# What best steps to take to ensure the representative sample?

### What is a representative sample?

The representative sample is a sample of a relatively appropriate size that has been selected by random procedures and the characteristics observed in it correspond to the population from which it was drawn (Ras, 1980; Cochran, 1976; Scheaffer, Mendenhall and Ott, 1987). It is not possible, in any case, to be certain of the degree of representativeness, but rather there is a reasonable probability of that representativeness.

## Representativeness

Is a function of several factors, it not only depends on the randomness and size of the sample, but also on the sampling design, very particular for each case, the use of key auxiliary information, the sampling design and a useful and useful sampling frame. updated. The term representative is used as long as the sample faithfully represents the variable under study, which has a probabilistic distribution in the population and the frequency distribution in the sample must be mirror or very similar to that of the population.

This highlights how complex the selection of a representative sample is. To do this, the following must be taken into account: the way the sample is selected, the estimators to be proposed and their precision, the determination of the sample size that takes into account the “aquaricity” or margin of error allowed, the level of confidence in the estimation and variability of the variable on which the Probabilistic Inference is going to be carried out.

Likewise, attention must be paid to the available sampling frame and the set of key auxiliary variables or covariates that are correlated with the variables of interest, which will allow improving the sampling design, with the formation of strata, selection of direct estimators, such as the Horvitz-Thompson, and indirect (ratio, regression and difference), and choose a sample size appropriate to a given precision, choose samples with probabilities proportional to a measure of size (PPT) and use calibrated estimates where adjustment has to be made. sampling weights depending on the non-response and the auxiliary information found, especially in complex samples.

Many times, when designing a probabilistic sample, concessions must be made, especially if the statistical population is asymmetric, there are even times when elements with probability one (1) of belonging to the sample are used and, if this is not done, the sample will not be representative enough.

A probabilistic sample in its structure approaches a greater degree of what is called representativeness when the value of the distance between the estimate of the sample and the value of the population parameter becomes smaller, this is known as aquaricity in the Statistical inference.

We can be in the presence of a sufficiently representative sample when the selection process assigns a probability of inclusion in advance to each element, if this probability is different from zero, if known, and not necessarily being equal for each element of the population. and, furthermore, if the sampling error is low, if aquarity exists and if a random process is used in its selection.

The best way we have to define a sufficiently representative sample is one where a probabilistic sampling strategy is used that allows estimating the value of the parameter with aquaricity, the minimum bias, the minimum Standard Error of the estimator of that parameter or the minimum error of estimate, which is a multiple of the Standard Error of the estimator.

## Importance of having a representative sample

Representative samples are known to collect results, knowledge, and observations that can be relied upon as representative of the broader population being studied. Therefore, representative sampling is usually the best method for market research .

If we do not have representation, we will surely have data that will be of no use to us. Therefore, it is important that we guarantee that the characteristics that matter to us and need to be investigated are found in the sample that is going to be the object of study.

Let’s take into account that we will always be prone to falling into sampling bias because there will always be people who do not answer the survey because they are busy, or answer it incompletely, so we will not be able to obtain the data we require.

Regarding the size of the sample , the larger it is, the more likely it is to be representative of the population.

That a sample is representative gives us greater certainty that the **people included are the ones we need** , and we also reduce possible bias . Therefore, if we want to avoid inaccuracy in our surveys, we must have a representative and balanced sample.

## How to obtain a representative sample?

There are established sampling methods to obtain a representative sample that have been tested and verified over time through academic, scientific and market research.

The most common types of sampling are probability or random sampling and non-probability sampling.

### Probability sampling

If we are going to have a probabilistic or random sampling , we must make sure we have updated information on the population from which we will draw the sample and survey the majority to ensure representativeness.

The sample will be chosen at random, which guarantees that each member of the population will have the same probability of selection and inclusion in the sample group.

### Non-probability sampling

In non-probabilistic sampling, the aim is to have different types of people to ensure a more balanced representative sample.

Knowing the demographic characteristics of our group will undoubtedly help to limit the profile of the desired sample and define the variables that interest us, such as gender, age, place of residence, etc.

By knowing these criteria, before obtaining the information, we can have the control to create a representative sample that is useful to us.

We must **avoid having a sample that does NOT reflect the target population** , the ideal is to have data that is as accurate as possible for the success of our project.

## Avoid making sampling errors

When a sample is not representative, then we will have a sampling error . If we want to have a representative sample of 100 employees, then we must choose a similar number of men and women. For example, if we have a sample biased towards a certain gender, then we will have an error in the sample.

Sample size is very important, but it does not guarantee that the population we need is accurately represented. More than size, representativeness is more related to the sampling frame , that is, to the list from which the people who are going to be, for example, part of a survey are selected .

Therefore, we must ensure that people from our target audience are included in that list to say that it is a representative sample.