io : equation of the form ignore = true or false

wo : equation of the form weights = w, where w is a data set

soo : equation of the form statopts = lst, where lst is a list containing a sequence of extra arguments to be passed to S; this option cannot occur together with the argument xa

no : equation of the form numeric = true or false

sso : equation of the form samplesize = N, where N is a positive integer

The StandardError function computes the standard error of the sampling distribution of the specified statistic. For example, the standard error of the sample mean of $n$ observations is $\frac{\mathrm{\sigma }}{\sqrt{n}}$, where ${\mathrm{\sigma }}^2$ is the variance of the original observations. Standard errors are particularly important in the large class of cases when the sampling distribution can be taken to be normal either exactly or to an adequate degree of approximation.  Standard error can be computed either for a particular data set or for a random variable.

In the data set case the sample size and all the relevant parameters (such as mean, standard deviation, etc.) will be estimated based on the specified data. All computations are performed under the assumption that the underlying sampling distribution is approximately normal.

In the random variable case, N specifies the sample size, either as index to the command name or as the value of the samplesize option.

The first parameter S is the name of a standard quantity, to be applied to either a data set or random variable, e.g. Statistics[Mean], Statistics[Median], Statistics[Variance]. See Statistics[DescriptiveStatistics] for a complete list of quantities.

The second parameter can be a data set (e.g., a Vector), a Matrix data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).

By default, all computations involving random variables are performed symbolically (see option numeric below).

All computations involving data are performed in floating-point; therefore, all data provided must have type/realcons and all returned solutions are floating-point, even if the problem is specified with exact values.

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

More information for some of these options is available in the Statistics[DescriptiveStatistics] help page.

ignore=truefalse -- This option controls how missing data is handled by the StandardError command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the StandardError command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.

weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight $1$.

More information for some of these options is available in the Statistics[RandomVariables] help page.

numeric=truefalse -- By default, the standard error is computed using exact arithmetic. To compute the standard error numerically, specify the numeric or numeric = true option.

samplesize=N -- The sample size, N, can be specified in two different ways: with the samplesize option or as an index to the StandardError command. If both are specified, the StandardError command uses the index for itself and passes the samplesize option as an extra argument to S, as part of xa; see below. If neither is specified, Maple uses the default value of 1000.

You can specify extra arguments to pass to S, in addition to the data set or the random variable. For example, to find the standard error of the 3rd (raw) moment, you would use Statistics[Moment] as the value of S and pass the value 3 as an extra argument. You can do this in two ways:

In the calling sequences above that contain the argument xa, you can just include these arguments in the call to StandardError, e.g., StandardError(Moment, X, 3);

In the calling sequences above that contain the argument soo, you can use the option statopts and enclose the arguments in a list, e.g., StandardError(Moment, X, statopts=[3]).

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$N≔\mathrm{RandomVariable}\left(\mathrm{Normal}\left(0\,1\right)\right)\:$

$S≔\mathrm{Sample}\left(N\,{10}^3\right)\:$

$\mathrm{StandardError}\left[{10}^3\right]\left(\mathrm{Mean}\,N\,\mathrm{numeric}\right)$

$0.03162277660$

$\mathrm{StandardError}\left(\mathrm{Mean}\,N\,\mathrm{numeric}\,\mathrm{samplesize}={10}^3\right)$

$0.03162277660$

$\mathrm{StandardError}\left(\mathrm{Mean}\,S\right)$

$0.0313121441956369$

$\mathrm{Bootstrap}\left('\mathrm{Mean}'\,S\,\mathrm{replications}={10}^3\,\mathrm{output}=\mathrm{standarderror}\right)$

$0.0296068781774789132$

$\mathrm{Bootstrap}\left('\mathrm{Mean}'\,N\,\mathrm{replications}={10}^3\,\mathrm{output}=\mathrm{standarderror}\,\mathrm{samplesize}={10}^3\right)$

$0.0309839567269692556$

$\mathrm{\mu }≔\mathrm{Mean}\left(S\right)$

$\mathrm{\mu }≔0.0611270855668661$

$\mathrm{\sigma }≔\mathrm{StandardDeviation}\left(S\right)$

$\mathrm{\sigma }≔0.990176940818334$

$\mathrm{StandardError}\left(\mathrm{Mean}\,\mathrm{Normal}\left(\mathrm{\mu }\,\mathrm{\sigma }\right)\,\mathrm{numeric}\,\mathrm{samplesize}={10}^3\right)$

$0.0313121441956369$

$M≔\mathrm{Matrix}\left(\left[\left[3\,1130\,114694\right]\,\left[4\,1527\,127368\right]\,\left[3\,907\,88464\right]\,\left[2\,878\,96484\right]\,\left[4\,995\,128007\right]\right]\right)$

$M≔\left[\begin{array}{ccc}3& 1130& 114694\\ 4& 1527& 127368\\ 3& 907& 88464\\ 2& 878& 96484\\ 4& 995& 128007\end{array}\right]$

$\mathrm{StandardError}\left(\mathrm{InterquartileRange}\,M\right)$

$\left[\begin{array}{ccc}0.668070576628882& 188.309251368715& 15668.6416411933\end{array}\right]$

$\mathrm{StandardError}\left(\mathrm{Moment}\,M\,2\,\mathrm{origin}=\left[3\,1000\,100000\right]\right)$

$\left[\begin{array}{ccc}0.219089023002066& 47944.4484082151& 1.44602293933851\times {10}^8\end{array}\right]$

$\mathrm{StandardError}\left(\mathrm{Moment}\,M\,\mathrm{statopts}=\left[2\,\mathrm{origin}=\left[3\,1000\,100000\right]\right]\right)$

$\left[\begin{array}{ccc}0.219089023002066& 47944.4484082151& 1.44602293933851\times {10}^8\end{array}\right]$

The A parameter was updated in Maple 16.