Omar Marroquin Pacheco
It is important to be clear about how a statistically representative sample is calculated, especially now that we are at an electoral moment and that opinion poll results will be presented.
A statistically representative sample is a part of a population that is small compared to the total size of the population, but is still capable of accurately representing the opinions or characteristics of the population as a whole.
The size of a statistically representative sample can be calculated using the
following formula:
n = (z * p * q) / e^2
where:
– n is the sample size
– z is the z value for the desired confidence level
– p is the proportion of the population that possesses the characteristic that is being
studying
– what is 1 – p
– e is the desired margin of error
In this case, the confidence level is 95%, the margin of error is 3%, and the proportion of the population that possesses the characteristic being studied is 0.5 (ie, half the population). Therefore, the sample size can be calculated as:
n = (1.96 * 0.5 * 0.5) / 0.03^2 = 1,067 ballots or people to be surveyed.
Therefore, 1,067 people must be surveyed to obtain a statistically representative sample of the population of 9 million people that corresponds to the Guatemalan electoral roll.
It is important to note that the sample size should be larger if the desired margin of error is smaller or if the desired confidence level is higher. Statistically it is assumed that for populations greater than 1 million people to infinity the number of ballots to be made for a statistically representative sample is 1,250
ballots or people to survey, this is already like a cooking recipe.
The margin of error and the level of confidence are two important concepts in a statistical survey:
- Margin of error: It is the measure of uncertainty or variability associated with the
results of the test. It represents the range within which it is likely that
Find the true population value for a given characteristic. It is usually expressed as a percentage and is used to indicate the precision of the sample with respect to the population under study. For example, if the margin of error is 5%, it means that the survey results may vary by up to 5% around the reported value.
- Confidence level: It is the degree of certainty or probability that the results of the
survey are representative of the entire population. It is usually expressed as a
percentage and is related to the margin of error. A confidence level of 95%
means that there is a 95% probability that the results will be within the range
of specified error, while a 99% confidence level would imply a
even higher probability.
The margin of error indicates the precision of the sample, and the confidence level reflects how confident we are that the results are representative of the entire population. Both factors are crucial to assess the validity of the results of a statistical survey.
As an example: Blood work For common tests, such as routine tests or metabolic profiles, small amounts of blood are usually drawn, usually around 5 to 10 milliliters (ml). However, for more specialized or complex tests, larger amounts of blood may be needed.
A person has more or less 5 liters of blood, that is, 5,000 milliliters, if 5 ml is extracted, that represents 0.1% of all the blood to determine what disease he may have.
In other words, with only 0.1% it is possible to determine what disease the patient may be suffering from, the same happens with surveys with only 0.1% it can be determined depending on the parameters used, if a 3% margin of error is used, that means that of the results obtained, 3% of the answers can be above or below those results.
When speaking of the degree of confidence of 95%, it should be interpreted as that of the results obtained, it can be extrapolated to the entire universe so that these same results can be observed both in the sample and in the entire universe, in this specific case the 9 million people from the electoral roll of Guatemala.
In summary, the determination of the number of ballots or people to be surveyed for universes greater than 1 million people, is determined by the degree of permissible error and the degree of confidence established but by statistical practice, whether it is a margin of error of 3 or 5% and the degree of confidence of 95% with taking the 1,250 ballots or people to be surveyed, these parameters are always covered.
