Saturday, 26 November 2016

Standard error (SE)

«These are the SEs for the descriptive statistics. The SE gives some idea about the variability possible in the statistic [1].» It «(...) is a measure of the variability of a statistic. It is an estimate of the standard deviation of a sampling distribution [2].» It «(...) is the standard deviation of the sampling distribution of a statistic, (...) (Everitt BS, 2003, cited in [3]). «The SE of the mean [SEM] (...) is the theoretical standard deviation of all sample means of size n drawn from a population and depends on both the population variance (sigma) and the sample size (n) (...) [4].» «The SEM can be seen to depict the relationship between the dispersion of individual observations around the population mean (the standard deviation), and the dispersion of sample means around the population mean (the SE). Different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and variance). (...) As the sample size increases, the dispersion of the sample means clusters more closely around the population mean and the SE decreases [3].» «The SE depends on three factors: the number of observations in the population (N), the number of observations in the sample (n), and the way that the random sample is chosen. If the population size is much larger than the sample size, then the sampling distribution has roughly the same SE, whether we sample with or without replacement . On the other hand, if the sample represents a significant fraction (say, 1/20) of the population size, the SE will be noticeably smaller, when we sample without replacement [2].» «The SE of the proportion (...) is the standard deviation of the distribution of the sample proportion over repeated samples [4].»
Bibliographic references:
[1] Annotated SPSS Output: Descriptive statistics [Internet]. Ats.ucla.edu. 2016 [cited 20 November 2016]. Available from: http://www.ats.ucla.edu/stat/spss/output/descriptives.htm.
[2] Statistics Dictionary [Internet]. Stattrek.com. 2016 [cited 20 November 2016]. Available from: http://stattrek.com/statistics/dictionary.aspx.
[3] Standard error [Internet]. En.wikipedia.org. 2016 [cited 20 November 2016]. Available from: https://en.wikipedia.org/wiki/Standard_error#cite_note-1.
[4] Statistics Glossary: S [Internet]. Statsoft.com. 2016 [cited 20 November 2016]. Available from: http://www.statsoft.com/textbook/statistics-glossary/s#Standard.