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40-581: (Redirected from S E ) [REDACTED] Look up se , SE , Se , 세 , sé , or Sé in Wiktionary, the free dictionary. SE , Se , or Sé may refer to: Abbreviations [ edit ] Standard Edition (e.g. Java Platform, Standard Edition ) Special Edition Second Edition (e.g. Windows 98 Second Edition ) Student Edition Arts and entertainment [ edit ] Sé (album) , by Lúnasa, 2006 Se (instrument) ,

80-624: A standard deviation of σ {\displaystyle \sigma } . The mean value calculated from the sample, x ¯ {\displaystyle {\bar {x}}} , will have an associated standard error on the mean , σ x ¯ {\displaystyle {\sigma }_{\bar {x}}} , given by: σ x ¯ = σ n . {\displaystyle {\sigma }_{\bar {x}}={\frac {\sigma }{\sqrt {n}}}.} Practically this tells us that when trying to estimate

120-458: A Gaussian. To estimate the standard error of a Student t-distribution it is sufficient to use the sample standard deviation "s" instead of σ , and we could use this value to calculate confidence intervals. Note: The Student's probability distribution is approximated well by the Gaussian distribution when the sample size is over 100. For such samples one can use the latter distribution, which

160-425: A Japanese kana Northern Sami language , ISO 639-1 code se Standard English , in linguistics Se (letter) (Ս,ս) an Armenian letter Science and technology [ edit ] Se (unit of measurement) , a Japanese unit of area .se , Internet country code top-level domain for Sweden Se , a text editor Selenium , symbol Se, a chemical element Special Euclidean group Standard error , of

200-402: A distribution of different means, and this distribution has its own mean and variance . Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean. Therefore, the relationship between the standard error of

240-474: A station Sé, Hungary Sé, Macau Sé (Angra do Heroísmo) , Terceira, Azores, Portugal Sé (Braga) , Portugal Sé (Bragança) , Faro, Portugal Sé (Funchal) , Madeira, Portugal Sé, Lamego , Portugal Sé (Lisbon) , Portugal Sé, Portalegre, Portugal Sé (Porto) , Portugal SE postcode area , London, England Sergipe (SE), a state of Brazil Sweden , ISO country code SE Language [ edit ] Se (kana) (せ and セ),

280-478: A statistic Status epilepticus , a medical state of persistent seizure Synthetic environment , a computer simulation iPhone SE , a series of budget smartphones by Apple Macintosh SE , an Apple personal computer Other uses [ edit ] Southeast (direction) S. E. (name) , initials used by several people Lisbon Cathedral , or simply the Sé, Portugal Sé da Guarda , Portugal Split end,

320-934: A traditional Chinese musical instrument Businesses and organizations [ edit ] Societas Europaea , a form of company registered under European Union law Sea Ltd (NYSE: SE), tech conglomerate headquartered in Singapore Slovenské elektrárne , electric utility company in Slovakia XL Airways France , IATA airline designator SE Southeastern (train operating company) , or SE Trains Limited, in England Places [ edit ] Sè, Atlantique , Benin Sè, Mono , Benin Subprefecture of Sé , São Paulo, Brazil Sé (district of São Paulo) Sé (São Paulo Metro) ,

360-632: A type of wide receiver in American football Somatic experiencing , a method of alternative therapy Asüna SE , a compact car marketed in Canada Secondary School Entrance Examination , a standardized examination from 1962 to 1977 See also [ edit ] Single-ended (disambiguation) Windows 11 SE , a computer operating system Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with

400-489: Is a sample of n {\displaystyle n} independent observations from a population with mean x ¯ {\displaystyle {\bar {x}}} and standard deviation σ {\displaystyle \sigma } , then we can define the total T = ( x 1 + x 2 + ⋯ + x n ) {\displaystyle T=(x_{1}+x_{2}+\cdots +x_{n})} which due to

440-418: Is equal to the sample mean, SE {\displaystyle \operatorname {SE} } is equal to the standard error for the sample mean, and 1.96 is the approximate value of the 97.5 percentile point of the normal distribution : In particular, the standard error of a sample statistic (such as sample mean ) is the actual or estimated standard deviation of the sample mean in the process by which it

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480-597: Is large (approximately at 5% or more) in an enumerative study , the estimate of the standard error must be corrected by multiplying by a ''finite population correction'' (a.k.a.: FPC ): FPC = N − n N − 1 {\displaystyle \operatorname {FPC} ={\sqrt {\frac {N-n}{N-1}}}} which, for large N : FPC ≈ 1 − n N = 1 − f {\displaystyle \operatorname {FPC} \approx {\sqrt {1-{\frac {n}{N}}}}={\sqrt {1-f}}} to account for

520-540: Is much simpler. Also, even though the 'true' distribution of the population is unknown, assuming normality of the sampling distribution makes sense for a reasonable sample size, and under certain sampling conditions, see CLT . If these conditions are not met, then using a Bootstrap distribution to estimate the Standard Error is often a good workaround, but it can be computationally intensive. An example of how SE {\displaystyle \operatorname {SE} }

560-598: Is only an estimator for the true "standard error", it is common to see other notations here such as: σ ^ x ¯ := σ x n  or  s x ¯   := s n . {\displaystyle {\widehat {\sigma }}_{\bar {x}}:={\frac {\sigma _{x}}{\sqrt {n}}}\qquad {\text{ or }}\qquad {s}_{\bar {x}}\ :={\frac {s}{\sqrt {n}}}.} A common source of confusion occurs when failing to distinguish clearly between: When

600-438: Is small (e.g. a small proportion of a finite population is studied). In this case people often do not correct for the finite population, essentially treating it as an "approximately infinite" population. If one is interested in measuring an existing finite population that will not change over time, then it is necessary to adjust for the population size (called an enumerative study ). When the sampling fraction (often termed f )

640-477: Is the standard deviation of the Student t-distribution. T-distributions are slightly different from Gaussian, and vary depending on the size of the sample. Small samples are somewhat more likely to underestimate the population standard deviation and have a mean that differs from the true population mean, and the Student t-distribution accounts for the probability of these events with somewhat heavier tails compared to

680-459: Is used is to make confidence intervals of the unknown population mean. If the sampling distribution is normally distributed , the sample mean, the standard error, and the quantiles of the normal distribution can be used to calculate confidence intervals for the true population mean. The following expressions can be used to calculate the upper and lower 95% confidence limits, where x ¯ {\displaystyle {\bar {x}}}

720-584: The Bienaymé formula , will have variance Var ⁡ ( T ) = ( Var ⁡ ( x 1 ) + Var ⁡ ( x 2 ) + ⋯ + Var ⁡ ( x n ) ) = n σ 2 . {\displaystyle \operatorname {Var} (T)={\big (}\operatorname {Var} (x_{1})+\operatorname {Var} (x_{2})+\cdots +\operatorname {Var} (x_{n}){\big )}=n\sigma ^{2}.} where we've approximated

760-637: The law of total variance . If N {\displaystyle N} has a Poisson distribution , then E ⁡ ( N ) = Var ⁡ ( N ) {\displaystyle \operatorname {E} (N)=\operatorname {Var} (N)} with estimator n = N {\displaystyle n=N} . Hence the estimator of Var ⁡ ( T ) {\displaystyle \operatorname {Var} (T)} becomes n S X 2 + n X ¯ 2 {\displaystyle nS_{X}^{2}+n{\bar {X}}^{2}} , leading

800-504: The Wikimedia System Administrators, please include the details below. Request from 172.68.168.236 via cp1112 cp1112, Varnish XID 944991441 Upstream caches: cp1112 int Error: 429, Too Many Requests at Thu, 28 Nov 2024 08:35:53 GMT Standard error The sampling distribution of a mean is generated by repeated sampling from the same population and recording of the sample means obtained. This forms

840-562: The added precision gained by sampling close to a larger percentage of the population. The effect of the FPC is that the error becomes zero when the sample size n is equal to the population size N . This happens in survey methodology when sampling without replacement . If sampling with replacement, then FPC does not come into play. If values of the measured quantity A are not statistically independent but have been obtained from known locations in parameter space  x , an unbiased estimate of

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880-447: The correction factor for small samples of n < 20. See unbiased estimation of standard deviation for further discussion. The standard error on the mean may be derived from the variance of a sum of independent random variables, given the definition of variance and some properties thereof. If x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}}

920-412: The following formula for standard error: S t a n d a r d   E r r o r ⁡ ( X ¯ ) = S X 2 + X ¯ 2 n {\displaystyle \operatorname {Standard~Error} ({\bar {X}})={\sqrt {\frac {S_{X}^{2}+{\bar {X}}^{2}}{n}}}} (since

960-405: The mean and standard deviation of the sample data or the mean with the standard error. This often leads to confusion about their interchangeability. However, the mean and standard deviation are descriptive statistics , whereas the standard error of the mean is descriptive of the random sampling process. The standard deviation of the sample data is a description of the variation in measurements, while

1000-436: The mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size. In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean. In regression analysis , the term "standard error" refers either to the square root of the reduced chi-squared statistic or

1040-578: The mean is then Var ⁡ ( x ¯ ) = Var ⁡ ( T n ) = 1 n 2 Var ⁡ ( T ) = 1 n 2 n σ 2 = σ 2 n . {\displaystyle \operatorname {Var} ({\bar {x}})=\operatorname {Var} \left({\frac {T}{n}}\right)={\frac {1}{n^{2}}}\operatorname {Var} (T)={\frac {1}{n^{2}}}n\sigma ^{2}={\frac {\sigma ^{2}}{n}}.} The standard error is, by definition,

1080-538: The population being sampled is seldom known. Therefore, the standard error of the mean is usually estimated by replacing σ {\displaystyle \sigma } with the sample standard deviation σ x {\displaystyle \sigma _{x}} instead: σ x ¯   ≈ σ x n . {\displaystyle {\sigma }_{\bar {x}}\ \approx {\frac {\sigma _{x}}{\sqrt {n}}}.} As this

1120-400: The sample differ from the sample mean. If the population standard deviation is finite, the standard error of the mean of the sample will tend to zero with increasing sample size, because the estimate of the population mean will improve, while the standard deviation of the sample will tend to approximate the population standard deviation as the sample size increases. The formula given above for

1160-457: The sample size is small, using the standard deviation of the sample instead of the true standard deviation of the population will tend to systematically underestimate the population standard deviation, and therefore also the standard error. With n = 2, the underestimate is about 25%, but for n = 6, the underestimate is only 5%. Gurland and Tripathi (1971) provide a correction and equation for this effect. Sokal and Rohlf (1981) give an equation of

1200-895: The sample variance needs to be computed according to the Markov chain central limit theorem . There are cases when a sample is taken without knowing, in advance, how many observations will be acceptable according to some criterion. In such cases, the sample size N {\displaystyle N} is a random variable whose variation adds to the variation of X {\displaystyle X} such that, Var ⁡ ( T ) = E ⁡ ( N ) Var ⁡ ( X ) + Var ⁡ ( N ) ( E ⁡ ( X ) ) 2 {\displaystyle \operatorname {Var} (T)=\operatorname {E} (N)\operatorname {Var} (X)+\operatorname {Var} (N){\big (}\operatorname {E} (X){\big )}^{2}} which follows from

1240-411: The standard deviation is the square root of the variance). In many practical applications, the true value of σ is unknown. As a result, we need to use a distribution that takes into account that spread of possible σ' s. When the true underlying distribution is known to be Gaussian, although with unknown σ, then the resulting estimated distribution follows the Student t-distribution. The standard error

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1280-436: The standard deviation of x ¯ {\displaystyle {\bar {x}}} which is the square root of the variance: σ x ¯ = σ 2 n = σ n . {\displaystyle \sigma _{\bar {x}}={\sqrt {\frac {\sigma ^{2}}{n}}}={\frac {\sigma }{\sqrt {n}}}.} For correlated random variables

1320-400: The standard deviations, i.e., the uncertainties, of the measurements themselves with the best value for the standard deviation of the population. The mean of these measurements x ¯ {\displaystyle {\bar {x}}} is given by x ¯ = T / n . {\displaystyle {\bar {x}}=T/n.} The variance of

1360-431: The standard error assumes that the population is infinite. Nonetheless, it is often used for finite populations when people are interested in measuring the process that created the existing finite population (this is called an analytic study ). Though the above formula is not exactly correct when the population is finite, the difference between the finite- and infinite-population versions will be small when sampling fraction

1400-401: The standard error for a particular regression coefficient (as used in, say, confidence intervals ). Suppose a statistically independent sample of n {\displaystyle n} observations x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} is taken from a statistical population with

1440-417: The standard error of the mean is a probabilistic statement about how the sample size will provide a better bound on estimates of the population mean, in light of the central limit theorem. Put simply, the standard error of the sample mean is an estimate of how far the sample mean is likely to be from the population mean, whereas the standard deviation of the sample is the degree to which individuals within

1480-515: The title Se . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Se&oldid=1251948896 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages se">se Too Many Requests If you report this error to

1520-437: The true standard error of the mean (actually a correction on the standard deviation part) may be obtained by multiplying the calculated standard error of the sample by the factor  f : f = 1 + ρ 1 − ρ , {\displaystyle f={\sqrt {\frac {1+\rho }{1-\rho }}},} where the sample bias coefficient ρ is the widely used Prais–Winsten estimate of

1560-416: The value of a population mean, due to the factor 1 / n {\displaystyle 1/{\sqrt {n}}} , reducing the error on the estimate by a factor of two requires acquiring four times as many observations in the sample; reducing it by a factor of ten requires a hundred times as many observations. The standard deviation σ {\displaystyle \sigma } of

1600-443: Was generated. In other words, it is the actual or estimated standard deviation of the sampling distribution of the sample statistic. The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean ), or S E . Standard errors provide simple measures of uncertainty in a value and are often used because: In scientific and technical literature, experimental data are often summarized either using

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