability, advantages and disadvantages

For the method to be applicable, a criterion is required for the formation of the strata, which depends on the objective of the study.

Quota sampling is suitable when you want to know the preferences, differences or characteristics by sectors to direct specific campaigns according to the stratum or segment.

Its use is also useful when for some reason it is interesting to know the characteristics or interests of minority sectors, or when they do not want to leave them out of the study.

To be applicable, the weight or significance of each stratum must be known with respect to the total population. It is very important that this knowledge is reliable, otherwise erroneous results will be obtained.

Advantage

-Reduce study times, because the fees per stratum are usually small

-Simplifies the analysis of the data.

-Minimizes costs because the study is applied to small but well representative samples of the total population.

Disadvantages

-As the strata are defined a priori, it is possible that certain sectors of the population are left out of the study.

-By establishing a limited number of strata, it is possible that detail is being lost in the study.

-By obviating or incorporating some stratum as part of another, wrong conclusions may be drawn in the study.

-It makes it impossible to estimate the maximum sampling error.

Simple application example

We want to do a statistical study on the level of anxiety in a population of 2000 people.

The researcher directing the research intuits that differences in the results must be found depending on age and sex. For this reason he decides to form three age strata denoted as follows: First_Age, Second_Age and Third_Age. Regarding the sex segment, the two usual types are defined: Male and Female.

First_Age is defined, the one between 18 and 25 years old, Second_Age the one between 26 and 50 years old and finally Third_Age the one between 50 and 80 years old.

Analyzing the data of the total population it is necessary to:

45% of the population belongs to the First_Age.

40% are in the Second_Age.

Finally, only 15% of the study population belongs to the Third Age.

Using an appropriate methodology, which is not detailed here, a sample of 300 people is determined to be statistically significant.

Determination of quotas by age

The next step will then be to find the corresponding quotas for the Age segment, which is done as follows:

First_Age: 300 * 45% = 300 * 45/100 = 135

Second_Age: 300 * 40% = 300 * 40/100 = 120

Third_Age: 300 * 15% = 300 * 15/100 = 45

It is verified that the sum of the quotas gives the total size of the sample.

Determination of quotas by age and sex

So far, the sex segment of the population has not been taken into account. Two strata have already been defined for this segment: Female and Male. Again we must analyze the data of the total population, which yield the following information:

-60% of the total population are female.

-Meanwhile, 40% of the population to be studied belongs to the male sex.

It is important to note that the previous percentages regarding the distribution of the population according to sex do not take age into account.

Given that no more information is available, the assumption will be made that these sex proportions are equally distributed in the 3 Age strata that have been defined for this study. With these considerations, we now proceed to establish the quotas by Age and Sex, which means that there will now be 6 sub-strata:

S1 = First_Age and Female: 135 * 60% = 135 * 60/100 = 81

S2 = First_Age and Male: 135 * 40% = 135 * 40/100 = 54

S3 = Second_Age and Female: 120 * 60% = 120 * 60/100 = 72

S4 = Second_Age and Male: 120 * 40% = 120 * 40/100 = 48

S5 = Third_Age and Female: 45 * 60% = 45 * 60/100 = 27

S6 = Third_Age and Male: 45 * 40% = 45 * 40/100 = 18

Application of surveys and study of the results

Once the six (6) segments and their corresponding quotas have been established, 300 surveys are prepared that will be applied according to the quotas already calculated.

The surveys will be applied as follows, 81 surveys are taken and the first 81 people who are in the S1 segment are interviewed. Then it is done in the same way with the remaining five segments.

The study sequence is as follows:

-Analyze the results of the survey, which are then discussed, analyzing the results by segment.

-Make comparisons between the results by segment.

-Finally develop hypotheses that explain the causes of these results.

Difference with stratified random sampling

In our example in which we apply quota sampling, the first thing to do is establish the quotas and then carry out the study. Of course, these quotas are not whimsical at all, because they have been based on previous statistical information on the total population.

If you do not have prior information on the study population, it is preferable to reverse the procedure, that is, first define the sample size and once the sample size has been established, proceed to apply the survey in randomly.

One way to ensure randomness would be to use a random number generator and survey employees whose employee number matches that of the random generator.

Once the data is available, and since the objective of the study is to see the anxiety levels according to the age and sex strata, the data is separated according to the six categories that we had previously defined. But without establishing any prior fee.

It is for this reason that the stratified random sampling method is considered a probabilistic method. While the sampling by previously established quotas does not.

However, if the quotas are established with information based on population statistics, then the quota sampling method can be said to be approximately probabilistic.

Proposed exercise

The following exercise is proposed:

In a secondary school you want to do a survey on the preference between studying science or studying humanities.

Suppose the school has a total of 1000 students grouped into five levels according to the year of study. It is known that there are 350 students in the first year, 300 in the second, 200 in the third, 100 in the fourth and finally 50 in the fifth year. It is also known that 55% of the school's students are boys and 45% are girls.

Determine the strata and the quotas by stratum, in order to know the number of surveys to be applied according to the year of study and sex segments. Suppose further that the sample will be 10% of the total student population.

References

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5. Moore, D. 2005. Applied Basic Statistics. 2nd. Edition.
6. Netquest. Probability sampling: stratified sampling. Recovered from: netquest.com.
7. Wikipedia. Statistical sampling. Recovered from: en.wikipedia.org