ESTIMATION ERROR

The estimation error or margin of error is the biggest or smallest difference that is accepted when developing researches due to the level of confidence in consideration [1, 2, 3]. Whenever a sample of a population is taken and the population mean is to be estimated using calculations that involve the sample mean, the estimation error is involved [1, 2, 3]. The estimation error (ee) is the difference between the sample mean (X ) and the true population mean (µ) [1]. There are cases where the sample size is unknown, making it difficult to calculate the standard deviation. This is what is call the standard deviation paradox. When the population standard deviation is unknown, is possible to use a preliminary value and in practice this problem can be solved with the use of measurements already carried out over time or history of measurements data [4]. In most cases, when working with large populations, the population standard deviation is unknown. In these cases, the population standard deviation (σ) can be replaced by the standard deviation extracted from a sample of the population (s).

When the population standard deviation (σ) is unknown, there are three possibilities to define the confidence interval [5]. The diagram below illustrates these possibilities.

To define the estimation error addressed in this proposal, we start from the conditions that satisfy the cases I and II. The equations below allow the calculation of the estimation error for these cases [5].

Where:

e_e - estimation error

X – sample mean

µ - population mean

s - standard deviation extracted from sample population

N - sample size

t - t Student Coefficient

When we take to consideration metrology related researches, we understand that the estimation error cannot be less than uncertainty in measurement. If so, there is a possibility of compromising the reliability of the results since the minimum sample size may not be realistic.

REFERENCES

[1] Joao Pinheiro, Sonia Cunha, Gastão Gomes e Santiago Carvajal. Probabilidade e Estatística. Quantificando A Incerteza. Elsevier, 2012. ISBN 978-85-352-3757-3.

[2] Juan Carlos Lapponi. Estatística usando Excel. Rio de Janeiro, 2005. Elsevier, 8a reimpressão. ISBN 978-85-352-1574-8.

[3] Thompson, P. W. Understanding Sampling Distributions And Margin Of Error. Paper presented at 2nd Conference on Statistics Reasoning, Teaching, and Literacy. 2001.

[4] BARROS NETO, B. de; SCARMINIO, I. S.; BRUNS, R. E. Como fazer experimentos: pesquisa e desenvolvimento na ciência e na indústria. 3º ed. Campinas: UNICAMP, 2007. ISBN: 978-85-268-0753-2.

[5] Mann, Prem S. Introdução à estatística / Prem S. Mann. tradução Teresa Cristina Padilha de Souza; contribuições de Christopher Jay Lacke. - 8. ed. - Rio de Janeiro: LTC, 2015. ISBN 978-85-216-2885-9.